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DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
Public Types | Static Public Member Functions | List of all members
Dumux::LinearMaterial< ScalarT, ParamsT > Class Template Reference
Material and Fluid Framework » Fluid-Matrix Interactions

Linear capillary pressure and relative permeability <-> saturation relations. More...

#include <dumux/material/fluidmatrixinteractions/2p/linearmaterial.hh>

Description

template<class ScalarT, class ParamsT = LinearMaterialParams<ScalarT>>
class Dumux::LinearMaterial< ScalarT, ParamsT >

Linear capillary pressure and relative permeability <-> saturation relations.

The entry pressure is reached at \(\mathrm{ \overline{S}_w = 1}\), the maximum capillary pressure is observed at \(\mathrm{ \overline{S}_w = 0}\).

For general info: EffToAbsLaw

See also
LinearMaterialParams

Public Types

using Params = ParamsT
 
using Scalar = typename Params::Scalar
 

Static Public Member Functions

static Scalar pc (const Params &params, Scalar swe)
 The linear capillary pressure-saturation curve. More...
 
static Scalar sw (const Params &params, Scalar pc)
 The saturation-capillary pressure curve. More...
 
static Scalar endPointPc (const Params &params)
 The capillary pressure at Swe = 1.0 also called end point capillary pressure. More...
 
static Scalar dpc_dswe (const Params &params, Scalar swe)
 Returns the partial derivative of the capillary pressure w.r.t. the effective saturation. More...
 
static Scalar dsw_dpc (const Params &params, Scalar pc)
 Returns the partial derivative of the effective saturation to the capillary pressure. More...
 
static Scalar krw (const Params &params, Scalar swe)
 The relative permeability for the wetting phase. More...
 
static Scalar krn (const Params &params, Scalar swe)
 The relative permeability for the non-wetting phase. More...
 

Member Typedef Documentation

◆ Params

template<class ScalarT , class ParamsT = LinearMaterialParams<ScalarT>>
using Dumux::LinearMaterial< ScalarT, ParamsT >::Params = ParamsT

◆ Scalar

template<class ScalarT , class ParamsT = LinearMaterialParams<ScalarT>>
using Dumux::LinearMaterial< ScalarT, ParamsT >::Scalar = typename Params::Scalar

Member Function Documentation

◆ dpc_dswe()

template<class ScalarT , class ParamsT = LinearMaterialParams<ScalarT>>
static Scalar Dumux::LinearMaterial< ScalarT, ParamsT >::dpc_dswe ( const Params &  params,
Scalar  swe 
)
inlinestatic

Returns the partial derivative of the capillary pressure w.r.t. the effective saturation.

This is equivalent to \(\mathrm{ \frac{\partial p_C}{\partial \overline{S}_w} = - (p_{C,max} - p_{C,min}) }\)

Parameters
sweEffective saturation of the wetting phase \(\mathrm{[\overline{S}_w]}\) conversion from absolute saturation happened in EffToAbsLaw.
paramsA container object that is populated with the appropriate coefficients for the respective law. Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container is constructed accordingly. Afterwards the values are set there, too.
Returns
Partial derivative of \(\mathrm{[p_c]}\) w.r.t. effective saturation according to linear material relation.

◆ dsw_dpc()

template<class ScalarT , class ParamsT = LinearMaterialParams<ScalarT>>
static Scalar Dumux::LinearMaterial< ScalarT, ParamsT >::dsw_dpc ( const Params &  params,
Scalar  pc 
)
inlinestatic

Returns the partial derivative of the effective saturation to the capillary pressure.

Parameters
pcCapillary pressure \(\mathrm{[p_C]}\) in \(\mathrm{[Pa]}\).
paramsA container object that is populated with the appropriate coefficients for the respective law. Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container is constructed accordingly. Afterwards the values are set there, too.
Returns
Partial derivative of effective saturation w.r.t. \(\mathrm{[p_c]}\) according to linear relation.

◆ endPointPc()

template<class ScalarT , class ParamsT = LinearMaterialParams<ScalarT>>
static Scalar Dumux::LinearMaterial< ScalarT, ParamsT >::endPointPc ( const Params &  params)
inlinestatic

The capillary pressure at Swe = 1.0 also called end point capillary pressure.

Parameters
paramsA container object that is populated with the appropriate coefficients for the respective law. Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container is constructed accordingly. Afterwards the values are set there, too.

◆ krn()

template<class ScalarT , class ParamsT = LinearMaterialParams<ScalarT>>
static Scalar Dumux::LinearMaterial< ScalarT, ParamsT >::krn ( const Params &  params,
Scalar  swe 
)
inlinestatic

The relative permeability for the non-wetting phase.

Parameters
paramsA container object that is populated with the appropriate coefficients for the respective law. Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container is constructed accordingly. Afterwards the values are set there, too.
sweEffective saturation of the wetting phase \(\mathrm{[\overline{S}_w]}\) conversion from absolute saturation happened in EffToAbsLaw.
Returns
Relative permeability of the non-wetting phase calculated as linear relation.

◆ krw()

template<class ScalarT , class ParamsT = LinearMaterialParams<ScalarT>>
static Scalar Dumux::LinearMaterial< ScalarT, ParamsT >::krw ( const Params &  params,
Scalar  swe 
)
inlinestatic

The relative permeability for the wetting phase.

Parameters
paramsA container object that is populated with the appropriate coefficients for the respective law. Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container is constructed accordingly. Afterwards the values are set there, too.
sweEffective saturation of the wetting phase \(\mathrm{[\overline{S}_w]}\) conversion from absolute saturation happened in EffToAbsLaw.
Returns
Relative permeability of the wetting phase calculated as linear relation.

◆ pc()

template<class ScalarT , class ParamsT = LinearMaterialParams<ScalarT>>
static Scalar Dumux::LinearMaterial< ScalarT, ParamsT >::pc ( const Params &  params,
Scalar  swe 
)
inlinestatic

The linear capillary pressure-saturation curve.

This material law is linear: \(\mathrm{ p_C = (1 - \overline{S}_w ) (p_{C,max} - p_{C,entry}) + p_{C,entry} }\)

Parameters
sweEffective saturation of the wetting phase \(\overline{S}_w\) conversion from absolute saturation happened in EffToAbsLaw.
paramsA container object that is populated with the appropriate coefficients for the respective law. Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container is constructed accordingly. Afterwards the values are set there, too.
Returns
Capillary pressure calculated by linear constitutive relation.

◆ sw()

template<class ScalarT , class ParamsT = LinearMaterialParams<ScalarT>>
static Scalar Dumux::LinearMaterial< ScalarT, ParamsT >::sw ( const Params &  params,
Scalar  pc 
)
inlinestatic

The saturation-capillary pressure curve.

This is the inverse of the capillary pressure-saturation curve: \(\mathrm{ S_w = 1 - \frac{p_C - p_{C,entry}}{p_{C,max} - p_{C,entry}} }\)

Parameters
pcCapillary pressure \(\mathrm{[p_C]}\) in \(\mathrm{[Pa]}\).
paramsA container object that is populated with the appropriate coefficients for the respective law. Therefore, in the (problem specific) spatialParameters first, the material law is chosen, and then the params container is constructed accordingly. Afterwards the values are set there, too.
Returns
Effective wetting phase saturation calculated as inverse of the linear constitutive relation.
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