PiecewiseLinearTwoPhaseMaterial.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:
/*
  Copyright (C) 2009-2013 by Andreas Lauser
  Copyright (C) 2015 by IRIS AS

  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 2 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/>.
*/
#ifndef OPM_PIECEWISE_LINEAR_TWO_PHASE_MATERIAL_HPP
#define OPM_PIECEWISE_LINEAR_TWO_PHASE_MATERIAL_HPP

#include "PiecewiseLinearTwoPhaseMaterialParams.hpp"

#include <opm/common/ErrorMacros.hpp>
#include <opm/common/Exceptions.hpp>
#include <opm/material/common/MathToolbox.hpp>

#include <algorithm>
#include <cmath>
#include <cassert>

namespace Opm {
template <class TraitsT, class ParamsT = PiecewiseLinearTwoPhaseMaterialParams<TraitsT> >
class PiecewiseLinearTwoPhaseMaterial : public TraitsT
{
    typedef typename ParamsT::ValueVector ValueVector;

public:
    typedef TraitsT Traits;

    typedef ParamsT Params;

    typedef typename Traits::Scalar Scalar;

    static const int numPhases = Traits::numPhases;
    static_assert(numPhases == 2,
                  "The piecewise linear two-phase capillary pressure law only"
                  "applies to the case of two fluid phases");

    static const bool implementsTwoPhaseApi = true;

    static const bool implementsTwoPhaseSatApi = true;

    static const bool isSaturationDependent = true;

    static const bool isPressureDependent = false;

    static const bool isTemperatureDependent = false;

    static const bool isCompositionDependent = false;

    template <class Container, class FluidState>
    static void capillaryPressures(Container &values, const Params &params, const FluidState &fs)
    {
        typedef typename std::remove_reference<decltype(values[0])>::type Evaluation;

        values[Traits::wettingPhaseIdx] = 0.0; // reference phase
        values[Traits::nonWettingPhaseIdx] = pcnw<FluidState, Evaluation>(params, fs);
    }

    template <class Container, class FluidState>
    static void saturations(Container& /* values */, const Params& /* params */, const FluidState& /* fs */)
    { OPM_THROW(std::logic_error, "Not implemented: saturations()"); }

    template <class Container, class FluidState>
    static void relativePermeabilities(Container &values, const Params &params, const FluidState &fs)
    {
        typedef typename std::remove_reference<decltype(values[0])>::type Evaluation;

        values[Traits::wettingPhaseIdx] = krw<FluidState, Evaluation>(params, fs);
        values[Traits::nonWettingPhaseIdx] = krn<FluidState, Evaluation>(params, fs);
    }

    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation pcnw(const Params &params, const FluidState &fs)
    {
        typedef MathToolbox<typename FluidState::Scalar> FsToolbox;
        const auto& Sw =
            FsToolbox::template toLhs<Evaluation>(fs.saturation(Traits::wettingPhaseIdx));

        return twoPhaseSatPcnw(params, Sw);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatPcnw(const Params &params, const Evaluation& Sw)
    { return eval_(params.SwPcwnSamples(), params.pcnwSamples(), Sw); }

    template <class Evaluation>
    static Evaluation twoPhaseSatPcnwInv(const Params &params, const Evaluation& pcnw)
    { return eval_(params.pcnwSamples(), params.SwPcwnSamples(), pcnw); }

    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation Sw(const Params& /* params */, const FluidState& /* fs */)
    { OPM_THROW(std::logic_error, "Not implemented: Sw()"); }

    template <class Evaluation>
    static Evaluation twoPhaseSatSw(const Params& /* params */, const Evaluation& /* pC */)
    { OPM_THROW(std::logic_error, "Not implemented: twoPhaseSatSw()"); }

    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation Sn(const Params &params, const FluidState &fs)
    { return 1 - Sw<FluidState, Scalar>(params, fs); }

    template <class Evaluation>
    static Evaluation twoPhaseSatSn(const Params &params, const Evaluation& pC)
    { return 1 - twoPhaseSatSw(params, pC); }

    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation krw(const Params &params, const FluidState &fs)
    {
        typedef MathToolbox<typename FluidState::Scalar> FsToolbox;
        const auto& Sw =
            FsToolbox::template toLhs<Evaluation>(fs.saturation(Traits::wettingPhaseIdx));

        return twoPhaseSatKrw(params, Sw);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatKrw(const Params &params, const Evaluation& Sw)
    { return eval_(params.SwKrwSamples(), params.krwSamples(), Sw); }

    template <class Evaluation>
    static Evaluation twoPhaseSatKrwInv(const Params &params, const Evaluation& krw)
    { return eval_(params.krwSamples(), params.SwKrwSamples(), krw); }

    template <class FluidState, class Evaluation = typename FluidState::Scalar>
    static Evaluation krn(const Params &params, const FluidState &fs)
    {
        typedef MathToolbox<typename FluidState::Scalar> FsToolbox;
        const auto& Sw =
            FsToolbox::template toLhs<Evaluation>(fs.saturation(Traits::wettingPhaseIdx));

        return twoPhaseSatKrn(params, Sw);
    }

    template <class Evaluation>
    static Evaluation twoPhaseSatKrn(const Params &params, const Evaluation& Sw)
    { return eval_(params.SwKrnSamples(), params.krnSamples(), Sw); }

    template <class Evaluation>
    static Evaluation twoPhaseSatKrnInv(const Params &params, const Evaluation& krn)
    { return eval_(params.krnSamples(), params.SwKrnSamples(), krn); }

private:
    template <class Evaluation>
    static Evaluation eval_(const ValueVector &xValues,
                            const ValueVector &yValues,
                            const Evaluation& x)
    {
        if (xValues.front() < xValues.back())
            return evalAscending_(xValues, yValues, x);
        return evalDescending_(xValues, yValues, x);
    }

    template <class Evaluation>
    static Evaluation evalAscending_(const ValueVector &xValues,
                                     const ValueVector &yValues,
                                     const Evaluation& x)
    {
        typedef MathToolbox<Evaluation> Toolbox;

        if (x <= xValues.front())
            return yValues.front();
        if (x >= xValues.back())
            return yValues.back();

        size_t segIdx = findSegmentIndex_(xValues, Toolbox::value(x));

        Scalar x0 = xValues[segIdx];
        Scalar x1 = xValues[segIdx + 1];

        Scalar y0 = yValues[segIdx];
        Scalar y1 = yValues[segIdx + 1];

        Scalar m = (y1 - y0)/(x1 - x0);

        return y0 + (x - x0)*m;
    }

    template <class Evaluation>
    static Evaluation evalDescending_(const ValueVector &xValues,
                                      const ValueVector &yValues,
                                      const Evaluation& x)
    {
        typedef MathToolbox<Evaluation> Toolbox;

        if (x >= xValues.front())
            return yValues.front();
        if (x <= xValues.back())
            return yValues.back();

        size_t segIdx = findSegmentIndexDescending_(xValues, Toolbox::value(x));

        Scalar x0 = xValues[segIdx];
        Scalar x1 = xValues[segIdx + 1];

        Scalar y0 = yValues[segIdx];
        Scalar y1 = yValues[segIdx + 1];

        Scalar m = (y1 - y0)/(x1 - x0);

        return y0 + (x - x0)*m;
    }

    template <class Evaluation>
    static Evaluation evalDeriv_(const ValueVector &xValues,
                                 const ValueVector &yValues,
                                 const Evaluation& x)
    {
        typedef MathToolbox<Evaluation> Toolbox;

        if (Toolbox::value(x) <= xValues.front())
            return Toolbox::createConstant(0.0);
        if (Toolbox::value(x) >= xValues.back())
            return Toolbox::createConstant(0.0);

        size_t segIdx = findSegmentIndex_(xValues, Toolbox::value(x));

        Scalar x0 = xValues[segIdx];
        Scalar x1 = xValues[segIdx + 1];

        Scalar y0 = yValues[segIdx];
        Scalar y1 = yValues[segIdx + 1];

        return Toolbox::createConstant((y1 - y0)/(x1 - x0));
    }

    static size_t findSegmentIndex_(const ValueVector &xValues, Scalar x)
    {
        assert(xValues.size() > 1); // we need at least two sampling points!
        size_t n = xValues.size() - 1;
        if (xValues.back() <= x)
            return n - 1;
        else if (x <= xValues.front())
            return 0;

        // bisection
        size_t lowIdx = 0, highIdx = n;
        while (lowIdx + 1 < highIdx) {
            size_t curIdx = (lowIdx + highIdx)/2;
            if (xValues[curIdx] < x)
                lowIdx = curIdx;
            else
                highIdx = curIdx;
        }

        return lowIdx;
    }

    static size_t findSegmentIndexDescending_(const ValueVector &xValues, Scalar x)
    {
        assert(xValues.size() > 1); // we need at least two sampling points!
        size_t n = xValues.size() - 1;
        if (x <= xValues.back())
            return n;
        else if (xValues.front() <= x)
            return 0;

        // bisection
        size_t lowIdx = 0, highIdx = n;
        while (lowIdx + 1 < highIdx) {
            size_t curIdx = (lowIdx + highIdx)/2;
            if (xValues[curIdx] >= x)
                lowIdx = curIdx;
            else
                highIdx = curIdx;
        }

        return lowIdx;
    }
};
} // namespace Opm

#endif