Provides the Forchheimer flux module. More...

#include <forchheimerfluxmodule.hh>

Inheritance diagram for Opm::ForchheimerExtensiveQuantities< TypeTag >:

Public Member Functions
const Evaluation &	ergunCoefficient () const
	Return the Ergun coefficent at the face's integration point. More...

Evaluation &	mobilityPassabilityRatio (unsigned 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 (unsigned phaseIdx) const
	Return the pressure potential gradient of a fluid phase at the face's integration point [Pa/m]. More...

const EvalDimVector &	filterVelocity (unsigned phaseIdx) const
	Return the filter velocity of a fluid phase at the face's integration point [m/s]. More...

const Evaluation &	volumeFlux (unsigned phaseIdx) const
	Return the volume flux of a fluid phase at the face's integration point . More...

Protected Member Functions
void	calculateGradients_ (const ElementContext &elemCtx, unsigned faceIdx, unsigned timeIdx)

template<class FluidState >
void	calculateBoundaryGradients_ (const ElementContext &elemCtx, unsigned boundaryFaceIdx, unsigned timeIdx, const FluidState &fluidState)

void	calculateFluxes_ (const ElementContext &elemCtx, unsigned scvfIdx, unsigned timeIdx)
	Calculate the volumetric fluxes of all phases. More...

void	calculateBoundaryFluxes_ (const ElementContext &elemCtx, unsigned bfIdx, unsigned timeIdx)
	Calculate the volumetric flux rates of all phases at the domain boundary. More...

void	calculateForchheimerFlux_ (unsigned phaseIdx)

void	forchheimerResid_ (DimEvalVector &residual, unsigned phaseIdx) const

void	gradForchheimerResid_ (DimEvalVector &residual, DimEvalMatrix &gradResid, unsigned phaseIdx)

bool	isDiagonal_ (const DimMatrix &K) const
	Check whether all off-diagonal entries of a tensor are zero. More...

short	upstreamIndex_ (unsigned phaseIdx) const

short	downstreamIndex_ (unsigned phaseIdx) const

void	calculateFilterVelocity_ (unsigned phaseIdx)

Protected Attributes
DimVector	sqrtK_

Evaluation	ergunCoefficient_

Evaluation	mobilityPassabilityRatio_ [numPhases]

Evaluation	density_ [numPhases]

DimMatrix	K_

Evaluation	mobility_ [numPhases]

EvalDimVector	filterVelocity_ [numPhases]

Evaluation	volumeFlux_ [numPhases]

EvalDimVector	potentialGrad_ [numPhases]

short	upstreamDofIdx_ [numPhases]

short	downstreamDofIdx_ [numPhases]

short	interiorDofIdx_

short	exteriorDofIdx_

Detailed Description

template<class TypeTag>
class Opm::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 approach can be used. Like the Darcy approach, it is a relation of with the fluid velocity in terms of the gradient of pressure potential. However, this relation is not linear (as in the Darcy case) any more.

Therefore, the Newton scheme is used to solve the Forchheimer equation. This velocity is then used like the Darcy velocity e.g. by the local residual.

Note that 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

◆ calculateBoundaryFluxes_()

template<class TypeTag >

void Opm::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryFluxes_	(	const ElementContext &	elemCtx,
		unsigned	bfIdx,
		unsigned	timeIdx
	)

inlineprotected

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

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

◆ calculateBoundaryGradients_()

template<class TypeTag >

template<class FluidState >

void Opm::ForchheimerExtensiveQuantities< TypeTag >::calculateBoundaryGradients_	(	const ElementContext &	elemCtx,
		unsigned	boundaryFaceIdx,
		unsigned	timeIdx,
		const FluidState &	fluidState
	)

inlineprotected

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

◆ calculateFilterVelocity_()

template<class TypeTag >

void Opm::DarcyExtensiveQuantities< TypeTag >::calculateFilterVelocity_ ( unsigned phaseIdx )

inlineprotectedinherited

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

◆ calculateFluxes_()

template<class TypeTag >

void Opm::ForchheimerExtensiveQuantities< TypeTag >::calculateFluxes_	(	const ElementContext &	elemCtx,
		unsigned	scvfIdx,
		unsigned	timeIdx
	)

inlineprotected

Calculate the volumetric fluxes of all phases.

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

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

◆ calculateForchheimerFlux_()

template<class TypeTag >

void Opm::ForchheimerExtensiveQuantities< TypeTag >::calculateForchheimerFlux_ ( unsigned phaseIdx )

inlineprotected

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

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

◆ calculateGradients_()

template<class TypeTag >

void Opm::ForchheimerExtensiveQuantities< TypeTag >::calculateGradients_	(	const ElementContext &	elemCtx,
		unsigned	faceIdx,
		unsigned	timeIdx
	)

inlineprotected

◆ downstreamIndex_()

template<class TypeTag >

short Opm::DarcyExtensiveQuantities< TypeTag >::downstreamIndex_ ( unsigned phaseIdx ) const

inlineprotectedinherited

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

◆ ergunCoefficient()

template<class TypeTag >

const Evaluation & Opm::ForchheimerExtensiveQuantities< TypeTag >::ergunCoefficient ( ) const

inline

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

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

◆ filterVelocity()

template<class TypeTag >

const EvalDimVector & Opm::DarcyExtensiveQuantities< TypeTag >::filterVelocity ( unsigned phaseIdx ) const

inlineinherited

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

Parameters

phaseIdx The index of the fluid phase

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

◆ forchheimerResid_()

template<class TypeTag >

void Opm::ForchheimerExtensiveQuantities< TypeTag >::forchheimerResid_	(	DimEvalVector &	residual,
		unsigned	phaseIdx
	)		const

inlineprotected

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

◆ gradForchheimerResid_()

template<class TypeTag >

void Opm::ForchheimerExtensiveQuantities< TypeTag >::gradForchheimerResid_	(	DimEvalVector &	residual,
		DimEvalMatrix &	gradResid,
		unsigned	phaseIdx
	)

inlineprotected

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

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

◆ intrinsicPermability()

template<class TypeTag >

const DimMatrix & Opm::DarcyExtensiveQuantities< TypeTag >::intrinsicPermability ( ) const

inlineinherited

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

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

◆ isDiagonal_()

template<class TypeTag >

bool Opm::ForchheimerExtensiveQuantities< TypeTag >::isDiagonal_ ( const DimMatrix & K ) const

inlineprotected

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

Parameters

K	the tensor that is to be checked.

Returns: True iff all off-diagonals are zero.

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

◆ mobilityPassabilityRatio()

template<class TypeTag >

Evaluation & Opm::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio ( unsigned 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 Opm::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio_.

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

◆ potentialGrad()

template<class TypeTag >

const EvalDimVector & Opm::DarcyExtensiveQuantities< TypeTag >::potentialGrad ( unsigned phaseIdx ) const

inlineinherited

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

Parameters

phaseIdx The index of the fluid phase

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

◆ upstreamIndex_()

template<class TypeTag >

short Opm::DarcyExtensiveQuantities< TypeTag >::upstreamIndex_ ( unsigned phaseIdx ) const

inlineprotectedinherited

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

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

◆ volumeFlux()

template<class TypeTag >

const Evaluation & Opm::DarcyExtensiveQuantities< TypeTag >::volumeFlux ( unsigned 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

phaseIdx The index of the fluid phase

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

Member Data Documentation

◆ density_

template<class TypeTag >

Evaluation Opm::ForchheimerExtensiveQuantities< TypeTag >::density_[numPhases]

protected

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

◆ downstreamDofIdx_

template<class TypeTag >

short Opm::DarcyExtensiveQuantities< TypeTag >::downstreamDofIdx_[numPhases]

protectedinherited

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

◆ ergunCoefficient_

template<class TypeTag >

Evaluation Opm::ForchheimerExtensiveQuantities< TypeTag >::ergunCoefficient_

protected

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

◆ exteriorDofIdx_

template<class TypeTag >

short Opm::DarcyExtensiveQuantities< TypeTag >::exteriorDofIdx_

protectedinherited

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

◆ filterVelocity_

template<class TypeTag >

EvalDimVector Opm::DarcyExtensiveQuantities< TypeTag >::filterVelocity_[numPhases]

protectedinherited

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

◆ interiorDofIdx_

template<class TypeTag >

short Opm::DarcyExtensiveQuantities< TypeTag >::interiorDofIdx_

protectedinherited

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

◆ K_

template<class TypeTag >

DimMatrix Opm::DarcyExtensiveQuantities< TypeTag >::K_

protectedinherited

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

◆ mobility_

template<class TypeTag >

Evaluation Opm::DarcyExtensiveQuantities< TypeTag >::mobility_[numPhases]

protectedinherited

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

◆ mobilityPassabilityRatio_

template<class TypeTag >

Evaluation Opm::ForchheimerExtensiveQuantities< TypeTag >::mobilityPassabilityRatio_[numPhases]

protected

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

◆ potentialGrad_

template<class TypeTag >

EvalDimVector Opm::DarcyExtensiveQuantities< TypeTag >::potentialGrad_[numPhases]

protectedinherited

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

◆ sqrtK_

template<class TypeTag >

DimVector Opm::ForchheimerExtensiveQuantities< TypeTag >::sqrtK_

protected

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

◆ upstreamDofIdx_

template<class TypeTag >

short Opm::DarcyExtensiveQuantities< TypeTag >::upstreamDofIdx_[numPhases]

protectedinherited

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

◆ volumeFlux_

template<class TypeTag >

Evaluation Opm::DarcyExtensiveQuantities< TypeTag >::volumeFlux_[numPhases]

protectedinherited

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

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

forchheimerfluxmodule.hh

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

◆ calculateBoundaryFluxes_()

◆ calculateBoundaryGradients_()

◆ calculateFilterVelocity_()

◆ calculateFluxes_()

◆ calculateForchheimerFlux_()

◆ calculateGradients_()

◆ downstreamIndex_()

◆ ergunCoefficient()

◆ filterVelocity()

◆ forchheimerResid_()

◆ gradForchheimerResid_()

◆ intrinsicPermability()

◆ isDiagonal_()

◆ mobilityPassabilityRatio()

◆ potentialGrad()

◆ upstreamIndex_()

◆ volumeFlux()

Member Data Documentation

◆ density_

◆ downstreamDofIdx_

◆ ergunCoefficient_

◆ exteriorDofIdx_

◆ filterVelocity_

◆ interiorDofIdx_

◆ K_

◆ mobility_

◆ mobilityPassabilityRatio_

◆ potentialGrad_

◆ sqrtK_

◆ upstreamDofIdx_

◆ volumeFlux_