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PorousFlowCapillaryPressureVG Class Reference

van Genuchten form of capillary pressure. More...

#include <PorousFlowCapillaryPressureVG.h>

Inheritance diagram for PorousFlowCapillaryPressureVG:
[legend]

Public Member Functions

 PorousFlowCapillaryPressureVG (const InputParameters &parameters)
 
virtual Real capillaryPressureCurve (Real saturation) const override
 Raw capillary pressure curve (does not include logarithmic extension) More...
 
virtual Real dCapillaryPressureCurve (Real saturation) const override
 Derivative of raw capillary pressure wrt true saturation. More...
 
virtual Real d2CapillaryPressureCurve (Real saturation) const override
 Second derivative of raw capillary pressure wrt true saturation. More...
 
virtual Real effectiveSaturation (Real pc) const override
 Effective saturation as a function of capillary pressure. More...
 
virtual Real dEffectiveSaturation (Real pc) const override
 Derivative of effective saturation wrt capillary pressure. More...
 
virtual Real d2EffectiveSaturation (Real pc) const override
 Second derivative of effective saturation wrt capillary pressure. More...
 
virtual void initialize () final
 
virtual void execute () final
 
virtual void finalize () final
 
virtual void initialSetup () override
 
virtual Real capillaryPressure (Real saturation) const
 Capillary pressure is calculated as a function of true saturation. More...
 
virtual Real dCapillaryPressure (Real saturation) const
 Derivative of capillary pressure wrt true saturation. More...
 
virtual Real d2CapillaryPressure (Real saturation) const
 Second derivative of capillary pressure wrt true saturation. More...
 

Protected Member Functions

Real effectiveSaturationFromSaturation (Real saturation) const
 Effective saturation of liquid phase given liquid saturation and residual liquid saturation. More...
 
Real extensionSaturation () const
 Calculates the saturation where the logarithmic extension to capillary pressure meets the raw curve using Newton's method. More...
 
Real interceptFunction (Real s) const
 Calculates the saturation where the logarithmic extension to capillary pressure at low saturation. More...
 
Real interceptFunctionDeriv (Real s) const
 Calculates the saturation where the logarithmic extension to capillary pressure at low saturation. More...
 
Real capillaryPressureLogExt (Real s) const
 The capillary pressure in the logarithmic extension. More...
 
Real dCapillaryPressureLogExt (Real s) const
 The derivative of capillary pressure in the logarithmic extension. More...
 
Real d2CapillaryPressureLogExt (Real s) const
 The second derivative of capillary pressure in the logarithmic extension. More...
 

Protected Attributes

const Real _m
 van Genuchten exponent m More...
 
const Real _alpha
 van Genuchten capillary coefficient alpha More...
 
const Real _s_scale
 capillary pressure = f(Seff * s_scale) - pc_sscale, where f is the van Genuchten function. For almost all simulations s_scale=1 will be appropriate More...
 
const Real _pc_sscale
 pc_sscale = f(s_scale), where f is the van Genuchten function More...
 
const Real _sat_lr
 Liquid residual saturation. More...
 
const Real _dseff_ds
 Derivative of effective saturation with respect to saturation. More...
 
bool _log_ext
 Flag to use a logarithmic extension for low saturation. More...
 
const Real _pc_max
 Maximum capillary pressure (Pa). Note: must be <= 0. More...
 
Real _sat_ext
 Saturation where the logarithmic extension meets the raw curve. More...
 
Real _pc_ext
 Capillary pressure where the extension meets the raw curve. More...
 
Real _slope_ext
 Gradient of the logarithmic extension. More...
 
const Real _log10
 log(10) More...
 

Detailed Description

van Genuchten form of capillary pressure.

From van Genuchten, M. Th., A closed for equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc., 44, 892-898 (1980)

Definition at line 24 of file PorousFlowCapillaryPressureVG.h.

Constructor & Destructor Documentation

PorousFlowCapillaryPressureVG::PorousFlowCapillaryPressureVG ( const InputParameters &  parameters)

Definition at line 35 of file PorousFlowCapillaryPressureVG.C.

36  : PorousFlowCapillaryPressure(parameters),
37  _m(getParam<Real>("m")),
38  _alpha(getParam<Real>("alpha")),
39  _s_scale(getParam<Real>("s_scale")),
41 {
42 }
const Real _m
van Genuchten exponent m
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.
const Real _alpha
van Genuchten capillary coefficient alpha
PorousFlowCapillaryPressure(const InputParameters &parameters)
const Real _s_scale
capillary pressure = f(Seff * s_scale) - pc_sscale, where f is the van Genuchten function. For almost all simulations s_scale=1 will be appropriate
const Real _pc_sscale
pc_sscale = f(s_scale), where f is the van Genuchten function
Real capillaryPressure(Real seff, Real alpha, Real m, Real pc_max)
Capillary pressure as a function of effective saturation.

Member Function Documentation

Real PorousFlowCapillaryPressure::capillaryPressure ( Real  saturation) const
virtualinherited

Capillary pressure is calculated as a function of true saturation.

Note that this method includes the ability to use a logarithmic extension at low saturation.

Parameters
saturationtrue saturation
Returns
capillary pressure (Pa)

Definition at line 59 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlow2PhasePS::capillaryPressure(), PorousFlowCapillaryPressure::finalize(), PorousFlowCapillaryPressure::initialSetup(), PorousFlowFluidStateWaterNCG::thermophysicalProperties(), and PorousFlowFluidStateBrineCO2::thermophysicalProperties().

60 {
61  if (_log_ext && saturation < _sat_ext)
63  else
65 }
Real capillaryPressureLogExt(Real s) const
The capillary pressure in the logarithmic extension.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
bool _log_ext
Flag to use a logarithmic extension for low saturation.
virtual Real capillaryPressureCurve(Real saturation) const =0
Raw capillary pressure curve (does not include logarithmic extension)
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real PorousFlowCapillaryPressureVG::capillaryPressureCurve ( Real  saturation) const
overridevirtual

Raw capillary pressure curve (does not include logarithmic extension)

Parameters
saturationtrue saturation
Returns
capillary pressure (Pa)

Implements PorousFlowCapillaryPressure.

Definition at line 45 of file PorousFlowCapillaryPressureVG.C.

46 {
49 }
const Real _m
van Genuchten exponent m
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.
Real effectiveSaturationFromSaturation(Real saturation) const
Effective saturation of liquid phase given liquid saturation and residual liquid saturation.
const Real _alpha
van Genuchten capillary coefficient alpha
const Real _s_scale
capillary pressure = f(Seff * s_scale) - pc_sscale, where f is the van Genuchten function. For almost all simulations s_scale=1 will be appropriate
const Real _pc_sscale
pc_sscale = f(s_scale), where f is the van Genuchten function
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real capillaryPressure(Real seff, Real alpha, Real m, Real pc_max)
Capillary pressure as a function of effective saturation.
Real PorousFlowCapillaryPressure::capillaryPressureLogExt ( Real  s) const
protectedinherited

The capillary pressure in the logarithmic extension.

Parameters
sliquid saturation
Returns
capillary pressure in logarithmic extension

Definition at line 92 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::capillaryPressure(), and PorousFlowCapillaryPressure::finalize().

93 {
94  return _pc_ext * std::pow(10.0, _slope_ext * (saturation - _sat_ext));
95 }
Real _slope_ext
Gradient of the logarithmic extension.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real _pc_ext
Capillary pressure where the extension meets the raw curve.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real PorousFlowCapillaryPressure::d2CapillaryPressure ( Real  saturation) const
virtualinherited

Second derivative of capillary pressure wrt true saturation.

Parameters
saturationtrue saturation
Returns
second derivative of capillary pressure with respect to true saturation

Definition at line 77 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowFluidStateFlashBase::computeQpProperties(), PorousFlow2PhasePS::d2CapillaryPressure_dS2(), and PorousFlowCapillaryPressure::finalize().

78 {
79  if (_log_ext && saturation < _sat_ext)
81  else
83 }
Real d2CapillaryPressureLogExt(Real s) const
The second derivative of capillary pressure in the logarithmic extension.
virtual Real d2CapillaryPressureCurve(Real saturation) const =0
Second derivative of raw capillary pressure wrt true saturation.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
bool _log_ext
Flag to use a logarithmic extension for low saturation.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real PorousFlowCapillaryPressureVG::d2CapillaryPressureCurve ( Real  saturation) const
overridevirtual

Second derivative of raw capillary pressure wrt true saturation.

Parameters
saturationtrue saturation
Returns
second derivative of capillary pressure with respect to true saturation

Implements PorousFlowCapillaryPressure.

Definition at line 60 of file PorousFlowCapillaryPressureVG.C.

61 {
65 }
const Real _m
van Genuchten exponent m
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.
Real d2CapillaryPressure(Real seff, Real alpha, Real m, Real pc_max)
Second derivative of capillary pressure wrt effective saturation.
Real effectiveSaturationFromSaturation(Real saturation) const
Effective saturation of liquid phase given liquid saturation and residual liquid saturation.
const Real _alpha
van Genuchten capillary coefficient alpha
const Real _s_scale
capillary pressure = f(Seff * s_scale) - pc_sscale, where f is the van Genuchten function. For almost all simulations s_scale=1 will be appropriate
const Real _dseff_ds
Derivative of effective saturation with respect to saturation.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real PorousFlowCapillaryPressure::d2CapillaryPressureLogExt ( Real  s) const
protectedinherited

The second derivative of capillary pressure in the logarithmic extension.

Parameters
sliquid saturation
Returns
second derivative of capillary pressure in logarithmic extension

Definition at line 104 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::d2CapillaryPressure(), and PorousFlowCapillaryPressure::finalize().

105 {
106  return _pc_ext * _slope_ext * _slope_ext * _log10 * _log10 *
107  std::pow(10.0, _slope_ext * (saturation - _sat_ext));
108 }
Real _slope_ext
Gradient of the logarithmic extension.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real _pc_ext
Capillary pressure where the extension meets the raw curve.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real PorousFlowCapillaryPressureVG::d2EffectiveSaturation ( Real  pc) const
overridevirtual

Second derivative of effective saturation wrt capillary pressure.

Parameters
pccapillary pressure
Returns
second derivative of effective saturation wrt capillary pressure

Implements PorousFlowCapillaryPressure.

Definition at line 82 of file PorousFlowCapillaryPressureVG.C.

83 {
84  return (1.0 / _s_scale) *
86 }
const Real _m
van Genuchten exponent m
const Real _alpha
van Genuchten capillary coefficient alpha
const Real _s_scale
capillary pressure = f(Seff * s_scale) - pc_sscale, where f is the van Genuchten function. For almost all simulations s_scale=1 will be appropriate
Real d2EffectiveSaturation(Real p, Real alpha, Real m)
Second derivative of effective saturation wrt porepressure.
const Real _pc_sscale
pc_sscale = f(s_scale), where f is the van Genuchten function
Real PorousFlowCapillaryPressure::dCapillaryPressure ( Real  saturation) const
virtualinherited

Derivative of capillary pressure wrt true saturation.

Parameters
saturationtrue saturation
Returns
derivative of capillary pressure with respect to true saturation

Definition at line 68 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowFluidStateFlashBase::computeQpProperties(), PorousFlow2PhasePS::dCapillaryPressure_dS(), and PorousFlowCapillaryPressure::finalize().

69 {
70  if (_log_ext && saturation < _sat_ext)
72  else
74 }
virtual Real dCapillaryPressureCurve(Real saturation) const =0
Derivative of raw capillary pressure wrt true saturation.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
bool _log_ext
Flag to use a logarithmic extension for low saturation.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real dCapillaryPressureLogExt(Real s) const
The derivative of capillary pressure in the logarithmic extension.
Real PorousFlowCapillaryPressureVG::dCapillaryPressureCurve ( Real  saturation) const
overridevirtual

Derivative of raw capillary pressure wrt true saturation.

Parameters
saturationtrue saturation
Returns
derivative of capillary pressure with respect to true saturation

Implements PorousFlowCapillaryPressure.

Definition at line 52 of file PorousFlowCapillaryPressureVG.C.

53 {
56  _s_scale;
57 }
const Real _m
van Genuchten exponent m
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.
Real effectiveSaturationFromSaturation(Real saturation) const
Effective saturation of liquid phase given liquid saturation and residual liquid saturation.
const Real _alpha
van Genuchten capillary coefficient alpha
const Real _s_scale
capillary pressure = f(Seff * s_scale) - pc_sscale, where f is the van Genuchten function. For almost all simulations s_scale=1 will be appropriate
Real dCapillaryPressure(Real seff, Real alpha, Real m, Real pc_max)
Derivative of capillary pressure wrt effective saturation.
const Real _dseff_ds
Derivative of effective saturation with respect to saturation.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real PorousFlowCapillaryPressure::dCapillaryPressureLogExt ( Real  s) const
protectedinherited

The derivative of capillary pressure in the logarithmic extension.

Parameters
sliquid saturation
Returns
derivative of capillary pressure in logarithmic extension

Definition at line 98 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::dCapillaryPressure(), and PorousFlowCapillaryPressure::finalize().

99 {
100  return _pc_ext * _slope_ext * _log10 * std::pow(10.0, _slope_ext * (saturation - _sat_ext));
101 }
Real _slope_ext
Gradient of the logarithmic extension.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real _pc_ext
Capillary pressure where the extension meets the raw curve.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real PorousFlowCapillaryPressureVG::dEffectiveSaturation ( Real  pc) const
overridevirtual

Derivative of effective saturation wrt capillary pressure.

Parameters
pccapillary pressure (Pa)
Returns
derivative of effective saturation wrt capillary pressure

Implements PorousFlowCapillaryPressure.

Definition at line 75 of file PorousFlowCapillaryPressureVG.C.

76 {
77  return (1.0 / _s_scale) *
79 }
const Real _m
van Genuchten exponent m
const Real _alpha
van Genuchten capillary coefficient alpha
const Real _s_scale
capillary pressure = f(Seff * s_scale) - pc_sscale, where f is the van Genuchten function. For almost all simulations s_scale=1 will be appropriate
const Real _pc_sscale
pc_sscale = f(s_scale), where f is the van Genuchten function
Real dEffectiveSaturation(Real p, Real alpha, Real m)
Derivative of effective saturation wrt porepressure.
Real PorousFlowCapillaryPressureVG::effectiveSaturation ( Real  pc) const
overridevirtual

Effective saturation as a function of capillary pressure.

Parameters
pccapillary pressure (Pa)
Returns
effective saturation

Implements PorousFlowCapillaryPressure.

Definition at line 68 of file PorousFlowCapillaryPressureVG.C.

69 {
70  return (1.0 / _s_scale) *
72 }
const Real _m
van Genuchten exponent m
const Real _alpha
van Genuchten capillary coefficient alpha
Real effectiveSaturation(Real p, Real alpha, Real m)
Effective saturation as a function of porepressure.
const Real _s_scale
capillary pressure = f(Seff * s_scale) - pc_sscale, where f is the van Genuchten function. For almost all simulations s_scale=1 will be appropriate
const Real _pc_sscale
pc_sscale = f(s_scale), where f is the van Genuchten function
Real PorousFlowCapillaryPressure::effectiveSaturationFromSaturation ( Real  saturation) const
protectedinherited

Effective saturation of liquid phase given liquid saturation and residual liquid saturation.

Note: not to be mistaken with effectiveSaturation(pc) which is a function of capillary pressure.

Parameters
saturationtrue saturation
Returns
effective saturation

Definition at line 86 of file PorousFlowCapillaryPressure.C.

Referenced by capillaryPressureCurve(), PorousFlowCapillaryPressureBC::capillaryPressureCurve(), d2CapillaryPressureCurve(), PorousFlowCapillaryPressureBC::d2CapillaryPressureCurve(), dCapillaryPressureCurve(), PorousFlowCapillaryPressureBC::dCapillaryPressureCurve(), and PorousFlowCapillaryPressure::finalize().

87 {
88  return (saturation - _sat_lr) / (1.0 - _sat_lr);
89 }
const Real _sat_lr
Liquid residual saturation.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
virtual void PorousFlowCapillaryPressure::execute ( )
inlinefinalvirtualinherited

Definition at line 39 of file PorousFlowCapillaryPressure.h.

39 {};
Real PorousFlowCapillaryPressure::extensionSaturation ( ) const
protectedinherited

Calculates the saturation where the logarithmic extension to capillary pressure meets the raw curve using Newton's method.

Returns
saturation where logarithmic extension begins

Definition at line 111 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::finalize(), and PorousFlowCapillaryPressure::initialSetup().

112 {
113  // Initial guess for saturation where extension matches curve
114  Real sat = _sat_lr + 0.01;
115 
116  // Calculate the saturation where the extension matches the derivative of the
117  // raw capillary pressure curve
118  const unsigned int max_its = 20;
119  const Real nr_tol = 1.0e-8;
120  unsigned int iter = 0;
121 
122  while (std::abs(interceptFunction(sat)) > nr_tol)
123  {
124  sat = sat - interceptFunction(sat) / interceptFunctionDeriv(sat);
125 
126  iter++;
127  if (iter > max_its)
128  break;
129  }
130 
131  return sat;
132 }
Real interceptFunction(Real s) const
Calculates the saturation where the logarithmic extension to capillary pressure at low saturation...
const Real _sat_lr
Liquid residual saturation.
Real interceptFunctionDeriv(Real s) const
Calculates the saturation where the logarithmic extension to capillary pressure at low saturation...
virtual void PorousFlowCapillaryPressure::finalize ( )
inlinefinalvirtualinherited

Definition at line 40 of file PorousFlowCapillaryPressure.h.

40 {};
virtual void PorousFlowCapillaryPressure::initialize ( )
inlinefinalvirtualinherited

Definition at line 38 of file PorousFlowCapillaryPressure.h.

38 {};
void PorousFlowCapillaryPressure::initialSetup ( )
overridevirtualinherited

Definition at line 46 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::finalize().

47 {
48  // If _log_ext = true, calculate the saturation where the the logarithmic
49  // extension meets the raw capillary pressure curve.
50  if (_log_ext)
51  {
54  _slope_ext = (std::log10(_pc_ext) - std::log10(_pc_max)) / _sat_ext;
55  }
56 }
Real _slope_ext
Gradient of the logarithmic extension.
Real extensionSaturation() const
Calculates the saturation where the logarithmic extension to capillary pressure meets the raw curve u...
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.
virtual Real capillaryPressure(Real saturation) const
Capillary pressure is calculated as a function of true saturation.
Real _pc_ext
Capillary pressure where the extension meets the raw curve.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
bool _log_ext
Flag to use a logarithmic extension for low saturation.
Real PorousFlowCapillaryPressure::interceptFunction ( Real  s) const
protectedinherited

Calculates the saturation where the logarithmic extension to capillary pressure at low saturation.

Parameters
seffective saturation
Returns
capillary pressure function in the logarithmic extension

Definition at line 135 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::extensionSaturation(), and PorousFlowCapillaryPressure::finalize().

136 {
139 
140  return std::log10(pc) - saturation * dpc / (_log10 * pc) - std::log10(_pc_max);
141 }
virtual Real dCapillaryPressureCurve(Real saturation) const =0
Derivative of raw capillary pressure wrt true saturation.
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.
virtual Real capillaryPressureCurve(Real saturation) const =0
Raw capillary pressure curve (does not include logarithmic extension)
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real PorousFlowCapillaryPressure::interceptFunctionDeriv ( Real  s) const
protectedinherited

Calculates the saturation where the logarithmic extension to capillary pressure at low saturation.

Parameters
seffective saturation
Returns
derivative of logarithmic extension function

Definition at line 144 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::extensionSaturation(), and PorousFlowCapillaryPressure::finalize().

145 {
149 
150  return saturation * (dpc * dpc / pc - d2pc) / (_log10 * pc);
151 }
virtual Real dCapillaryPressureCurve(Real saturation) const =0
Derivative of raw capillary pressure wrt true saturation.
virtual Real d2CapillaryPressureCurve(Real saturation) const =0
Second derivative of raw capillary pressure wrt true saturation.
virtual Real capillaryPressureCurve(Real saturation) const =0
Raw capillary pressure curve (does not include logarithmic extension)
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)

Member Data Documentation

const Real PorousFlowCapillaryPressureVG::_alpha
protected
const Real PorousFlowCapillaryPressure::_dseff_ds
protectedinherited
const Real PorousFlowCapillaryPressure::_log10
protectedinherited
bool PorousFlowCapillaryPressure::_log_ext
protectedinherited
const Real PorousFlowCapillaryPressureVG::_m
protected
Real PorousFlowCapillaryPressure::_pc_ext
protectedinherited
const Real PorousFlowCapillaryPressure::_pc_max
protectedinherited
const Real PorousFlowCapillaryPressureVG::_pc_sscale
protected

pc_sscale = f(s_scale), where f is the van Genuchten function

Definition at line 45 of file PorousFlowCapillaryPressureVG.h.

Referenced by capillaryPressureCurve(), d2EffectiveSaturation(), dEffectiveSaturation(), and effectiveSaturation().

const Real PorousFlowCapillaryPressureVG::_s_scale
protected

capillary pressure = f(Seff * s_scale) - pc_sscale, where f is the van Genuchten function. For almost all simulations s_scale=1 will be appropriate

Definition at line 43 of file PorousFlowCapillaryPressureVG.h.

Referenced by capillaryPressureCurve(), d2CapillaryPressureCurve(), d2EffectiveSaturation(), dCapillaryPressureCurve(), dEffectiveSaturation(), and effectiveSaturation().

Real PorousFlowCapillaryPressure::_sat_ext
protectedinherited
const Real PorousFlowCapillaryPressure::_sat_lr
protectedinherited
Real PorousFlowCapillaryPressure::_slope_ext
protectedinherited

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