Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
Ewoms::ForchheimerExtensiveQuantities< TypeTag > Class Template Reference
Flow Models » Modules » Flux

Provides the Forchheimer flux module. More...

#include <forchheimerfluxmodule.hh>

Inheritance diagram for Ewoms::ForchheimerExtensiveQuantities< TypeTag >:
Inheritance graph

Public Member Functions

Scalar ergunCoefficient () const
 Return the Ergun coefficent at the face's integration point. More...
 
Scalar mobilityPassabilityRatio (int phaseIdx) const
 Return the ratio of the mobility divided by the passability at the face's integration point for a given fluid phase. More...
 
const DimMatrix & intrinsicPermability () const
 Returns the intrinsic permeability tensor for a given sub-control volume face. More...
 
const EvalDimVector & potentialGrad (int phaseIdx) const
 Return the pressure potential gradient of a fluid phase at the face's integration point [Pa/m]. More...
 
const EvalDimVector & filterVelocity (int phaseIdx) const
 Return the filter velocity of a fluid phase at the face's integration point [m/s]. More...
 
const Evaluation & volumeFlux (int phaseIdx) const
 Return the volume flux of a fluid phase at the face's integration point $[m^3/s / m^2]$. More...
 

Protected Member Functions

void calculateGradients_ (const ElementContext &elemCtx, int faceIdx, int timeIdx)
 
template<class FluidState >
void calculateBoundaryGradients_ (const ElementContext &elemCtx, int boundaryFaceIdx, int timeIdx, const FluidState &fluidState, const typename FluidSystem::ParameterCache &paramCache)
 
void calculateFluxes_ (const ElementContext &elemCtx, int scvfIdx, int timeIdx)
 Calculate the volumetric fluxes of all phases. More...
 
void calculateBoundaryFluxes_ (const ElementContext &elemCtx, int bfIdx, int timeIdx)
 Calculate the volumetric flux rates of all phases at the domain boundary. More...
 
void calculateForchheimerFlux_ (int phaseIdx)
 
void forchheimerResid_ (DimVector &residual, int phaseIdx) const
 
void gradForchheimerResid_ (DimVector &residual, DimMatrix &gradResid, int phaseIdx)
 
bool isDiagonal_ (const DimMatrix &K) const
 Check whether all off-diagonal entries of a tensor are zero. More...
 
short upstreamIndex_ (int phaseIdx) const
 
short downstreamIndex_ (int phaseIdx) const
 
void calculateFilterVelocity_ (int phaseIdx)
 

Protected Attributes

DimMatrix sqrtK_
 
Scalar ergunCoefficient_
 
Scalar mobilityPassabilityRatio_ [numPhases]
 
Scalar density_ [numPhases]
 
DimMatrix K_
 
short interiorDofIdx_
 
short exteriorDofIdx_
 
short upstreamDofIdx_ [numPhases]
 
short downstreamDofIdx_ [numPhases]
 
Evaluation mobility_ [numPhases]
 
EvalDimVector filterVelocity_ [numPhases]
 
Evaluation volumeFlux_ [numPhases]
 
EvalDimVector potentialGrad_ [numPhases]
 

Detailed Description

template<class TypeTag>
class Ewoms::ForchheimerExtensiveQuantities< TypeTag >

Provides the Forchheimer flux module.

The commonly used Darcy relation looses its validity for Reynolds numbers $ Re > 1$. If one encounters flow velocities in porous media above this threshold, the Forchheimer relation can be used. Like the Darcy relation, it relates the gradient in potential to velocity. However, this relation is not linear (as in the Darcy case) any more.

Therefore, the Newton scheme is used to solve the non-linear relation. This velocity is then used like the Darcy velocity e.g. by the local residual.

For Reynolds numbers above $\approx 500$ the standard Forchheimer relation also looses it's validity.

The Forchheimer equation is given by the following relation:

\[ \nabla p_\alpha - \rho_\alpha \vec{g} = - \frac{\mu_\alpha}{k_{r,\alpha}} K^{-1}\vec{v}_\alpha - \frac{\rho_\alpha C_E}{\eta_{r,\alpha}} \sqrt{K}^{-1} \left| \vec{v}_\alpha \right| \vec{v}_\alpha \]

Where $C_E$ is the modified Ergun parameter and $\eta_{r,\alpha}$ is the passability which is given by a closure relation (usually it is assumed to be identical to the relative permeability). To avoid numerical problems, the relation implemented by this class multiplies both sides with $\frac{k_{r_alpha}}{mu} K$, so we get

\[ \frac{k_{r_alpha}}{mu} K \left( \nabla p_\alpha - \rho_\alpha \vec{g}\right) = - \vec{v}_\alpha - \frac{\rho_\alpha C_E}{\eta_{r,\alpha}} \frac{k_{r_alpha}}{mu} \sqrt{K} \left| \vec{v}_\alpha \right| \vec{v}_\alpha \]

Member Function Documentation

template<class TypeTag >
void Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryFluxes_ ( const ElementContext &  elemCtx,
int  bfIdx,
int  timeIdx 
)
inlineprotected

Calculate the volumetric flux rates of all phases at the domain boundary.

References Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateForchheimerFlux_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::filterVelocity_, and Ewoms::DarcyExtensiveQuantities< TypeTag >::volumeFlux_.

template<class TypeTag >
template<class FluidState >
void Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryGradients_ ( const ElementContext &  elemCtx,
int  boundaryFaceIdx,
int  timeIdx,
const FluidState &  fluidState,
const typename FluidSystem::ParameterCache &  paramCache 
)
inlineprotected

References Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::density_, Ewoms::ForchheimerExtensiveQuantities< TypeTag >::ergunCoefficient_, Ewoms::DarcyExtensiveQuantities< TypeTag >::interiorDofIdx_, Ewoms::ForchheimerExtensiveQuantities< TypeTag >::isDiagonal_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::K_, Ewoms::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio_, and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::sqrtK_.

template<class TypeTag >
void Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateFilterVelocity_ ( int  phaseIdx)
inlineprotectedinherited

References Ewoms::DarcyExtensiveQuantities< TypeTag >::filterVelocity_, Ewoms::DarcyExtensiveQuantities< TypeTag >::K_, Ewoms::DarcyExtensiveQuantities< TypeTag >::mobility_, and Ewoms::DarcyExtensiveQuantities< TypeTag >::potentialGrad_.

template<class TypeTag >
void Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateFluxes_ ( const ElementContext &  elemCtx,
int  scvfIdx,
int  timeIdx 
)
inlineprotected

Calculate the volumetric fluxes of all phases.

The pressure potentials and upwind directions must already be determined before calling this method!

References Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateForchheimerFlux_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::ergunCoefficient_, Ewoms::DarcyExtensiveQuantities< TypeTag >::filterVelocity_, and Ewoms::DarcyExtensiveQuantities< TypeTag >::volumeFlux_.

template<class TypeTag >
void Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateForchheimerFlux_ ( int  phaseIdx)
inlineprotected

References Ewoms::DarcyExtensiveQuantities< TypeTag >::filterVelocity_, and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::gradForchheimerResid_().

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryFluxes_(), and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateFluxes_().

template<class TypeTag >
void Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_ ( const ElementContext &  elemCtx,
int  faceIdx,
int  timeIdx 
)
inlineprotected

References Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::density_, Ewoms::ForchheimerExtensiveQuantities< TypeTag >::ergunCoefficient_, Ewoms::DarcyExtensiveQuantities< TypeTag >::exteriorDofIdx_, Ewoms::DarcyExtensiveQuantities< TypeTag >::interiorDofIdx_, Ewoms::ForchheimerExtensiveQuantities< TypeTag >::isDiagonal_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::K_, Ewoms::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio_, Ewoms::ForchheimerExtensiveQuantities< TypeTag >::sqrtK_, and Ewoms::DarcyExtensiveQuantities< TypeTag >::upstreamIndex_().

template<class TypeTag >
short Ewoms::DarcyExtensiveQuantities< TypeTag >::downstreamIndex_ ( int  phaseIdx) const
inlineprotectedinherited

References Ewoms::DarcyExtensiveQuantities< TypeTag >::downstreamDofIdx_.

template<class TypeTag >
Scalar Ewoms::ForchheimerExtensiveQuantities< TypeTag >::ergunCoefficient ( ) const
inline

Return the Ergun coefficent at the face's integration point.

References Ewoms::ForchheimerExtensiveQuantities< TypeTag >::ergunCoefficient_.

template<class TypeTag >
const EvalDimVector& Ewoms::DarcyExtensiveQuantities< TypeTag >::filterVelocity ( int  phaseIdx) const
inlineinherited

Return the filter velocity of a fluid phase at the face's integration point [m/s].

Parameters
phaseIdxThe index of the fluid phase

References Ewoms::DarcyExtensiveQuantities< TypeTag >::filterVelocity_.

template<class TypeTag >
void Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_ ( DimVector &  residual,
int  phaseIdx 
) const
inlineprotected

References Ewoms::ForchheimerExtensiveQuantities< TypeTag >::density_, Ewoms::ForchheimerExtensiveQuantities< TypeTag >::ergunCoefficient_, Ewoms::DarcyExtensiveQuantities< TypeTag >::filterVelocity_, Ewoms::DarcyExtensiveQuantities< TypeTag >::K_, Ewoms::DarcyExtensiveQuantities< TypeTag >::mobility_, Ewoms::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio_, Ewoms::DarcyExtensiveQuantities< TypeTag >::potentialGrad_, and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::sqrtK_.

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::gradForchheimerResid_().

template<class TypeTag >
void Ewoms::ForchheimerExtensiveQuantities< TypeTag >::gradForchheimerResid_ ( DimVector &  residual,
DimMatrix &  gradResid,
int  phaseIdx 
)
inlineprotected

References Ewoms::DarcyExtensiveQuantities< TypeTag >::filterVelocity_, and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_().

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateForchheimerFlux_().

template<class TypeTag >
const DimMatrix& Ewoms::DarcyExtensiveQuantities< TypeTag >::intrinsicPermability ( ) const
inlineinherited

Returns the intrinsic permeability tensor for a given sub-control volume face.

References Ewoms::DarcyExtensiveQuantities< TypeTag >::K_.

template<class TypeTag >
bool Ewoms::ForchheimerExtensiveQuantities< TypeTag >::isDiagonal_ ( const DimMatrix &  K) const
inlineprotected

Check whether all off-diagonal entries of a tensor are zero.

Parameters
Kthe tensor that is to be checked.
Returns
True iff all off-diagonals are zero.

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_().

template<class TypeTag >
Scalar Ewoms::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio ( int  phaseIdx) const
inline

Return the ratio of the mobility divided by the passability at the face's integration point for a given fluid phase.

Usually, that's the inverse of the viscosity.

References Ewoms::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio_.

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_().

template<class TypeTag >
const EvalDimVector& Ewoms::DarcyExtensiveQuantities< TypeTag >::potentialGrad ( int  phaseIdx) const
inlineinherited

Return the pressure potential gradient of a fluid phase at the face's integration point [Pa/m].

Parameters
phaseIdxThe index of the fluid phase

References Ewoms::DarcyExtensiveQuantities< TypeTag >::potentialGrad_.

template<class TypeTag >
short Ewoms::DarcyExtensiveQuantities< TypeTag >::upstreamIndex_ ( int  phaseIdx) const
inlineprotectedinherited

References Ewoms::DarcyExtensiveQuantities< TypeTag >::upstreamDofIdx_.

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_().

template<class TypeTag >
const Evaluation& Ewoms::DarcyExtensiveQuantities< TypeTag >::volumeFlux ( int  phaseIdx) const
inlineinherited

Return the volume flux of a fluid phase at the face's integration point $[m^3/s / m^2]$.

This is the fluid volume of a phase per second and per square meter of face area.

Parameters
phaseIdxThe index of the fluid phase

References Ewoms::DarcyExtensiveQuantities< TypeTag >::volumeFlux_.

Member Data Documentation

template<class TypeTag >
Scalar Ewoms::ForchheimerExtensiveQuantities< TypeTag >::density_[numPhases]
protected

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_(), and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_().

template<class TypeTag >
short Ewoms::DarcyExtensiveQuantities< TypeTag >::downstreamDofIdx_[numPhases]
protectedinherited

Referenced by Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateGradients_(), and Ewoms::DarcyExtensiveQuantities< TypeTag >::downstreamIndex_().

template<class TypeTag >
Scalar Ewoms::ForchheimerExtensiveQuantities< TypeTag >::ergunCoefficient_
protected

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateFluxes_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::ergunCoefficient(), and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_().

template<class TypeTag >
short Ewoms::DarcyExtensiveQuantities< TypeTag >::exteriorDofIdx_
protectedinherited

Referenced by Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateGradients_(), and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_().

template<class TypeTag >
EvalDimVector Ewoms::DarcyExtensiveQuantities< TypeTag >::filterVelocity_[numPhases]
protectedinherited

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryFluxes_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateBoundaryFluxes_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateFilterVelocity_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateFluxes_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateFluxes_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateForchheimerFlux_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::filterVelocity(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_(), and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::gradForchheimerResid_().

template<class TypeTag >
short Ewoms::DarcyExtensiveQuantities< TypeTag >::interiorDofIdx_
protectedinherited

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateGradients_(), and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_().

template<class TypeTag >
DimMatrix Ewoms::DarcyExtensiveQuantities< TypeTag >::K_
protectedinherited

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateFilterVelocity_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_(), and Ewoms::DarcyExtensiveQuantities< TypeTag >::intrinsicPermability().

template<class TypeTag >
Evaluation Ewoms::DarcyExtensiveQuantities< TypeTag >::mobility_[numPhases]
protectedinherited

Referenced by Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateFilterVelocity_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateGradients_(), and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_().

template<class TypeTag >
Scalar Ewoms::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio_[numPhases]
protected

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_(), and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio().

template<class TypeTag >
EvalDimVector Ewoms::DarcyExtensiveQuantities< TypeTag >::potentialGrad_[numPhases]
protectedinherited

Referenced by Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateFilterVelocity_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_(), and Ewoms::DarcyExtensiveQuantities< TypeTag >::potentialGrad().

template<class TypeTag >
DimMatrix Ewoms::ForchheimerExtensiveQuantities< TypeTag >::sqrtK_
protected

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_(), and Ewoms::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_().

template<class TypeTag >
short Ewoms::DarcyExtensiveQuantities< TypeTag >::upstreamDofIdx_[numPhases]
protectedinherited

Referenced by Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateBoundaryGradients_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateGradients_(), and Ewoms::DarcyExtensiveQuantities< TypeTag >::upstreamIndex_().

template<class TypeTag >
Evaluation Ewoms::DarcyExtensiveQuantities< TypeTag >::volumeFlux_[numPhases]
protectedinherited

Referenced by Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryFluxes_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateBoundaryFluxes_(), Ewoms::ForchheimerExtensiveQuantities< TypeTag >::calculateFluxes_(), Ewoms::DarcyExtensiveQuantities< TypeTag >::calculateFluxes_(), and Ewoms::DarcyExtensiveQuantities< TypeTag >::volumeFlux().

The documentation for this class was generated from the following file: