InitStateEquil_impl.hpp

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
/*
  This file is part of the Open Porous Media project (OPM).
 
  OPM is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 3 of the License, or
  (at your option) any later version.
 
  OPM is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.
 
  You should have received a copy of the GNU General Public License
  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
 
  Consult the COPYING file in the top-level source directory of this
  module for the precise wording of the license and the list of
  copyright holders.
*/
#ifndef OPM_INIT_STATE_EQUIL_IMPL_HPP
#define OPM_INIT_STATE_EQUIL_IMPL_HPP
 
#include <dune/grid/common/mcmgmapper.hh>
 
#include <opm/common/OpmLog/OpmLog.hpp>
 
#include <opm/grid/utility/RegionMapping.hpp>
 
#include <opm/input/eclipse/EclipseState/EclipseState.hpp>
#include <opm/input/eclipse/EclipseState/Tables/PbvdTable.hpp>
#include <opm/input/eclipse/EclipseState/Tables/PdvdTable.hpp>
#include <opm/input/eclipse/EclipseState/Tables/RsconstTable.hpp>
#include <opm/input/eclipse/EclipseState/Tables/RsvdTable.hpp>
#include <opm/input/eclipse/EclipseState/Tables/RtempvdTable.hpp>
#include <opm/input/eclipse/EclipseState/Tables/RvvdTable.hpp>
#include <opm/input/eclipse/EclipseState/Tables/RvwvdTable.hpp>
#include <opm/input/eclipse/EclipseState/Tables/SaltvdTable.hpp>
#include <opm/input/eclipse/EclipseState/Tables/SaltpvdTable.hpp>
 
#include <opm/input/eclipse/Units/UnitSystem.hpp>
 
#include <opm/material/fluidmatrixinteractions/EclMaterialLawManager.hpp>
#include <opm/material/fluidsystems/BlackOilFluidSystem.hpp>
 
#include <opm/simulators/flow/equil/EquilibrationHelpers.hpp>
#include <opm/simulators/flow/equil/InitStateEquil.hpp>
 
#include <opm/simulators/utils/DeferredLoggingErrorHelpers.hpp>
 
#include <fmt/format.h>
 
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstddef>
#include <limits>
#include <numbers>
#include <stdexcept>
 
namespace Opm {
namespace EQUIL {
 
namespace Details {
 
template <typename CellRange, class Scalar>
void verticalExtent(const CellRange&      cells,
                    const std::vector<std::pair<Scalar, Scalar>>& cellZMinMax,
                    const Parallel::Communication& comm,
                    std::array<Scalar,2>& span)
{
    span[0] = std::numeric_limits<Scalar>::max();
    span[1] = std::numeric_limits<Scalar>::lowest();
 
    // Define vertical span as
    //
    //   [minimum(node depth(cells)), maximum(node depth(cells))]
    //
    // Note: The implementation of 'RK4IVP<>' implicitly
    // imposes the requirement that cell centroids are all
    // within this vertical span.  That requirement is not
    // checked.
    for (const auto& cell : cells) {
        if (cellZMinMax[cell].first < span[0]) { span[0] = cellZMinMax[cell].first; }
        if (cellZMinMax[cell].second > span[1]) { span[1] = cellZMinMax[cell].second; }
    }
    span[0] = comm.min(span[0]);
    span[1] = comm.max(span[1]);
}
 
template<class Scalar>
void subdivisionCentrePoints(const Scalar left,
                             const Scalar right,
                             const int                               numIntervals,
                             std::vector<std::pair<Scalar, Scalar>>& subdiv)
{
    const auto h = (right - left) / numIntervals;
 
    auto end = left;
    for (auto i = 0*numIntervals; i < numIntervals; ++i) {
        const auto start = end;
        end = left + (i + 1)*h;
 
        subdiv.emplace_back((start + end) / 2, h);
    }
}
 
template <typename CellID, typename Scalar>
std::vector<std::pair<Scalar, Scalar>>
horizontalSubdivision(const CellID cell,
                      const std::pair<Scalar, Scalar> topbot,
                      const int    numIntervals)
{
    auto subdiv = std::vector<std::pair<Scalar, Scalar>>{};
    subdiv.reserve(2 * numIntervals);
 
    if (topbot.first > topbot.second) {
        throw std::out_of_range {
            "Negative thickness (inverted top/bottom faces) in cell "
            + std::to_string(cell)
        };
    }
 
    subdivisionCentrePoints(topbot.first, topbot.second,
                            2*numIntervals, subdiv);
 
    return subdiv;
}
 
template <class Scalar, class Element>
Scalar cellCenterDepth(const Element& element)
{
    typedef typename Element::Geometry Geometry;
    static constexpr int zCoord = Element::dimension - 1;
    Scalar zz = 0.0;
 
    const Geometry& geometry = element.geometry();
    const int corners = geometry.corners();
    for (int i=0; i < corners; ++i)
        zz += geometry.corner(i)[zCoord];
 
    return zz/corners;
}
 
template <class Scalar, class Element>
std::pair<Scalar,Scalar> cellCenterXY(const Element& element)
{
    typedef typename Element::Geometry Geometry;
    static constexpr int xCoord = Element::dimension - 3;
    static constexpr int yCoord = Element::dimension - 2;
    Scalar yy = 0.0;
    Scalar xx = 0.0;
 
 
    const Geometry& geometry = element.geometry();
    const int corners = geometry.corners();
    for (int i=0; i < corners; ++i) {
        xx += geometry.corner(i)[xCoord];
        yy += geometry.corner(i)[yCoord];
    }
    return  std::make_pair(xx/corners, yy/corners);
}
 
template <class Scalar, class Element>
std::pair<Scalar,Scalar> cellZSpan(const Element& element)
{
    typedef typename Element::Geometry Geometry;
    static constexpr int zCoord = Element::dimension - 1;
    Scalar bot = 0.0;
    Scalar top = 0.0;
 
    const Geometry& geometry = element.geometry();
    const int corners = geometry.corners();
    assert(corners == 8);
    for (int i=0; i < 4; ++i)
        bot += geometry.corner(i)[zCoord];
    for (int i=4; i < corners; ++i)
        top += geometry.corner(i)[zCoord];
 
    return std::make_pair(bot/4, top/4);
}
 
template <class Scalar, class Element>
std::pair<Scalar,Scalar> cellZMinMax(const Element& element)
{
    typedef typename Element::Geometry Geometry;
    static constexpr int zCoord = Element::dimension - 1;
    const Geometry& geometry = element.geometry();
    const int corners = geometry.corners();
    assert(corners == 8);
    auto min = std::numeric_limits<Scalar>::max();
    auto max = std::numeric_limits<Scalar>::lowest();
 
 
    for (int i=0; i < corners; ++i) {
        min = std::min(min, static_cast<Scalar>(geometry.corner(i)[zCoord]));
        max = std::max(max, static_cast<Scalar>(geometry.corner(i)[zCoord]));
    }
    return std::make_pair(min, max);
}
 
template<class Scalar>
void computeBlockDip(const CellCornerData<Scalar>& cellCorners,
                                  Scalar& dipAngle, Scalar& dipAzimuth)
{
    const auto& Xc = cellCorners.X;
    const auto& Yc = cellCorners.Y;
    const auto& Zc = cellCorners.Z;
 
    Scalar v1x = Xc[1] - Xc[0];
    Scalar v1y = Yc[1] - Yc[0];
    Scalar v1z = Zc[1] - Zc[0];
 
    Scalar v2x = Xc[2] - Xc[0];
    Scalar v2y = Yc[2] - Yc[0];
    Scalar v2z = Zc[2] - Zc[0];
 
    // Cross product to get normal vector
    Scalar nx = v1y * v2z - v1z * v2y;
    Scalar ny = v1z * v2x - v1x * v2z;
    Scalar nz = v1x * v2y - v1y * v2x;
 
    // Normalize the normal vector
    Scalar norm = std::hypot(nx, ny, nz);
 
    if (norm > 1e-10) {
        nx /= norm;
        ny /= norm;
        nz /= norm;
 
        // Dip angle is the angle between normal and vertical (0,0,1)
        dipAngle = std::acos(std::abs(nz));
 
        // Dip azimuth (direction of dip)
        if (std::abs(nx) > 1e-10 || std::abs(ny) > 1e-10) {
            dipAzimuth = std::atan2(ny, nx);
            // Convert to 0-2π range
            dipAzimuth = std::fmod(dipAzimuth + 2*std::numbers::pi_v<Scalar>, 2*std::numbers::pi_v<Scalar>);
        } else {
            dipAzimuth = 0.0; // Vertical cell
        }
 
        // Clamp dip angle to reasonable values
        const Scalar maxDip = std::numbers::pi_v<Scalar>/2 - static_cast<Scalar>(1e-6);
        dipAngle = std::min(dipAngle, maxDip);
    } else {
        // Degenerate cell - assume horizontal
        dipAngle = 0.0;
        dipAzimuth = 0.0;
    }
}
 
template <class Scalar, class Element>
CellCornerData<Scalar> getCellCornerXY(const Element& element)
{
    typedef typename Element::Geometry Geometry;
    const Geometry& geometry = element.geometry();
    static constexpr int zCoord = Element::dimension - 1;
    static constexpr int yCoord = Element::dimension - 2;
    static constexpr int xCoord = Element::dimension - 3;
    const int corners = geometry.corners();
    assert(corners == 8);
    std::array<Scalar, 8> X {};
    std::array<Scalar, 8> Y {};
    std::array<Scalar, 8> Z {};
    // Get all 8 corners of the hexahedral cell (maybe expensive)
    for (int i = 0; i < corners; ++i) {
         auto corner = geometry.corner(i);
         X[i] = corner[xCoord];
         Y[i] = corner[yCoord];
         Z[i] = corner[zCoord];
    }
 
    return CellCornerData<Scalar>{X, Y, Z};
}
 
template<class Scalar>
Scalar calculateTrueVerticalDepth(Scalar z, Scalar x, Scalar y,
                                Scalar dipAngle, Scalar dipAzimuth,
                                const std::array<Scalar, 3>& referencePoint)
{
    // For True Vertical Depth calculation:
    // TVD = reference_depth + (z - reference_z) * cos(dipAngle)
    //       + lateral_distance * sin(dipAngle) * cos(azimuth_difference)
 
    // Calculate lateral displacement from reference point
    Scalar dx = x - referencePoint[0];
    Scalar dy = y - referencePoint[1];
    Scalar dz = z - referencePoint[2];
 
    // If no dip, TVD is simply the depth
    if (std::abs(dipAngle) < 1e-10) {
        return referencePoint[2] + dz;
    }
 
    // Calculate the direction from reference point to current point
    Scalar pointAzimuth = std::atan2(dy, dx);
 
    // Calculate the angle between dip direction and point direction
    Scalar azimuthDiff = pointAzimuth - dipAzimuth;
 
    // Calculate lateral distance
    Scalar lateralDist = std::hypot(dx, dy);
 
    // Project lateral distance onto dip direction
    Scalar lateralInDipDir = lateralDist * std::cos(azimuthDiff);
 
    // True Vertical Depth calculation
    // TVD increases with depth (more negative z means deeper)
    // For a dipping plane: TVD = vertical_component + dip_component
    Scalar tvd = referencePoint[2] + dz * std::cos(dipAngle) + lateralInDipDir * std::sin(dipAngle);
 
    return tvd;
}
 
template<class Scalar, class RHS>
RK4IVP<Scalar,RHS>::RK4IVP(const RHS& f,
                           const std::array<Scalar,2>& span,
                           const Scalar y0,
                           const int N)
    : N_(N)
    , span_(span)
{
    const Scalar h = stepsize();
    const Scalar h2 = h / 2;
    const Scalar h6 = h / 6;
 
    y_.reserve(N + 1);
    f_.reserve(N + 1);
 
    y_.push_back(y0);
    f_.push_back(f(span_[0], y0));
 
    for (int i = 0; i < N; ++i) {
        const Scalar x = span_[0] + i*h;
        const Scalar y = y_.back();
 
        const Scalar k1 = f_[i];
        const Scalar k2 = f(x + h2, y + h2*k1);
        const Scalar k3 = f(x + h2, y + h2*k2);
        const Scalar k4 = f(x + h, y + h*k3);
 
        y_.push_back(y + h6*(k1 + 2*(k2 + k3) + k4));
        f_.push_back(f(x + h, y_.back()));
    }
 
    assert (y_.size() == typename std::vector<Scalar>::size_type(N + 1));
}
 
template<class Scalar, class RHS>
Scalar RK4IVP<Scalar,RHS>::
operator()(const Scalar x) const
{
    // Dense output (O(h**3)) according to Shampine
    // (Hermite interpolation)
    const Scalar h = stepsize();
    int i = (x - span_[0]) / h;
 
    // Crude handling of evaluation point outside "span_";
    if (i  <  0) { i = 0;      }
    if (N_ <= i) { i = N_ - 1; }
 
    // Relative to the interval actually used, so that a point at the end of
    // the span lands on t = 1 of the final interval rather than t = 0.
    const Scalar t = (x - (span_[0] + i*h)) / h;
 
    const Scalar y0 = y_[i], y1 = y_[i + 1];
    const Scalar f0 = f_[i], f1 = f_[i + 1];
 
    Scalar u = (1 - 2*t) * (y1 - y0);
    u += h * ((t - 1)*f0 + t*f1);
    u *= t * (t - 1);
    u += (1 - t)*y0 + t*y1;
 
    return u;
}
 
template<class Scalar, class RHS>
Scalar RK4IVP<Scalar,RHS>::
stepsize() const
{
    return (span_[1] - span_[0]) / N_;
}
 
namespace PhasePressODE {
 
template<class FluidSystem>
Water<FluidSystem>::
Water(const TabulatedFunction& tempVdTable,
      const TabulatedFunction& saltVdTable,
      const int pvtRegionIdx,
      const Scalar normGrav)
    : tempVdTable_(tempVdTable)
    , saltVdTable_(saltVdTable)
    , pvtRegionIdx_(pvtRegionIdx)
    , g_(normGrav)
{
}
 
template<class FluidSystem>
typename Water<FluidSystem>::Scalar
Water<FluidSystem>::
operator()(const Scalar depth,
           const Scalar press) const
{
    return this->density(depth, press) * g_;
}
 
template<class FluidSystem>
typename Water<FluidSystem>::Scalar
Water<FluidSystem>::
density(const Scalar depth,
        const Scalar press) const
{
    // The initializing algorithm can give depths outside the range due to numerical noise i.e. we extrapolate
    Scalar saltConcentration = saltVdTable_.eval(depth, /*extrapolate=*/true);
    Scalar temp = tempVdTable_.eval(depth, /*extrapolate=*/true);
    Scalar rho = FluidSystem::waterPvt().inverseFormationVolumeFactor(pvtRegionIdx_,
                                                                      temp,
                                                                      press,
                                                                      Scalar{0.0} /*=Rsw*/,
                                                                      saltConcentration);
    rho *= FluidSystem::referenceDensity(FluidSystem::waterPhaseIdx, pvtRegionIdx_);
    return rho;
}
 
template<class FluidSystem, class RS>
Oil<FluidSystem,RS>::
Oil(const TabulatedFunction& tempVdTable,
    const RS& rs,
    const int pvtRegionIdx,
    const Scalar normGrav)
    : tempVdTable_(tempVdTable)
    , rs_(rs)
    , pvtRegionIdx_(pvtRegionIdx)
    , g_(normGrav)
{
}
 
template<class FluidSystem, class RS>
typename Oil<FluidSystem,RS>::Scalar
Oil<FluidSystem,RS>::
operator()(const Scalar depth,
           const Scalar press) const
{
    return this->density(depth, press) * g_;
}
 
template<class FluidSystem, class RS>
typename Oil<FluidSystem,RS>::Scalar
Oil<FluidSystem,RS>::
density(const Scalar depth,
        const Scalar press) const
{
    const Scalar temp = tempVdTable_.eval(depth, /*extrapolate=*/true);
    Scalar rs = 0.0;
    if (FluidSystem::enableDissolvedGas() || FluidSystem::enableConstantRs())
        rs = rs_(depth, press, temp);
 
    Scalar bOil = 0.0;
    if (rs >= FluidSystem::oilPvt().saturatedGasDissolutionFactor(pvtRegionIdx_, temp, press)) {
        bOil = FluidSystem::oilPvt().saturatedInverseFormationVolumeFactor(pvtRegionIdx_, temp, press);
    }
    else {
        bOil = FluidSystem::oilPvt().inverseFormationVolumeFactor(pvtRegionIdx_, temp, press, rs);
    }
    Scalar rho = bOil * FluidSystem::referenceDensity(FluidSystem::oilPhaseIdx, pvtRegionIdx_);
    if (FluidSystem::enableDissolvedGas() || FluidSystem::enableConstantRs()) {
        rho += rs * bOil * FluidSystem::referenceDensity(FluidSystem::gasPhaseIdx, pvtRegionIdx_);
    }
 
    return rho;
}
 
template<class FluidSystem, class RV, class RVW>
Gas<FluidSystem,RV,RVW>::
Gas(const TabulatedFunction& tempVdTable,
    const RV& rv,
    const RVW& rvw,
    const int pvtRegionIdx,
    const Scalar normGrav)
    : tempVdTable_(tempVdTable)
    , rv_(rv)
    , rvw_(rvw)
    , pvtRegionIdx_(pvtRegionIdx)
    , g_(normGrav)
{
}
 
template<class FluidSystem, class RV, class RVW>
typename Gas<FluidSystem,RV,RVW>::Scalar
Gas<FluidSystem,RV,RVW>::
operator()(const Scalar depth,
           const Scalar press) const
{
    return this->density(depth, press) * g_;
}
 
template<class FluidSystem, class RV, class RVW>
typename Gas<FluidSystem,RV,RVW>::Scalar
Gas<FluidSystem,RV,RVW>::
density(const Scalar depth,
        const Scalar press) const
{
    const Scalar temp = tempVdTable_.eval(depth, /*extrapolate=*/true);
    Scalar rv = 0.0;
    if (FluidSystem::enableVaporizedOil())
        rv = rv_(depth, press, temp);
 
    Scalar rvw = 0.0;
    if (FluidSystem::enableVaporizedWater())
        rvw = rvw_(depth, press, temp);
 
    Scalar bGas = 0.0;
 
    if (FluidSystem::enableVaporizedOil() && FluidSystem::enableVaporizedWater()) {
        if (rv >= FluidSystem::gasPvt().saturatedOilVaporizationFactor(pvtRegionIdx_, temp, press)
            && rvw >= FluidSystem::gasPvt().saturatedWaterVaporizationFactor(pvtRegionIdx_, temp, press))
        {
            bGas = FluidSystem::gasPvt().saturatedInverseFormationVolumeFactor(pvtRegionIdx_, temp, press);
        } else {
            bGas = FluidSystem::gasPvt().inverseFormationVolumeFactor(pvtRegionIdx_, temp, press, rv, rvw);
        }
        Scalar rho = bGas * FluidSystem::referenceDensity(FluidSystem::gasPhaseIdx, pvtRegionIdx_);
        rho += rv * bGas * FluidSystem::referenceDensity(FluidSystem::oilPhaseIdx, pvtRegionIdx_)
               + rvw * bGas * FluidSystem::referenceDensity(FluidSystem::waterPhaseIdx, pvtRegionIdx_);
        return rho;
    }
 
    if (FluidSystem::enableVaporizedOil()){
        if (rv >= FluidSystem::gasPvt().saturatedOilVaporizationFactor(pvtRegionIdx_, temp, press)) {
            bGas = FluidSystem::gasPvt().saturatedInverseFormationVolumeFactor(pvtRegionIdx_, temp, press);
        } else {
            bGas = FluidSystem::gasPvt().inverseFormationVolumeFactor(pvtRegionIdx_,
                                                                      temp,
                                                                      press,
                                                                      rv,
                                                                      Scalar{0.0}/*=rvw*/);
        }
        Scalar rho = bGas * FluidSystem::referenceDensity(FluidSystem::gasPhaseIdx, pvtRegionIdx_);
        rho += rv * bGas * FluidSystem::referenceDensity(FluidSystem::oilPhaseIdx, pvtRegionIdx_);
        return rho;
     }
 
    if (FluidSystem::enableVaporizedWater()){
        if (rvw >= FluidSystem::gasPvt().saturatedWaterVaporizationFactor(pvtRegionIdx_, temp, press)) {
            bGas = FluidSystem::gasPvt().saturatedInverseFormationVolumeFactor(pvtRegionIdx_, temp, press);
        }
        else {
            bGas = FluidSystem::gasPvt().inverseFormationVolumeFactor(pvtRegionIdx_,
                                                                      temp,
                                                                      press,
                                                                      Scalar{0.0} /*=rv*/,
                                                                      rvw);
        }
        Scalar rho = bGas * FluidSystem::referenceDensity(FluidSystem::gasPhaseIdx, pvtRegionIdx_);
        rho += rvw * bGas * FluidSystem::referenceDensity(FluidSystem::waterPhaseIdx, pvtRegionIdx_);
        return rho;
    }
 
    // immiscible gas
    bGas = FluidSystem::gasPvt().inverseFormationVolumeFactor(pvtRegionIdx_, temp,
                                                              press,
                                                              Scalar{0.0} /*=rv*/,
                                                              Scalar{0.0} /*=rvw*/);
    Scalar rho = bGas * FluidSystem::referenceDensity(FluidSystem::gasPhaseIdx, pvtRegionIdx_);
 
    return rho;
}
 
}
 
template<class FluidSystem, class Region>
template<class ODE>
PressureTable<FluidSystem,Region>::
PressureFunction<ODE>::PressureFunction(const ODE&      ode,
                                        const InitCond& ic,
                                        const int       nsample,
                                        const VSpan&    span)
    : initial_(ic)
{
    this->value_[Direction::Up] = std::make_unique<Distribution>
        (ode, VSpan {{ ic.depth, span[0] }}, ic.pressure, nsample);
 
    this->value_[Direction::Down] = std::make_unique<Distribution>
        (ode, VSpan {{ ic.depth, span[1] }}, ic.pressure, nsample);
}
 
template<class FluidSystem, class Region>
template<class ODE>
PressureTable<FluidSystem,Region>::
PressureFunction<ODE>::PressureFunction(const PressureFunction& rhs)
    : initial_(rhs.initial_)
{
    this->value_[Direction::Up] =
        std::make_unique<Distribution>(*rhs.value_[Direction::Up]);
 
    this->value_[Direction::Down] =
        std::make_unique<Distribution>(*rhs.value_[Direction::Down]);
}
 
template<class FluidSystem, class Region>
template<class ODE>
typename PressureTable<FluidSystem,Region>::template PressureFunction<ODE>&
PressureTable<FluidSystem,Region>::
PressureFunction<ODE>::
operator=(const PressureFunction& rhs)
{
    this->initial_ = rhs.initial_;
 
    this->value_[Direction::Up] =
        std::make_unique<Distribution>(*rhs.value_[Direction::Up]);
 
    this->value_[Direction::Down] =
        std::make_unique<Distribution>(*rhs.value_[Direction::Down]);
 
    return *this;
}
 
template<class FluidSystem, class Region>
template<class ODE>
typename PressureTable<FluidSystem,Region>::template PressureFunction<ODE>&
PressureTable<FluidSystem,Region>::
PressureFunction<ODE>::
operator=(PressureFunction&& rhs)
{
    this->initial_ = rhs.initial_;
    this->value_   = std::move(rhs.value_);
 
    return *this;
}
 
template<class FluidSystem, class Region>
template<class ODE>
typename PressureTable<FluidSystem,Region>::Scalar
PressureTable<FluidSystem,Region>::
PressureFunction<ODE>::
value(const Scalar depth) const
{
    if (depth < this->initial_.depth) {
        // Value above initial condition depth.
        return (*this->value_[Direction::Up])(depth);
    }
    else if (depth > this->initial_.depth) {
        // Value below initial condition depth.
        return (*this->value_[Direction::Down])(depth);
    }
    else {
        // Value *at* initial condition depth.
        return this->initial_.pressure;
    }
}
 
 
template<class FluidSystem, class Region>
template<typename PressFunc>
void PressureTable<FluidSystem,Region>::
checkPtr(const PressFunc*   phasePress,
         const std::string& phaseName) const
{
    if (phasePress != nullptr) { return; }
 
    throw std::invalid_argument {
        "Phase pressure function for \"" + phaseName
        + "\" most not be null"
    };
}
 
template<class FluidSystem, class Region>
typename PressureTable<FluidSystem,Region>::Strategy
PressureTable<FluidSystem,Region>::
selectEquilibrationStrategy(const Region& reg) const
{
    if (!this->oilActive()) {
        if (reg.datum() > reg.zwoc()) { // Datum in water zone
            return &PressureTable::equil_WOG;
        }
        return &PressureTable::equil_GOW;
    }
 
    if (reg.datum() > reg.zwoc()) {      // Datum in water zone
        return &PressureTable::equil_WOG;
    }
    else if (reg.datum() < reg.zgoc()) { // Datum in gas zone
        return &PressureTable::equil_GOW;
    }
    else {                               // Datum in oil zone
        return &PressureTable::equil_OWG;
    }
}
 
template<class FluidSystem, class Region>
void  PressureTable<FluidSystem,Region>::
copyInPointers(const PressureTable& rhs)
{
    if (rhs.oil_ != nullptr) {
        this->oil_ = std::make_unique<OPress>(*rhs.oil_);
    }
 
    if (rhs.gas_ != nullptr) {
        this->gas_ = std::make_unique<GPress>(*rhs.gas_);
    }
 
    if (rhs.wat_ != nullptr) {
        this->wat_ = std::make_unique<WPress>(*rhs.wat_);
    }
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
PhaseSaturations<MaterialLawManager,FluidSystem,Region,CellID>::
PhaseSaturations(MaterialLawManager& matLawMgr,
                 const std::vector<Scalar>& swatInit)
    : matLawMgr_(matLawMgr)
    , swatInit_ (swatInit)
{
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
PhaseSaturations<MaterialLawManager,FluidSystem,Region,CellID>::
PhaseSaturations(const PhaseSaturations& rhs)
        : matLawMgr_(rhs.matLawMgr_)
        , swatInit_ (rhs.swatInit_)
        , sat_      (rhs.sat_)
        , press_    (rhs.press_)
{
    // Note: We don't need to do anything to the 'fluidState_' here.
    this->setEvaluationPoint(*rhs.evalPt_.position,
                             *rhs.evalPt_.region,
                             *rhs.evalPt_.ptable);
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
const PhaseQuantityValue<typename FluidSystem::Scalar>&
PhaseSaturations<MaterialLawManager,FluidSystem,Region,CellID>::
deriveSaturations(const Position& x,
                  const Region&   reg,
                  const PTable&   ptable)
{
    this->setEvaluationPoint(x, reg, ptable);
    this->initializePhaseQuantities();
 
    if (ptable.gasActive())   { this->deriveGasSat();   }
 
    if (ptable.waterActive()) { this->deriveWaterSat(); }
 
 
    if (this->isOverlappingTransition()) {
        this->fixUnphysicalTransition();
    }
 
    if (ptable.oilActive()) { this->deriveOilSat(); }
 
    this->accountForScaledSaturations();
 
    return this->sat_;
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
void PhaseSaturations<MaterialLawManager,FluidSystem,Region,CellID>::
setEvaluationPoint(const Position& x,
                   const Region&   reg,
                   const PTable&   ptable)
{
    this->evalPt_.position = &x;
    this->evalPt_.region   = &reg;
    this->evalPt_.ptable   = &ptable;
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
void PhaseSaturations<MaterialLawManager,FluidSystem,Region,CellID>::
initializePhaseQuantities()
{
    this->sat_.reset();
    this->press_.reset();
 
    const auto  depth  = this->evalPt_.position->depth;
    const auto& ptable = *this->evalPt_.ptable;
 
    if (ptable.oilActive()) {
        this->press_.oil = ptable.oil(depth);
    }
 
    if (ptable.gasActive()) {
        this->press_.gas = ptable.gas(depth);
    }
 
    if (ptable.waterActive()) {
        this->press_.water = ptable.water(depth);
    }
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
void PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::deriveOilSat()
{
    this->sat_.oil = 1.0 - this->sat_.water - this->sat_.gas;
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
void PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::deriveGasSat()
{
    auto& sg = this->sat_.gas;
 
    const auto isIncr = true; // dPcgo/dSg >= 0 for all Sg.
    const auto oilActive = this->evalPt_.ptable->oilActive();
 
    if (this->isConstCapPress(this->gasPos())) {
        // Sharp interface between phases.  Can derive phase saturation
        // directly from knowing where 'depth' of evaluation point is
        // relative to depth of O/G contact.
        const auto gas_contact = oilActive? this->evalPt_.region->zgoc() : this->evalPt_.region->zwoc();
        sg = this->fromDepthTable(gas_contact,
                                  this->gasPos(), isIncr);
    }
    else {
        // Capillary pressure curve is non-constant, meaning there is a
        // transition zone between the gas and oil phases.  Invert capillary
        // pressure relation
        //
        //    Pcgo(Sg) = Pg - Po
        //
        // Note that Pcgo is defined to be (Pg - Po), not (Po - Pg).
        const auto pw = oilActive? this->press_.oil : this->press_.water;
        const auto pcgo = this->press_.gas - pw;
        sg = this->invertCapPress(pcgo, this->gasPos(), isIncr);
    }
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
void PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::deriveWaterSat()
{
    auto& sw = this->sat_.water;
 
    const auto oilActive = this->evalPt_.ptable->oilActive();
    if (!oilActive) {
        // for 2p gas+water we set the water saturation to 1.0 - sg
        sw = 1.0 - this->sat_.gas;
    }
    else {
        const auto isIncr = false; // dPcow/dSw <= 0 for all Sw.
 
        if (this->isConstCapPress(this->waterPos())) {
            // Sharp interface between phases.  Can derive phase saturation
            // directly from knowing where 'depth' of evaluation point is
            // relative to depth of O/W contact.
            sw = this->fromDepthTable(this->evalPt_.region->zwoc(),
                                    this->waterPos(), isIncr);
        }
        else {
            // Capillary pressure curve is non-constant, meaning there is a
            // transition zone between the oil and water phases.  Invert
            // capillary pressure relation
            //
            //    Pcow(Sw) = Po - Pw
            //
            // unless the model uses "SWATINIT".  In the latter case, pick the
            // saturation directly from the SWATINIT array of the pertinent
            // cell.
            const auto pcow = this->press_.oil - this->press_.water;
 
            if (this->swatInit_.empty()) {
                sw = this->invertCapPress(pcow, this->waterPos(), isIncr);
            }
            else {
                auto [swout, newSwatInit] = this->applySwatInit(pcow);
                if (newSwatInit)
                    sw = this->invertCapPress(pcow, this->waterPos(), isIncr);
                else {
                    sw = swout;
                }
            }
        }
    }
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
void PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
fixUnphysicalTransition()
{
    auto& sg = this->sat_.gas;
    auto& sw = this->sat_.water;
 
    // Overlapping gas/oil and oil/water transition zones can lead to
    // unphysical phase saturations when individual saturations are derived
    // directly from inverting O/G and O/W capillary pressure curves.
    //
    // Recalculate phase saturations using the implied gas/water capillary
    // pressure: Pg - Pw.
    const auto pcgw = this->press_.gas - this->press_.water;
    if (! this->swatInit_.empty()) {
        // Re-scale Pc to reflect imposed sw for vanishing oil phase.  This
        // seems consistent with ECLIPSE, but fails to honour SWATINIT in
        // case of non-trivial gas/oil capillary pressure.
        auto [swout, newSwatInit] = this->applySwatInit(pcgw, sw);
        if (newSwatInit){
            const auto isIncr = false; // dPcow/dSw <= 0 for all Sw.
            sw = this->invertCapPress(pcgw, this->waterPos(), isIncr);
        }
        else {
            sw = swout;
        }
    }
 
    sw = satFromSumOfPcs<FluidSystem>
        (this->matLawMgr_, this->waterPos(), this->gasPos(),
         this->evalPt_.position->cell, pcgw);
    sg = 1.0 - sw;
 
    this->fluidState_.setSaturation(this->oilPos(), 1.0 - sw - sg);
    this->fluidState_.setSaturation(this->gasPos(), sg);
    this->fluidState_.setSaturation(this->waterPos(), this->evalPt_
                                    .ptable->waterActive() ? sw : 0.0);
 
    // Pcgo = Pg - Po => Po = Pg - Pcgo
    this->computeMaterialLawCapPress();
    this->press_.oil = this->press_.gas - this->materialLawCapPressGasOil();
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
void PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
accountForScaledSaturations()
{
    const auto gasActive = this->evalPt_.ptable->gasActive();
    const auto watActive = this->evalPt_.ptable->waterActive();
    const auto oilActive = this->evalPt_.ptable->oilActive();
 
    auto sg = gasActive? this->sat_.gas : 0.0;
    auto sw = watActive? this->sat_.water : 0.0;
    auto so = oilActive? this->sat_.oil : 0.0;
 
    this->fluidState_.setSaturation(this->waterPos(), sw);
    this->fluidState_.setSaturation(this->oilPos(), so);
    this->fluidState_.setSaturation(this->gasPos(), sg);
 
    const auto& scaledDrainageInfo = this->matLawMgr_
        .oilWaterScaledEpsInfoDrainage(this->evalPt_.position->cell);
 
    const auto thresholdSat = 1.0e-6;
    if (watActive && ((sw + thresholdSat) > scaledDrainageInfo.Swu)) {
        // Water saturation exceeds maximum possible value.  Reset oil phase
        // pressure to that which corresponds to maximum possible water
        // saturation value.
        this->fluidState_.setSaturation(this->waterPos(), scaledDrainageInfo.Swu);
        if (oilActive) {
            this->fluidState_.setSaturation(this->oilPos(), so + sw - scaledDrainageInfo.Swu);
        } else if (gasActive) {
            this->fluidState_.setSaturation(this->gasPos(), sg + sw - scaledDrainageInfo.Swu);
        }
        sw = scaledDrainageInfo.Swu;
        this->computeMaterialLawCapPress();
 
        if (oilActive) {
            // Pcow = Po - Pw => Po = Pw + Pcow
            this->press_.oil = this->press_.water + this->materialLawCapPressOilWater();
        } else {
            // Pcgw = Pg - Pw => Pg = Pw + Pcgw
            this->press_.gas = this->press_.water + this->materialLawCapPressGasWater();
        }
 
    }
    if (gasActive && ((sg + thresholdSat) > scaledDrainageInfo.Sgu)) {
        // Gas saturation exceeds maximum possible value.  Reset oil phase
        // pressure to that which corresponds to maximum possible gas
        // saturation value.
        this->fluidState_.setSaturation(this->gasPos(), scaledDrainageInfo.Sgu);
        if (oilActive) {
            this->fluidState_.setSaturation(this->oilPos(), so + sg - scaledDrainageInfo.Sgu);
        } else if (watActive) {
            this->fluidState_.setSaturation(this->waterPos(), sw + sg - scaledDrainageInfo.Sgu);
        }
        sg = scaledDrainageInfo.Sgu;
        this->computeMaterialLawCapPress();
 
        if (oilActive) {
            // Pcgo = Pg - Po => Po = Pg - Pcgo
            this->press_.oil = this->press_.gas - this->materialLawCapPressGasOil();
        } else {
            // Pcgw = Pg - Pw => Pw = Pg - Pcgw
            this->press_.water =  this->press_.gas - this->materialLawCapPressGasWater();
        }
    }
 
    if (watActive && ((sw - thresholdSat) < scaledDrainageInfo.Swl)) {
        // Water saturation less than minimum possible value in cell.  Reset
        // water phase pressure to that which corresponds to minimum
        // possible water saturation value.
        this->fluidState_.setSaturation(this->waterPos(), scaledDrainageInfo.Swl);
        if (oilActive) {
            this->fluidState_.setSaturation(this->oilPos(), so + sw - scaledDrainageInfo.Swl);
        } else if (gasActive) {
            this->fluidState_.setSaturation(this->gasPos(), sg + sw - scaledDrainageInfo.Swl);
        }
        sw = scaledDrainageInfo.Swl;
        this->computeMaterialLawCapPress();
 
        if (oilActive) {
            // Pcwo = Po - Pw => Pw = Po - Pcow
            this->press_.water = this->press_.oil - this->materialLawCapPressOilWater();
        } else {
            // Pcgw = Pg - Pw => Pw = Pg - Pcgw
            this->press_.water = this->press_.gas - this->materialLawCapPressGasWater();
        }
    }
 
    if (gasActive && ((sg - thresholdSat) < scaledDrainageInfo.Sgl)) {
        // Gas saturation less than minimum possible value in cell.  Reset
        // gas phase pressure to that which corresponds to minimum possible
        // gas saturation.
        this->fluidState_.setSaturation(this->gasPos(), scaledDrainageInfo.Sgl);
        if (oilActive) {
            this->fluidState_.setSaturation(this->oilPos(), so + sg - scaledDrainageInfo.Sgl);
        } else if (watActive) {
            this->fluidState_.setSaturation(this->waterPos(), sw + sg - scaledDrainageInfo.Sgl);
        }
        sg = scaledDrainageInfo.Sgl;
        this->computeMaterialLawCapPress();
 
        if (oilActive) {
            // Pcgo = Pg - Po => Pg = Po + Pcgo
            this->press_.gas = this->press_.oil + this->materialLawCapPressGasOil();
        } else {
            // Pcgw = Pg - Pw => Pg = Pw + Pcgw
            this->press_.gas = this->press_.water + this->materialLawCapPressGasWater();
        }
    }
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
std::pair<typename FluidSystem::Scalar, bool>
PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
applySwatInit(const Scalar pcow)
{
    return this->applySwatInit(pcow, this->swatInit_[this->evalPt_.position->cell]);
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
std::pair<typename FluidSystem::Scalar, bool>
PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
applySwatInit(const Scalar pcow, const Scalar sw)
{
    return this->matLawMgr_.applySwatinit(this->evalPt_.position->cell, pcow, sw);
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
void PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
computeMaterialLawCapPress()
{
    const auto& matParams = this->matLawMgr_
        .materialLawParams(this->evalPt_.position->cell);
 
    this->matLawCapPress_.fill(0.0);
    MaterialLaw::capillaryPressures(this->matLawCapPress_,
                                    matParams, this->fluidState_);
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
typename FluidSystem::Scalar
PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
materialLawCapPressGasOil() const
{
    return this->matLawCapPress_[this->oilPos()]
        + this->matLawCapPress_[this->gasPos()];
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
typename FluidSystem::Scalar
PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
materialLawCapPressOilWater() const
{
    return this->matLawCapPress_[this->oilPos()]
        - this->matLawCapPress_[this->waterPos()];
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
typename FluidSystem::Scalar
PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
materialLawCapPressGasWater() const
{
    return this->matLawCapPress_[this->gasPos()]
        - this->matLawCapPress_[this->waterPos()];
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
bool PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
isConstCapPress(const PhaseIdx phaseIdx) const
{
    return isConstPc<FluidSystem>
        (this->matLawMgr_, phaseIdx, this->evalPt_.position->cell);
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
bool PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
isOverlappingTransition() const
{
    return this->evalPt_.ptable->gasActive()
        && this->evalPt_.ptable->waterActive()
        && ((this->sat_.gas + this->sat_.water) > 1.0);
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
typename FluidSystem::Scalar
PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
fromDepthTable(const Scalar   contactdepth,
               const PhaseIdx phasePos,
               const bool     isincr) const
{
    return satFromDepth<FluidSystem>
        (this->matLawMgr_, this->evalPt_.position->depth,
         contactdepth, static_cast<int>(phasePos),
         this->evalPt_.position->cell, isincr);
}
 
template <class MaterialLawManager, class FluidSystem, class Region, typename CellID>
typename FluidSystem::Scalar
PhaseSaturations<MaterialLawManager, FluidSystem, Region, CellID>::
invertCapPress(const Scalar pc,
               const PhaseIdx phasePos,
               const bool     isincr) const
{
    return satFromPc<FluidSystem>
        (this->matLawMgr_, static_cast<int>(phasePos),
         this->evalPt_.position->cell, pc, isincr);
}
 
template<class FluidSystem, class Region>
PressureTable<FluidSystem,Region>::
PressureTable(const Scalar gravity,
              const int    samplePoints)
    : gravity_(gravity)
    , nsample_(samplePoints)
{
}
 
template <class FluidSystem, class Region>
PressureTable<FluidSystem,Region>::
PressureTable(const PressureTable<FluidSystem,Region>& rhs)
    : gravity_(rhs.gravity_)
    , nsample_(rhs.nsample_)
{
    this->copyInPointers(rhs);
}
 
template <class FluidSystem, class Region>
PressureTable<FluidSystem,Region>::
PressureTable(PressureTable<FluidSystem,Region>&& rhs)
    : gravity_(rhs.gravity_)
    , nsample_(rhs.nsample_)
    , oil_    (std::move(rhs.oil_))
    , gas_    (std::move(rhs.gas_))
    , wat_    (std::move(rhs.wat_))
{
}
 
template <class FluidSystem, class Region>
PressureTable<FluidSystem,Region>&
PressureTable<FluidSystem,Region>::
operator=(const PressureTable<FluidSystem,Region>& rhs)
{
    this->gravity_ = rhs.gravity_;
    this->nsample_ = rhs.nsample_;
    this->copyInPointers(rhs);
 
    return *this;
}
 
template <class FluidSystem, class Region>
PressureTable<FluidSystem,Region>&
PressureTable<FluidSystem,Region>::
operator=(PressureTable<FluidSystem,Region>&& rhs)
{
    this->gravity_ = rhs.gravity_;
    this->nsample_ = rhs.nsample_;
 
    this->oil_ = std::move(rhs.oil_);
    this->gas_ = std::move(rhs.gas_);
    this->wat_ = std::move(rhs.wat_);
 
    return *this;
}
 
template <class FluidSystem, class Region>
void PressureTable<FluidSystem,Region>::
equilibrate(const Region& reg,
            const VSpan&  span)
{
    // One of the PressureTable::equil_*() member functions.
    auto equil = this->selectEquilibrationStrategy(reg);
 
    (this->*equil)(reg, span);
}
 
template <class FluidSystem, class Region>
bool PressureTable<FluidSystem,Region>::
oilActive() const
{
    return FluidSystem::phaseIsActive(FluidSystem::oilPhaseIdx);
}
 
template <class FluidSystem, class Region>
bool PressureTable<FluidSystem,Region>::
gasActive() const
{
    return FluidSystem::phaseIsActive(FluidSystem::gasPhaseIdx);
}
 
template <class FluidSystem, class Region>
bool PressureTable<FluidSystem,Region>::
waterActive() const
{
    return FluidSystem::phaseIsActive(FluidSystem::waterPhaseIdx);
}
 
template <class FluidSystem, class Region>
typename FluidSystem::Scalar
PressureTable<FluidSystem,Region>::
oil(const Scalar depth) const
{
    this->checkPtr(this->oil_.get(), "OIL");
 
    return this->oil_->value(depth);
}
 
template <class FluidSystem, class Region>
typename FluidSystem::Scalar
PressureTable<FluidSystem,Region>::
gas(const Scalar depth) const
{
    this->checkPtr(this->gas_.get(), "GAS");
 
    return this->gas_->value(depth);
}
 
 
template <class FluidSystem, class Region>
typename FluidSystem::Scalar
PressureTable<FluidSystem,Region>::
water(const Scalar depth) const
{
    this->checkPtr(this->wat_.get(), "WATER");
 
    return this->wat_->value(depth);
}
 
template <class FluidSystem, class Region>
void PressureTable<FluidSystem, Region>::
equil_WOG(const Region& reg, const VSpan& span)
{
    // Datum depth in water zone.  Calculate phase pressure for water first,
    // followed by oil and gas if applicable.
 
    if (! this->waterActive()) {
        throw std::invalid_argument {
            "Don't know how to interpret EQUIL datum depth in "
            "WATER zone in model without active water phase"
        };
    }
 
    {
        const auto ic = typename WPress::InitCond {
            reg.datum(), reg.pressure()
        };
 
        this->makeWatPressure(ic, reg, span);
    }
 
    if (this->oilActive()) {
        // Pcow = Po - Pw => Po = Pw + Pcow
        const auto ic = typename OPress::InitCond {
            reg.zwoc(),
            this->water(reg.zwoc()) + reg.pcowWoc()
        };
 
        this->makeOilPressure(ic, reg, span);
    }
 
    if (this->gasActive() && this->oilActive()) {
        // Pcgo = Pg - Po => Pg = Po + Pcgo
        const auto ic = typename GPress::InitCond {
            reg.zgoc(),
            this->oil(reg.zgoc()) + reg.pcgoGoc()
        };
 
        this->makeGasPressure(ic, reg, span);
    } else if (this->gasActive() && !this->oilActive()) {
        // No oil phase set Pg = Pw + Pcgw
        const auto ic = typename GPress::InitCond {
            reg.zwoc(), // The WOC is really the GWC for gas/water cases
            this->water(reg.zwoc()) + reg.pcowWoc() // Pcow(WOC) is really Pcgw(GWC) for gas/water cases
        };
        this->makeGasPressure(ic, reg, span);
    }
}
 
template <class FluidSystem, class Region>
void PressureTable<FluidSystem, Region>::
equil_GOW(const Region& reg, const VSpan& span)
{
    // Datum depth in gas zone.  Calculate phase pressure for gas first,
    // followed by oil and water if applicable.
 
    if (! this->gasActive()) {
        throw std::invalid_argument {
            "Don't know how to interpret EQUIL datum depth in "
            "GAS zone in model without active gas phase"
        };
    }
 
    {
        const auto ic = typename GPress::InitCond {
            reg.datum(), reg.pressure()
        };
 
        this->makeGasPressure(ic, reg, span);
    }
 
    if (this->oilActive()) {
        // Pcgo = Pg - Po => Po = Pg - Pcgo
        const auto ic = typename OPress::InitCond {
            reg.zgoc(),
            this->gas(reg.zgoc()) - reg.pcgoGoc()
        };
        this->makeOilPressure(ic, reg, span);
    }
 
    if (this->waterActive() && this->oilActive()) {
        // Pcow = Po - Pw => Pw = Po - Pcow
        const auto ic = typename WPress::InitCond {
            reg.zwoc(),
            this->oil(reg.zwoc()) - reg.pcowWoc()
        };
 
        this->makeWatPressure(ic, reg, span);
    } else if (this->waterActive() && !this->oilActive()) {
        // No oil phase set Pw = Pg - Pcgw
        const auto ic = typename WPress::InitCond {
            reg.zwoc(), // The WOC is really the GWC for gas/water cases
            this->gas(reg.zwoc()) - reg.pcowWoc() // Pcow(WOC) is really Pcgw(GWC) for gas/water cases
        };
        this->makeWatPressure(ic, reg, span);
    }
}
 
template <class FluidSystem, class Region>
void PressureTable<FluidSystem, Region>::
equil_OWG(const Region& reg, const VSpan& span)
{
    // Datum depth in oil zone.  Calculate phase pressure for oil first,
    // followed by gas and water if applicable.
 
    if (! this->oilActive()) {
        throw std::invalid_argument {
            "Don't know how to interpret EQUIL datum depth in "
            "OIL zone in model without active oil phase"
        };
    }
 
    {
        const auto ic = typename OPress::InitCond {
            reg.datum(), reg.pressure()
        };
 
        this->makeOilPressure(ic, reg, span);
    }
 
    if (this->waterActive()) {
        // Pcow = Po - Pw => Pw = Po - Pcow
        const auto ic = typename WPress::InitCond {
            reg.zwoc(),
            this->oil(reg.zwoc()) - reg.pcowWoc()
        };
 
        this->makeWatPressure(ic, reg, span);
    }
 
    if (this->gasActive()) {
        // Pcgo = Pg - Po => Pg = Po + Pcgo
        const auto ic = typename GPress::InitCond {
            reg.zgoc(),
            this->oil(reg.zgoc()) + reg.pcgoGoc()
        };
        this->makeGasPressure(ic, reg, span);
    }
}
 
template <class FluidSystem, class Region>
void PressureTable<FluidSystem, Region>::
makeOilPressure(const typename OPress::InitCond& ic,
                const Region&                    reg,
                const VSpan&                     span)
{
    const auto drho = OilPressODE {
        reg.tempVdTable(), reg.dissolutionCalculator(),
        reg.pvtIdx(), this->gravity_
    };
 
    this->oil_ = std::make_unique<OPress>(drho, ic, this->nsample_, span);
}
 
template <class FluidSystem, class Region>
void PressureTable<FluidSystem, Region>::
makeGasPressure(const typename GPress::InitCond& ic,
                const Region&                    reg,
                const VSpan&                     span)
{
    const auto drho = GasPressODE {
        reg.tempVdTable(), reg.evaporationCalculator(), reg.waterEvaporationCalculator(),
        reg.pvtIdx(), this->gravity_
    };
 
    this->gas_ = std::make_unique<GPress>(drho, ic, this->nsample_, span);
}
 
template <class FluidSystem, class Region>
void PressureTable<FluidSystem, Region>::
makeWatPressure(const typename WPress::InitCond& ic,
                const Region&                    reg,
                const VSpan&                     span)
{
    const auto drho = WatPressODE {
        reg.tempVdTable(), reg.saltVdTable(), reg.pvtIdx(), this->gravity_
    };
 
    this->wat_ = std::make_unique<WPress>(drho, ic, this->nsample_, span);
}
 
}
 
namespace DeckDependent {
 
std::vector<EquilRecord>
getEquil(const EclipseState& state)
{
    const auto& init = state.getInitConfig();
 
    if(!init.hasEquil()) {
        throw std::domain_error("Deck does not provide equilibration data.");
    }
 
    const auto& equil = init.getEquil();
    return { equil.begin(), equil.end() };
}
 
template<class GridView>
std::vector<int>
equilnum(const EclipseState& eclipseState,
         const GridView& gridview)
{
    std::vector<int> eqlnum(gridview.size(0), 0);
 
    if (eclipseState.fieldProps().has_int("EQLNUM")) {
        const auto& e = eclipseState.fieldProps().get_int("EQLNUM");
        std::ranges::transform(e, eqlnum.begin(), [](int n) { return n - 1; });
    }
    OPM_BEGIN_PARALLEL_TRY_CATCH();
    const int num_regions = eclipseState.getTableManager().getEqldims().getNumEquilRegions();
    if (std::ranges::any_of(eqlnum, [num_regions](int n){return n >= num_regions;})) {
        throw std::runtime_error("Values larger than maximum Equil regions " +
                                 std::to_string(num_regions) + " provided in EQLNUM");
    }
    if (std::ranges::any_of(eqlnum, [](int n){return n < 0;})) {
        throw std::runtime_error("zero or negative values provided in EQLNUM");
    }
    OPM_END_PARALLEL_TRY_CATCH("Invalied EQLNUM numbers: ", gridview.comm());
 
    return eqlnum;
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
template<class MaterialLawManager>
InitialStateComputer<FluidSystem,
                     Grid,
                     GridView,
                     ElementMapper,
                     CartesianIndexMapper>::
InitialStateComputer(MaterialLawManager& materialLawManager,
                     const EclipseState& eclipseState,
                     const Grid& grid,
                     const GridView& gridView,
                     const CartesianIndexMapper& cartMapper,
                     const Scalar grav,
                     const int num_pressure_points,
                     const bool applySwatInit)
    : temperature_(grid.size(/*codim=*/0), eclipseState.getTableManager().rtemp()),
      saltConcentration_(grid.size(/*codim=*/0)),
      saltSaturation_(grid.size(/*codim=*/0)),
      pp_(FluidSystem::numPhases,
          std::vector<Scalar>(grid.size(/*codim=*/0))),
      sat_(FluidSystem::numPhases,
           std::vector<Scalar>(grid.size(/*codim=*/0))),
      rs_(grid.size(/*codim=*/0)),
      rv_(grid.size(/*codim=*/0)),
      rvw_(grid.size(/*codim=*/0)),
      cartesianIndexMapper_(cartMapper),
      num_pressure_points_(num_pressure_points)
{
    //Check for presence of kw SWATINIT
    if (applySwatInit) {
        if (eclipseState.fieldProps().has_double("SWATINIT")) {
            if constexpr (std::is_same_v<Scalar,double>) {
                swatInit_ = eclipseState.fieldProps().get_double("SWATINIT");
            } else {
                const auto& input = eclipseState.fieldProps().get_double("SWATINIT");
                swatInit_.resize(input.size());
                std::ranges::copy(input, swatInit_.begin());
            }
        }
    }
 
    // Querry cell depth, cell top-bottom.
    // numerical aquifer cells might be specified with different depths.
    const auto& num_aquifers = eclipseState.aquifer().numericalAquifers();
    updateCellProps_(gridView, num_aquifers);
 
    // Get the equilibration records.
    const std::vector<EquilRecord> rec = getEquil(eclipseState);
    const auto& tables = eclipseState.getTableManager();
    // Create (inverse) region mapping.
    const RegionMapping<> eqlmap(equilnum(eclipseState, grid));
    const int invalidRegion = -1;
    regionPvtIdx_.resize(rec.size(), invalidRegion);
    setRegionPvtIdx(eclipseState, eqlmap);
 
    // Create Rs functions.
    rsFunc_.reserve(rec.size());
 
    auto getArray = [](const std::vector<double>& input)
    {
        if constexpr (std::is_same_v<Scalar,double>) {
            return input;
        } else {
            std::vector<Scalar> output;
            output.resize(input.size());
            std::ranges::copy(input, output.begin());
            return output;
        }
    };
 
    if (FluidSystem::enableDissolvedGas()) {
        for (std::size_t i = 0; i < rec.size(); ++i) {
            if (eqlmap.cells(i).empty()) {
                rsFunc_.push_back(std::shared_ptr<Miscibility::RsVD<FluidSystem>>());
                continue;
            }
            const int pvtIdx = regionPvtIdx_[i];
            if (!rec[i].liveOilInitConstantRs()) {
                const TableContainer& rsvdTables = tables.getRsvdTables();
                const TableContainer& pbvdTables = tables.getPbvdTables();
                if (rsvdTables.size() > 0) {
                    const RsvdTable& rsvdTable = rsvdTables.getTable<RsvdTable>(i);
                    auto depthColumn = getArray(rsvdTable.getColumn("DEPTH").vectorCopy());
                    auto rsColumn = getArray(rsvdTable.getColumn("RS").vectorCopy());
                    rsFunc_.push_back(std::make_shared<Miscibility::RsVD<FluidSystem>>(pvtIdx,
                                                                                       depthColumn, rsColumn));
                } else if (pbvdTables.size() > 0) {
                    const PbvdTable& pbvdTable = pbvdTables.getTable<PbvdTable>(i);
                    auto depthColumn = getArray(pbvdTable.getColumn("DEPTH").vectorCopy());
                    auto pbubColumn = getArray(pbvdTable.getColumn("PBUB").vectorCopy());
                    rsFunc_.push_back(std::make_shared<Miscibility::PBVD<FluidSystem>>(pvtIdx,
                                                                                       depthColumn, pbubColumn));
 
                } else {
                    throw std::runtime_error("Cannot initialise: RSVD or PBVD table not available.");
                }
 
            }
            else {
                if (rec[i].gasOilContactDepth() != rec[i].datumDepth()) {
                    throw std::runtime_error("Cannot initialise: when no explicit RSVD table is given, \n"
                                             "datum depth must be at the gas-oil-contact. "
                                             "In EQUIL region "+std::to_string(i + 1)+"  (counting from 1), this does not hold.");
                }
                const Scalar pContact = rec[i].datumDepthPressure();
                const Scalar TContact = 273.15 + 20; // standard temperature for now
                rsFunc_.push_back(std::make_shared<Miscibility::RsSatAtContact<FluidSystem>>(pvtIdx, pContact, TContact));
            }
        }
    }
    else if (FluidSystem::enableConstantRs() && tables.hasTables("RSCONST")) {
        const auto& rsconstTables = tables.getRsconstTables();
 
        if (rsconstTables.empty()) {
            for (std::size_t i = 0; i < rec.size(); ++i) {
                // Normal dead oil (no dissolved gas and rsconst)
                rsFunc_.push_back(std::make_shared<Miscibility::NoMixing<Scalar>>());
            }
        }
        else {
            const auto& rsconstTable = rsconstTables.getTable<RsconstTable>(0);
 
            const auto rsConst = rsconstTable.getRsColumn().front();
            const auto pBub = rsconstTable.getPbubColumn().front();
 
            const auto& units = eclipseState.getUnits();
 
            OpmLog::info(fmt::format("Using RSCONST keyword: Rs = {:.2} [{}], Pb = {:.2} [{}]",
                                     units.from_si(UnitSystem::measure::gas_oil_ratio, rsConst),
                                     units.name   (UnitSystem::measure::gas_oil_ratio),
                                     units.from_si(UnitSystem::measure::pressure, pBub),
                                     units.name   (UnitSystem::measure::pressure)));
 
            for (std::size_t i = 0; i < rec.size(); ++i) {
                rsFunc_.push_back(std::make_shared<Miscibility::RsConst<FluidSystem>>(rsConst, pBub));
            }
        }
    }
    else {
        for (std::size_t i = 0; i < rec.size(); ++i) {
            // Normal dead oil (no dissolved gas and rsconst)
            rsFunc_.push_back(std::make_shared<Miscibility::NoMixing<Scalar>>());
        }
    }
 
    rvFunc_.reserve(rec.size());
    if (FluidSystem::enableVaporizedOil()) {
        for (std::size_t i = 0; i < rec.size(); ++i) {
            if (eqlmap.cells(i).empty()) {
                rvFunc_.push_back(std::shared_ptr<Miscibility::RvVD<FluidSystem>>());
                continue;
            }
            const int pvtIdx = regionPvtIdx_[i];
            if (!rec[i].wetGasInitConstantRv()) {
                const TableContainer& rvvdTables = tables.getRvvdTables();
                const TableContainer& pdvdTables = tables.getPdvdTables();
 
                if (rvvdTables.size() > 0) {
                    const RvvdTable& rvvdTable = rvvdTables.getTable<RvvdTable>(i);
                    auto depthColumn = getArray(rvvdTable.getColumn("DEPTH").vectorCopy());
                    auto rvColumn = getArray(rvvdTable.getColumn("RV").vectorCopy());
                    rvFunc_.push_back(std::make_shared<Miscibility::RvVD<FluidSystem>>(pvtIdx,
                                                                                       depthColumn, rvColumn));
                } else if (pdvdTables.size() > 0) {
                    const PdvdTable& pdvdTable = pdvdTables.getTable<PdvdTable>(i);
                    auto depthColumn = getArray(pdvdTable.getColumn("DEPTH").vectorCopy());
                    auto pdewColumn = getArray(pdvdTable.getColumn("PDEW").vectorCopy());
                    rvFunc_.push_back(std::make_shared<Miscibility::PDVD<FluidSystem>>(pvtIdx,
                                                                                       depthColumn, pdewColumn));
                } else {
                    throw std::runtime_error("Cannot initialise: RVVD or PDCD table not available.");
                }
            }
            else {
                if (rec[i].gasOilContactDepth() != rec[i].datumDepth()) {
                    throw std::runtime_error(
                              "Cannot initialise: when no explicit RVVD table is given, \n"
                              "datum depth must be at the gas-oil-contact. "
                              "In EQUIL region "+std::to_string(i + 1)+" (counting from 1), this does not hold.");
                }
                const Scalar pContact = rec[i].datumDepthPressure() + rec[i].gasOilContactCapillaryPressure();
                const Scalar TContact = 273.15 + 20; // standard temperature for now
                rvFunc_.push_back(std::make_shared<Miscibility::RvSatAtContact<FluidSystem>>(pvtIdx,pContact, TContact));
            }
        }
    }
    else {
        for (std::size_t i = 0; i < rec.size(); ++i) {
            rvFunc_.push_back(std::make_shared<Miscibility::NoMixing<Scalar>>());
        }
    }
 
    rvwFunc_.reserve(rec.size());
    if (FluidSystem::enableVaporizedWater()) {
        for (std::size_t i = 0; i < rec.size(); ++i) {
            if (eqlmap.cells(i).empty()) {
                rvwFunc_.push_back(std::shared_ptr<Miscibility::RvwVD<FluidSystem>>());
                continue;
            }
            const int pvtIdx = regionPvtIdx_[i];
            if (!rec[i].humidGasInitConstantRvw()) {
                const TableContainer& rvwvdTables = tables.getRvwvdTables();
 
                if (rvwvdTables.size() > 0) {
                    const RvwvdTable& rvwvdTable = rvwvdTables.getTable<RvwvdTable>(i);
                    auto depthColumn = getArray(rvwvdTable.getColumn("DEPTH").vectorCopy());
                    auto rvwvdColumn = getArray(rvwvdTable.getColumn("RVWVD").vectorCopy());
                    rvwFunc_.push_back(std::make_shared<Miscibility::RvwVD<FluidSystem>>(pvtIdx,
                                                                                       depthColumn, rvwvdColumn));
                } else {
                    throw std::runtime_error("Cannot initialise: RVWVD table not available.");
                }
            }
            else {
                const auto oilActive = FluidSystem::phaseIsActive(FluidSystem::oilPhaseIdx);
                if (oilActive) {
                    if (rec[i].gasOilContactDepth() != rec[i].datumDepth()) {
                        rvwFunc_.push_back(std::make_shared<Miscibility::NoMixing<Scalar>>());
                        const auto msg = "No explicit RVWVD table is given for EQUIL region " + std::to_string(i + 1) +". \n"
                                        "and datum depth is not at the gas-oil-contact. \n"
                                        "Rvw is set to 0.0 in all cells. \n";
                        OpmLog::warning(msg);
                    } else {
                        // pg = po + Pcgo = po + (pg - po)
                        // for gas-condensate with initial no oil zone: water-oil contact depth (OWC) equal gas-oil contact depth (GOC)
                        const Scalar pContact = rec[i].datumDepthPressure() + rec[i].gasOilContactCapillaryPressure();
                        const Scalar TContact = 273.15 + 20; // standard temperature for now
                        rvwFunc_.push_back(std::make_shared<Miscibility::RvwSatAtContact<FluidSystem>>(pvtIdx,pContact, TContact));
                    }
                }
                else {
                     // two-phase gas-water sytem:  water-oil contact depth is taken equal to gas-water contact depth (GWC)
                     // and water-oil capillary pressure (Pcwo) is taken equal to gas-water capillary pressure (Pcgw) at GWC
                     if (rec[i].waterOilContactDepth() != rec[i].datumDepth()) {
                        rvwFunc_.push_back(std::make_shared<Miscibility::NoMixing<Scalar>>());
                        const auto msg = "No explicit RVWVD table is given for EQUIL region " + std::to_string(i + 1) +". \n"
                                         "and datum depth is not at the gas-water-contact. \n"
                                         "Rvw is set to 0.0 in all cells. \n";
                        OpmLog::warning(msg);
                    } else {
                        // pg = pw + Pcgw = pw + (pg - pw)
                        const Scalar pContact = rec[i].datumDepthPressure() + rec[i].waterOilContactCapillaryPressure();
                        const Scalar TContact = 273.15 + 20; // standard temperature for now
                        rvwFunc_.push_back(std::make_shared<Miscibility::RvwSatAtContact<FluidSystem>>(pvtIdx,pContact, TContact));
                    }
                }
            }
        }
    }
    else {
        for (std::size_t i = 0; i < rec.size(); ++i) {
            rvwFunc_.push_back(std::make_shared<Miscibility::NoMixing<Scalar>>());
        }
    }
 
    // EXTRACT the initial temperature
    updateInitialTemperature_(eclipseState, eqlmap);
 
    // EXTRACT the initial salt concentration
    updateInitialSaltConcentration_(eclipseState, eqlmap);
 
    // EXTRACT the initial salt saturation
    updateInitialSaltSaturation_(eclipseState, eqlmap);
 
    // Compute pressures, saturations, rs and rv factors.
    const auto& comm = grid.comm();
    calcPressSatRsRv(eqlmap, rec, materialLawManager, gridView, comm, grav);
 
    // modify the pressure and saturation for numerical aquifer cells
    applyNumericalAquifers_(gridView, num_aquifers,
                            eclipseState.runspec().co2Storage() ||
                            eclipseState.runspec().h2Storage());
 
    // Modify oil pressure in no-oil regions so that the pressures of present phases can
    // be recovered from the oil pressure and capillary relations.
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
template<class RMap>
void InitialStateComputer<FluidSystem,
                          Grid,
                          GridView,
                          ElementMapper,
                          CartesianIndexMapper>::
updateInitialTemperature_(const EclipseState& eclState, const RMap& reg)
{
    const int numEquilReg = rsFunc_.size();
    tempVdTable_.resize(numEquilReg);
    const auto& tables = eclState.getTableManager();
    if (!tables.hasTables("RTEMPVD")) {
        std::vector<Scalar> x = {0.0,1.0};
        std::vector<Scalar> y = {static_cast<Scalar>(tables.rtemp()),
                                 static_cast<Scalar>(tables.rtemp())};
        for (auto& table : this->tempVdTable_) {
            table.setXYContainers(x, y);
        }
    } else {
        const TableContainer& tempvdTables = tables.getRtempvdTables();
        for (std::size_t i = 0; i < tempvdTables.size(); ++i) {
            const RtempvdTable& tempvdTable = tempvdTables.getTable<RtempvdTable>(i);
            tempVdTable_[i].setXYContainers(tempvdTable.getDepthColumn(), tempvdTable.getTemperatureColumn());
            const auto& cells = reg.cells(i);
            for (const auto& cell : cells) {
                const Scalar depth = cellCenterDepth_[cell];
                this->temperature_[cell] = tempVdTable_[i].eval(depth, /*extrapolate=*/true);
            }
        }
    }
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
template<class RMap>
void InitialStateComputer<FluidSystem,
                          Grid,
                          GridView,
                          ElementMapper,
                          CartesianIndexMapper>::
updateInitialSaltConcentration_(const EclipseState& eclState, const RMap& reg)
{
    const int numEquilReg = rsFunc_.size();
    saltVdTable_.resize(numEquilReg);
    const auto& tables = eclState.getTableManager();
    const TableContainer& saltvdTables = tables.getSaltvdTables();
 
    // If no saltvd table is given, we create a trivial table for the density calculations
    if (saltvdTables.empty()) {
        std::vector<Scalar> x = {0.0,1.0};
        std::vector<Scalar> y = {0.0,0.0};
        for (auto& table : this->saltVdTable_) {
            table.setXYContainers(x, y);
        }
    } else {
        for (std::size_t i = 0; i < saltvdTables.size(); ++i) {
            const SaltvdTable& saltvdTable = saltvdTables.getTable<SaltvdTable>(i);
            saltVdTable_[i].setXYContainers(saltvdTable.getDepthColumn(), saltvdTable.getSaltColumn());
 
            const auto& cells = reg.cells(i);
            for (const auto& cell : cells) {
                const Scalar depth = cellCenterDepth_[cell];
                this->saltConcentration_[cell] = saltVdTable_[i].eval(depth, /*extrapolate=*/true);
            }
        }
    }
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
template<class RMap>
void InitialStateComputer<FluidSystem,
                          Grid,
                          GridView,
                          ElementMapper,
                          CartesianIndexMapper>::
updateInitialSaltSaturation_(const EclipseState& eclState, const RMap& reg)
{
    const int numEquilReg = rsFunc_.size();
    saltpVdTable_.resize(numEquilReg);
    const auto& tables = eclState.getTableManager();
    const TableContainer& saltpvdTables = tables.getSaltpvdTables();
 
    for (std::size_t i = 0; i < saltpvdTables.size(); ++i) {
        const SaltpvdTable& saltpvdTable = saltpvdTables.getTable<SaltpvdTable>(i);
        saltpVdTable_[i].setXYContainers(saltpvdTable.getDepthColumn(), saltpvdTable.getSaltpColumn());
 
        const auto& cells = reg.cells(i);
        for (const auto& cell : cells) {
            const Scalar depth = cellCenterDepth_[cell];
            this->saltSaturation_[cell] = saltpVdTable_[i].eval(depth, /*extrapolate=*/true);
        }
    }
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
void InitialStateComputer<FluidSystem,
                          Grid,
                          GridView,
                          ElementMapper,
                          CartesianIndexMapper>::
updateCellProps_(const GridView& gridView,
                 const NumericalAquifers& aquifer)
{
    ElementMapper elemMapper(gridView, Dune::mcmgElementLayout());
    int numElements = gridView.size(/*codim=*/0);
    cellCenterDepth_.resize(numElements);
    cellCenterXY_.resize(numElements);
    cellCorners_.resize(numElements);
    cellZSpan_.resize(numElements);
    cellZMinMax_.resize(numElements);
 
    auto elemIt = gridView.template begin</*codim=*/0>();
    const auto& elemEndIt = gridView.template end</*codim=*/0>();
    const auto num_aqu_cells = aquifer.allAquiferCells();
    for (; elemIt != elemEndIt; ++elemIt) {
        const Element& element = *elemIt;
        const unsigned int elemIdx = elemMapper.index(element);
        cellCenterDepth_[elemIdx] = Details::cellCenterDepth<Scalar>(element);
        cellCenterXY_[elemIdx] = Details::cellCenterXY<Scalar>(element);
        cellCorners_[elemIdx] = Details::getCellCornerXY<Scalar>(element);
        const auto cartIx = cartesianIndexMapper_.cartesianIndex(elemIdx);
        cellZSpan_[elemIdx] = Details::cellZSpan<Scalar>(element);
        cellZMinMax_[elemIdx] = Details::cellZMinMax<Scalar>(element);
        if (!num_aqu_cells.empty()) {
            const auto search = num_aqu_cells.find(cartIx);
            if (search != num_aqu_cells.end()) {
                const auto* aqu_cell = num_aqu_cells.at(cartIx);
                const Scalar depth_change_num_aqu = aqu_cell->depth - cellCenterDepth_[elemIdx];
                cellCenterDepth_[elemIdx] += depth_change_num_aqu;
                cellZSpan_[elemIdx].first += depth_change_num_aqu;
                cellZSpan_[elemIdx].second += depth_change_num_aqu;
                cellZMinMax_[elemIdx].first += depth_change_num_aqu;
                cellZMinMax_[elemIdx].second += depth_change_num_aqu;
            }
        }
    }
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
void InitialStateComputer<FluidSystem,
                          Grid,
                          GridView,
                          ElementMapper,
                          CartesianIndexMapper>::
applyNumericalAquifers_(const GridView& gridView,
                        const NumericalAquifers& aquifer,
                        const bool co2store_or_h2store)
{
    const auto num_aqu_cells = aquifer.allAquiferCells();
    if (num_aqu_cells.empty()) return;
 
    // Check if water phase is active, or in the case of CO2STORE and H2STORE, water is modelled as oil phase
    bool oil_as_brine = co2store_or_h2store && FluidSystem::phaseIsActive(FluidSystem::oilPhaseIdx);
    const auto watPos =  oil_as_brine? FluidSystem::oilPhaseIdx : FluidSystem::waterPhaseIdx;
    if (!FluidSystem::phaseIsActive(watPos)){
        throw std::logic_error  { "Water phase has to be active for numerical aquifer case" };
    }
 
    ElementMapper elemMapper(gridView, Dune::mcmgElementLayout());
    auto elemIt = gridView.template begin</*codim=*/0>();
    const auto& elemEndIt = gridView.template end</*codim=*/0>();
    const auto oilPos = FluidSystem::oilPhaseIdx;
    const auto gasPos = FluidSystem::gasPhaseIdx;
    for (; elemIt != elemEndIt; ++elemIt) {
        const Element& element = *elemIt;
        const unsigned int elemIdx = elemMapper.index(element);
        const auto cartIx = cartesianIndexMapper_.cartesianIndex(elemIdx);
        const auto search = num_aqu_cells.find(cartIx);
        if (search != num_aqu_cells.end()) {
            // numerical aquifer cells are filled with water initially
            this->sat_[watPos][elemIdx] = 1.;
 
            if (!co2store_or_h2store && FluidSystem::phaseIsActive(oilPos)) {
                this->sat_[oilPos][elemIdx] = 0.;
            }
 
            if (FluidSystem::phaseIsActive(gasPos)) {
                this->sat_[gasPos][elemIdx] = 0.;
            }
            const auto* aqu_cell = num_aqu_cells.at(cartIx);
            const auto msg = fmt::format("FOR AQUIFER CELL AT ({}, {}, {}) OF NUMERICAL "
                                         "AQUIFER {}, WATER SATURATION IS SET TO BE UNITY",
                                         aqu_cell->I+1, aqu_cell->J+1, aqu_cell->K+1, aqu_cell->aquifer_id);
            OpmLog::info(msg);
 
            // if pressure is specified for numerical aquifers, we use these pressure values
            // for numerical aquifer cells
            if (aqu_cell->init_pressure) {
                const Scalar pres = *(aqu_cell->init_pressure);
                this->pp_[watPos][elemIdx] = pres;
                if (FluidSystem::phaseIsActive(gasPos)) {
                    this->pp_[gasPos][elemIdx] = pres;
                }
                if (FluidSystem::phaseIsActive(oilPos)) {
                    this->pp_[oilPos][elemIdx] = pres;
                }
            }
        }
    }
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
template<class RMap>
void InitialStateComputer<FluidSystem,
                          Grid,
                          GridView,
                          ElementMapper,
                          CartesianIndexMapper>::
setRegionPvtIdx(const EclipseState& eclState, const RMap& reg)
{
    const auto& pvtnumData = eclState.fieldProps().get_int("PVTNUM");
 
    for (const auto& r : reg.activeRegions()) {
        const auto& cells = reg.cells(r);
        regionPvtIdx_[r] = pvtnumData[*cells.begin()] - 1;
    }
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
template<class RMap, class MaterialLawManager, class Comm>
void InitialStateComputer<FluidSystem,
                          Grid,
                          GridView,
                          ElementMapper,
                          CartesianIndexMapper>::
calcPressSatRsRv(const RMap& reg,
                 const std::vector<EquilRecord>& rec,
                 MaterialLawManager& materialLawManager,
                 const GridView& gridView,
                 const Comm& comm,
                 const Scalar grav)
{
    using PhaseSat = Details::PhaseSaturations<
        MaterialLawManager, FluidSystem, EquilReg<Scalar>, typename RMap::CellId
    >;
 
    auto ptable = Details::PressureTable<FluidSystem, EquilReg<Scalar>>{ grav, this->num_pressure_points_ };
    auto psat   = PhaseSat { materialLawManager, this->swatInit_ };
    auto vspan  = std::array<Scalar, 2>{};
 
    std::vector<int> regionIsEmpty(rec.size(), 0);
    for (std::size_t r = 0; r < rec.size(); ++r) {
        const auto& cells = reg.cells(r);
 
        Details::verticalExtent(cells, cellZMinMax_, comm, vspan);
 
        const auto acc = rec[r].initializationTargetAccuracy();
        if (acc > 0) {
            // The grid blocks are treated as being tilted
            // First check if the region has cells
            if (cells.empty()) {
                regionIsEmpty[r] = 1;
                continue;
            }
            const auto eqreg = EquilReg {
                rec[r], this->rsFunc_[r], this->rvFunc_[r], this->rvwFunc_[r],
                this->tempVdTable_[r], this->saltVdTable_[r], this->regionPvtIdx_[r]
            };
            // Ensure contacts are within the span
            vspan[0] = std::min(vspan[0], std::min(eqreg.zgoc(), eqreg.zwoc()));
            vspan[1] = std::max(vspan[1], std::max(eqreg.zgoc(), eqreg.zwoc()));
            ptable.equilibrate(eqreg, vspan);
            // For titled blocks, we can use a simple weightening based on title of the grid
            // this->equilibrateTiltedFaultBlockSimple(cells, eqreg, gridView, acc, ptable, psat);
            this->equilibrateTiltedFaultBlock(cells, eqreg, gridView, acc, ptable, psat);
        }
        else if (acc == 0) {
            if (cells.empty()) {
                regionIsEmpty[r] = 1;
                continue;
            }
            const auto eqreg = EquilReg {
                rec[r], this->rsFunc_[r], this->rvFunc_[r], this->rvwFunc_[r],
                this->tempVdTable_[r], this->saltVdTable_[r], this->regionPvtIdx_[r]
            };
            vspan[0] = std::min(vspan[0], std::min(eqreg.zgoc(), eqreg.zwoc()));
            vspan[1] = std::max(vspan[1], std::max(eqreg.zgoc(), eqreg.zwoc()));
            ptable.equilibrate(eqreg, vspan);
            // Centre-point method
            this->equilibrateCellCentres(cells, eqreg, ptable, psat);
        }
        else if (acc < 0) {
            if (cells.empty()) {
                regionIsEmpty[r] = 1;
                continue;
            }
            const auto eqreg = EquilReg {
                rec[r], this->rsFunc_[r], this->rvFunc_[r], this->rvwFunc_[r],
                this->tempVdTable_[r], this->saltVdTable_[r], this->regionPvtIdx_[r]
            };
            vspan[0] = std::min(vspan[0], std::min(eqreg.zgoc(), eqreg.zwoc()));
            vspan[1] = std::max(vspan[1], std::max(eqreg.zgoc(), eqreg.zwoc()));
            ptable.equilibrate(eqreg, vspan);
            // Horizontal subdivision
            this->equilibrateHorizontal(cells, eqreg, -acc, ptable, psat);
        }
    }
    comm.min(regionIsEmpty.data(),regionIsEmpty.size());
    if (comm.rank() == 0) {
        for (std::size_t r = 0; r < rec.size(); ++r) {
            if (regionIsEmpty[r]) //region is empty on all partitions
                OpmLog::warning("Equilibration region " + std::to_string(r + 1)
                                 + " has no active cells");
        }
    }
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
template<class CellRange, class EquilibrationMethod>
void InitialStateComputer<FluidSystem,
                          Grid,
                          GridView,
                          ElementMapper,
                          CartesianIndexMapper>::
cellLoop(const CellRange&      cells,
         EquilibrationMethod&& eqmethod)
{
    const auto oilPos = FluidSystem::oilPhaseIdx;
    const auto gasPos = FluidSystem::gasPhaseIdx;
    const auto watPos = FluidSystem::waterPhaseIdx;
 
    const auto oilActive = FluidSystem::phaseIsActive(oilPos);
    const auto gasActive = FluidSystem::phaseIsActive(gasPos);
    const auto watActive = FluidSystem::phaseIsActive(watPos);
 
    auto pressures   = Details::PhaseQuantityValue<Scalar>{};
    auto saturations = Details::PhaseQuantityValue<Scalar>{};
    Scalar Rs          = 0.0;
    Scalar Rv          = 0.0;
    Scalar Rvw         = 0.0;
 
    for (const auto& cell : cells) {
        eqmethod(cell, pressures, saturations, Rs, Rv, Rvw);
 
        if (oilActive) {
            this->pp_ [oilPos][cell] = pressures.oil;
            this->sat_[oilPos][cell] = saturations.oil;
        }
 
        if (gasActive) {
            this->pp_ [gasPos][cell] = pressures.gas;
            this->sat_[gasPos][cell] = saturations.gas;
        }
 
        if (watActive) {
            this->pp_ [watPos][cell] = pressures.water;
            this->sat_[watPos][cell] = saturations.water;
        }
 
        if (oilActive && gasActive) {
            this->rs_[cell] = Rs;
            this->rv_[cell] = Rv;
        }
 
        if (watActive && gasActive) {
            this->rvw_[cell] = Rvw;
        }
    }
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
template<class CellRange, class PressTable, class PhaseSat>
void InitialStateComputer<FluidSystem,
                          Grid,
                          GridView,
                          ElementMapper,
                          CartesianIndexMapper>::
equilibrateCellCentres(const CellRange&         cells,
                       const EquilReg<Scalar>&  eqreg,
                       const PressTable&        ptable,
                       PhaseSat&                psat)
{
    using CellPos = typename PhaseSat::Position;
    using CellID  = std::remove_cv_t<std::remove_reference_t<
        decltype(std::declval<CellPos>().cell)>>;
    this->cellLoop(cells, [this, &eqreg,  &ptable, &psat]
        (const CellID                 cell,
         Details::PhaseQuantityValue<Scalar>& pressures,
         Details::PhaseQuantityValue<Scalar>& saturations,
         Scalar&                      Rs,
         Scalar&                      Rv,
         Scalar&                      Rvw) -> void
    {
        const auto pos = CellPos {
            cell, cellCenterDepth_[cell]
        };
 
        saturations = psat.deriveSaturations(pos, eqreg, ptable);
        pressures   = psat.correctedPhasePressures();
 
        const auto temp = this->temperature_[cell];
 
        Rs = eqreg.dissolutionCalculator()
            (pos.depth, pressures.oil, temp, saturations.gas);
 
        Rv = eqreg.evaporationCalculator()
            (pos.depth, pressures.gas, temp, saturations.oil);
 
        Rvw = eqreg.waterEvaporationCalculator()
            (pos.depth, pressures.gas, temp, saturations.water);
    });
}
 
template<class FluidSystem,
         class Grid,
         class GridView,
         class ElementMapper,
         class CartesianIndexMapper>
template<class CellRange, class PressTable, class PhaseSat>
void InitialStateComputer<FluidSystem,
                          Grid,
                          GridView,
                          ElementMapper,
                          CartesianIndexMapper>::
equilibrateHorizontal(const CellRange&        cells,
                      const EquilReg<Scalar>& eqreg,
                      const int               acc,
                      const PressTable&       ptable,
                      PhaseSat&               psat)
{
    using CellPos = typename PhaseSat::Position;
    using CellID  = std::remove_cv_t<std::remove_reference_t<
        decltype(std::declval<CellPos>().cell)>>;
 
    this->cellLoop(cells, [this, acc, &eqreg, &ptable, &psat]
        (const CellID                 cell,
         Details::PhaseQuantityValue<Scalar>& pressures,
         Details::PhaseQuantityValue<Scalar>& saturations,
         Scalar&                      Rs,
         Scalar&                      Rv,
         Scalar&                      Rvw) -> void
    {
        pressures  .reset();
        saturations.reset();
 
        Scalar totfrac = 0.0;
        for (const auto& [depth, frac] : Details::horizontalSubdivision(cell, cellZSpan_[cell], acc)) {
            const auto pos = CellPos { cell, depth };
 
            saturations.axpy(psat.deriveSaturations(pos, eqreg, ptable), frac);
            pressures  .axpy(psat.correctedPhasePressures(), frac);
 
            totfrac += frac;
        }
 
        if (totfrac > 0.) {
            saturations /= totfrac;
            pressures /= totfrac;
        } else {
            // Fall back to centre point method for zero-thickness cells.
            const auto pos = CellPos {
                    cell, cellCenterDepth_[cell]
            };
 
            saturations = psat.deriveSaturations(pos, eqreg, ptable);
            pressures   = psat.correctedPhasePressures();
        }
 
        const auto temp = this->temperature_[cell];
        const auto cz   = cellCenterDepth_[cell];
 
        Rs = eqreg.dissolutionCalculator()
            (cz, pressures.oil, temp, saturations.gas);
 
        Rv = eqreg.evaporationCalculator()
            (cz, pressures.gas, temp, saturations.oil);
 
        Rvw = eqreg.waterEvaporationCalculator()
            (cz, pressures.gas, temp, saturations.water);
    });
}
 
template<class FluidSystem, class Grid, class GridView, class ElementMapper, class CartesianIndexMapper>
template<class CellRange, class PressTable, class PhaseSat>
void InitialStateComputer<FluidSystem, Grid, GridView, ElementMapper, CartesianIndexMapper>::
equilibrateTiltedFaultBlockSimple(const CellRange& cells,
                             const EquilReg<Scalar>& eqreg,
                             const GridView&         gridView,
                             const int               acc,
                             const PressTable&       ptable,
                             PhaseSat&               psat)
{
    using CellPos = typename PhaseSat::Position;
    using CellID  = std::remove_cv_t<std::remove_reference_t<
        decltype(std::declval<CellPos>().cell)>>;
 
    this->cellLoop(cells, [this, acc, &eqreg, &ptable, &psat, &gridView]
        (const CellID                 cell,
         Details::PhaseQuantityValue<Scalar>& pressures,
         Details::PhaseQuantityValue<Scalar>& saturations,
         Scalar&                      Rs,
         Scalar&                      Rv,
         Scalar&                      Rvw) -> void
    {
        pressures.reset();
        saturations.reset();
        Scalar totalWeight = 0.0;
 
        // We assume grid blocks are treated as being tilted
        const auto& [zmin, zmax] = cellZMinMax_[cell];
        const Scalar cellThickness = zmax - zmin;
        const Scalar halfThickness = cellThickness / 2.0;
 
        // Calculate dip parameters from corner point geometry
        Scalar dipAngle, dipAzimuth;
        Details::computeBlockDip(cellCorners_[cell], dipAngle, dipAzimuth);
 
        // Reference point for TVD calculations
                std::array<Scalar, 3> referencePoint = {
            cellCenterXY_[cell].first,
            cellCenterXY_[cell].second,
            cellCenterDepth_[cell]
        };
 
        //  We have acc levels within each half (upper and lower) of the block
        const int numLevelsPerHalf = std::min(20, acc);
 
        // Create subdivisions for upper and lower halves with cross-section weighting
        std::vector<std::pair<Scalar, Scalar>> levels;
 
        // Subdivide upper and lower halves separately
        for (int side = 0; side < 2; ++side) {
            Scalar halfStart = (side == 0) ? zmin : zmin + halfThickness;
 
            for (int i = 0; i < numLevelsPerHalf; ++i) {
                // Calculate depth at the center of this subdivision
                Scalar depth = halfStart + (i + 0.5) * (halfThickness / numLevelsPerHalf);
 
                // A simple way: we can estimate cross-section weight based on dip angle
                // For horizontal cells: weight = 1.0, for tilted cells: weight decreases with dip
                Scalar crossSectionWeight = (halfThickness / numLevelsPerHalf);
 
                // Apply dip correction to weight (cross-section area decreases with dip)
                if (std::abs(dipAngle) > 1e-10) {
                    crossSectionWeight /= std::cos(dipAngle);
                }
 
                levels.emplace_back(depth, crossSectionWeight);
            }
        }
 
        for (const auto& [depth, weight] : levels) {
            // Convert measured depth to True Vertical Depth for tilted blocks
            const auto& [x, y] = cellCenterXY_[cell];
            Scalar tvd = Details::calculateTrueVerticalDepth(
                depth, x, y, dipAngle, dipAzimuth, referencePoint);
 
            const auto pos = CellPos{cell, tvd};
 
            auto localSaturations = psat.deriveSaturations(pos, eqreg, ptable);
            auto localPressures = psat.correctedPhasePressures();
 
            // Apply cross-section weighted averaging
            saturations.axpy(localSaturations, weight);
            pressures.axpy(localPressures, weight);
            totalWeight += weight;
        }
 
        // Normalize results
        if (totalWeight > 1e-10) {
            saturations /= totalWeight;
            pressures /= totalWeight;
        } else {
            // Fallback to center point method using TVD
            const auto& [x, y] = cellCenterXY_[cell];
            Scalar tvdCenter = Details::calculateTrueVerticalDepth(
                cellCenterDepth_[cell], x, y, dipAngle, dipAzimuth, referencePoint);
            const auto pos = CellPos{cell, tvdCenter};
            saturations = psat.deriveSaturations(pos, eqreg, ptable);
            pressures = psat.correctedPhasePressures();
        }
 
        // Compute solution ratios at cell center TVD
        const auto temp = this->temperature_[cell];
        const auto& [x, y] = cellCenterXY_[cell];
        Scalar tvdCenter = Details::calculateTrueVerticalDepth(
            cellCenterDepth_[cell], x, y, dipAngle, dipAzimuth, referencePoint);
 
        Rs = eqreg.dissolutionCalculator()(tvdCenter, pressures.oil, temp, saturations.gas);
        Rv = eqreg.evaporationCalculator()(tvdCenter, pressures.gas, temp, saturations.oil);
        Rvw = eqreg.waterEvaporationCalculator()(tvdCenter, pressures.gas, temp, saturations.water);
    });
}
 
template<class FluidSystem, class Grid, class GridView, class ElementMapper, class CartesianIndexMapper>
template<class CellRange, class PressTable, class PhaseSat>
void InitialStateComputer<FluidSystem, Grid, GridView, ElementMapper, CartesianIndexMapper>::
equilibrateTiltedFaultBlock(const CellRange&        cells,
                             const EquilReg<Scalar>& eqreg,
                             const GridView&         gridView,
                             const int               acc,
                             const PressTable&       ptable,
                             PhaseSat&               psat)
{
    using CellPos = typename PhaseSat::Position;
    using CellID  = std::remove_cv_t<std::remove_reference_t<
        decltype(std::declval<CellPos>().cell)>>;
 
    std::vector<typename GridView::template Codim<0>::Entity> entityMap(gridView.size(0));
    for (const auto& entity : entities(gridView, Dune::Codim<0>())) {
        CellID idx = gridView.indexSet().index(entity);
        entityMap[idx] = entity;
    }
 
    // Face Area Calculation
    auto polygonArea = [](const std::vector<std::array<Scalar, 2>>& pts) {
        if (pts.size() < 3) return Scalar(0);
        Scalar area = 0;
        for (size_t i = 0; i < pts.size(); ++i) {
            size_t j = (i + 1) % pts.size();
            area += pts[i][0] * pts[j][1] - pts[j][0] * pts[i][1];
        }
        return std::abs(area) * Scalar(0.5);
    };
 
    // Compute horizontal cross-section at given depth
    auto computeCrossSectionArea = [&](const CellID cell, Scalar depth) -> Scalar {
        try {
            const auto& entity = entityMap[cell];
            const auto& geometry = entity.geometry();
            const int numCorners = geometry.corners();
 
            std::vector<std::array<Scalar, 3>> corners(numCorners);
            for (int i = 0; i < numCorners; ++i) {
                const auto& corner = geometry.corner(i);
                corners[i] = {static_cast<Scalar>(corner[0]), static_cast<Scalar>(corner[1]), static_cast<Scalar>(corner[2])};
            }
 
            // Find all intersections between horizontal plane and cell edges
            std::vector<std::array<Scalar, 2>> intersectionPoints;
            const Scalar tol = 1e-10;
 
            // Check all edges between corners (could be optimized further)
            for (size_t i = 0; i < corners.size(); ++i) {
                for (size_t j = i + 1; j < corners.size(); ++j) {
                    Scalar za = corners[i][2];
                    Scalar zb = corners[j][2];
 
                    if ((za - depth) * (zb - depth) <= 0.0 && std::abs(za - zb) > tol) {
                        // Edge crosses the horizontal plane
                        Scalar t = (depth - za) / (zb - za);
                        Scalar x = corners[i][0] + t * (corners[j][0] - corners[i][0]);
                        Scalar y = corners[i][1] + t * (corners[j][1] - corners[i][1]);
                        intersectionPoints.push_back({x, y});
                    }
                }
            }
 
            // Remove duplicates
            if (intersectionPoints.size() > 1) {
                auto pointsEqual = [tol](const std::array<Scalar, 2>& a, const std::array<Scalar, 2>& b) {
                    return std::abs(a[0] - b[0]) < tol && std::abs(a[1] - b[1]) < tol;
                };
 
                intersectionPoints.erase(
                    std::unique(intersectionPoints.begin(), intersectionPoints.end(), pointsEqual),
                    intersectionPoints.end()
                );
            }
 
            if (intersectionPoints.size() < 3) {
                // No valid grid found, use fallback
                return 0.0;
            }
 
            // Order points counter-clockwise around centroid
            Scalar cx = 0, cy = 0;
            for (const auto& p : intersectionPoints) {
                cx += p[0]; cy += p[1];
            }
            cx /= intersectionPoints.size();
            cy /= intersectionPoints.size();
 
            // Sorting
            auto angleCompare = [cx, cy](const std::array<Scalar, 2>& a, const std::array<Scalar, 2>& b) {
                return std::atan2(a[1] - cy, a[0] - cx) < std::atan2(b[1] - cy, b[0] - cx);
            };
 
            std::ranges::sort(intersectionPoints, angleCompare);
 
            return polygonArea(intersectionPoints);
 
        } catch (const std::exception& e) {
            return 0.0;
        }
    };
 
    auto cellProcessor = [this, acc, &eqreg, &ptable, &psat, &computeCrossSectionArea]
        (const CellID                 cell,
         Details::PhaseQuantityValue<Scalar>& pressures,
         Details::PhaseQuantityValue<Scalar>& saturations,
         Scalar&                      Rs,
         Scalar&                      Rv,
         Scalar&                      Rvw) -> void
    {
        pressures.reset();
        saturations.reset();
        Scalar totalWeight = 0.0;
 
        const auto& zmin = this->cellZMinMax_[cell].first;
        const auto& zmax = this->cellZMinMax_[cell].second;
        const Scalar cellThickness = zmax - zmin;
        const Scalar halfThickness = cellThickness / 2.0;
 
        // Calculate dip parameters from corner point geometry
        Scalar dipAngle, dipAzimuth;
        Details::computeBlockDip(this->cellCorners_[cell], dipAngle, dipAzimuth);
 
        // Reference point for TVD calculations
        std::array<Scalar, 3> referencePoint = {
            this->cellCenterXY_[cell].first,
            this->cellCenterXY_[cell].second,
            cellCenterDepth_[cell]
        };
 
        // We have acc levels within each half (upper and lower) of the block
        const int numLevelsPerHalf = std::min(20, acc);
 
        // Create subdivisions for upper and lower halves with cross-section weighting
        std::vector<std::pair<Scalar, Scalar>> levels;
 
        // Subdivide upper and lower halves separately
        for (int side = 0; side < 2; ++side) {
            Scalar halfStart = (side == 0) ? zmin : zmin + halfThickness;
 
            for (int i = 0; i < numLevelsPerHalf; ++i) {
                // Calculate depth at the center of this subdivision
                Scalar depth = halfStart + (i + 0.5) * (halfThickness / numLevelsPerHalf);
 
                // Compute cross-section area at this depth
                Scalar crossSectionArea = computeCrossSectionArea(cell, depth);
 
                // Weight is proportional to: area × Δz (volume element)
                Scalar weight = crossSectionArea * (halfThickness / numLevelsPerHalf);
 
                levels.emplace_back(depth, weight);
            }
        }
 
        // Maybe not necessary (for debug)
        bool hasValidAreas = false;
        for (const auto& level : levels) {
            if (level.second > 1e-10) {
                hasValidAreas = true;
                break;
            }
        }
 
        if (!hasValidAreas) {
            // Fallback to dip-based weighting as used in equilibrateTiltedFaultBlockSimple
            levels.clear();
            for (int side = 0; side < 2; ++side) {
                Scalar halfStart = (side == 0) ? zmin : zmin + halfThickness;
                for (int i = 0; i < numLevelsPerHalf; ++i) {
                    Scalar depth = halfStart + (i + 0.5) * (halfThickness / numLevelsPerHalf);
                    Scalar weight = (halfThickness / numLevelsPerHalf);
                    if (std::abs(dipAngle) > 1e-10) {
                        weight /= std::cos(dipAngle);
                    }
                    levels.emplace_back(depth, weight);
                }
            }
        }
 
        for (const auto& level : levels) {
            Scalar depth = level.first;
            Scalar weight = level.second;
 
            // Convert measured depth to True Vertical Depth for tilted blocks
            const auto& xy = this->cellCenterXY_[cell];
            Scalar tvd = Details::calculateTrueVerticalDepth(
                depth, xy.first, xy.second, dipAngle, dipAzimuth, referencePoint);
 
            const auto pos = CellPos{cell, tvd};
 
            auto localSaturations = psat.deriveSaturations(pos, eqreg, ptable);
            auto localPressures = psat.correctedPhasePressures();
 
            // Apply cross-section weighted averaging
            saturations.axpy(localSaturations, weight);
            pressures.axpy(localPressures, weight);
            totalWeight += weight;
        }
 
        if (totalWeight > 1e-10) {
            saturations /= totalWeight;
            pressures /= totalWeight;
        } else {
            // Fallback to center point method using TVD
            const auto& xy = this->cellCenterXY_[cell];
            Scalar tvdCenter = Details::calculateTrueVerticalDepth(
                this->cellCenterDepth_[cell], xy.first, xy.second, dipAngle, dipAzimuth, referencePoint);
            const auto pos = CellPos{cell, tvdCenter};
            saturations = psat.deriveSaturations(pos, eqreg, ptable);
            pressures = psat.correctedPhasePressures();
        }
 
        // Compute solution ratios at cell center TVD
        const auto temp = this->temperature_[cell];
        const auto& xy = this->cellCenterXY_[cell];
        Scalar tvdCenter = Details::calculateTrueVerticalDepth(
            this->cellCenterDepth_[cell], xy.first, xy.second, dipAngle, dipAzimuth, referencePoint);
 
        Rs = eqreg.dissolutionCalculator()(tvdCenter, pressures.oil, temp, saturations.gas);
        Rv = eqreg.evaporationCalculator()(tvdCenter, pressures.gas, temp, saturations.oil);
        Rvw = eqreg.waterEvaporationCalculator()(tvdCenter, pressures.gas, temp, saturations.water);
    };
 
    this->cellLoop(cells, cellProcessor);
}
}
} // namespace EQUIL
} // namespace Opm
 
#endif // OPM_INIT_STATE_EQUIL_IMPL_HPP