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Ewoms::ForchheimerExtensiveQuantities< TypeTag > Class Template Reference

Provides the Forchheimer flux module. More...

#include <forchheimerfluxmodule.hh>

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

Public Member Functions

const Evaluation & ergunCoefficient () const
 Return the Ergun coefficent at the face's integration point.
 
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...
 
- Public Member Functions inherited from Ewoms::DarcyExtensiveQuantities< TypeTag >
const DimMatrix & intrinsicPermability () const
 Returns the intrinsic permeability tensor for a given sub-control volume face.
 
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 $[m^3/s / m^2]$. 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, const typename FluidSystem::template ParameterCache< typename FluidState::Scalar > &paramCache)
 
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.
 
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...
 
- Protected Member Functions inherited from Ewoms::DarcyExtensiveQuantities< TypeTag >
short upstreamIndex_ (unsigned phaseIdx) const
 
short downstreamIndex_ (unsigned phaseIdx) const
 
void calculateGradients_ (const ElementContext &elemCtx, unsigned faceIdx, unsigned timeIdx)
 Calculate the gradients which are required to determine the volumetric fluxes. More...
 
template<class FluidState >
void calculateBoundaryGradients_ (const ElementContext &elemCtx, unsigned boundaryFaceIdx, unsigned timeIdx, const FluidState &fluidState, const typename FluidSystem::template ParameterCache< typename FluidState::Scalar > &paramCache)
 Calculate the gradients at the grid boundary which are required to determine the volumetric fluxes. More...
 
void calculateFluxes_ (const ElementContext &elemCtx, unsigned scvfIdx, unsigned timeIdx)
 Calculate the volumetric fluxes of all phases. More...
 
void calculateBoundaryFluxes_ (const ElementContext &elemCtx, unsigned boundaryFaceIdx, unsigned timeIdx)
 Calculate the volumetric fluxes at a boundary face of all fluid phases. More...
 
void calculateFilterVelocity_ (unsigned phaseIdx)
 

Protected Attributes

DimVector sqrtK_
 
Evaluation ergunCoefficient_
 
Evaluation mobilityPassabilityRatio_ [numPhases]
 
Evaluation density_ [numPhases]
 
- Protected Attributes inherited from Ewoms::DarcyExtensiveQuantities< TypeTag >
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 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 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

template<class TypeTag >
void Ewoms::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!

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.
template<class TypeTag >
Evaluation& Ewoms::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.


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