Detailed Description

The van Genuchten capillary pressure model.

The van Genuchten capillary pressure model ([40]) is:

\[p_c(S)=p_b (S_\text{eff}^{-1/m}-1)^{1-m}\]

with effective saturation defined as

\[S_\text{eff}=\frac{S-S_r}{S_{\text{max}}-S_r}.\]

Above, $S_r$ and $S_{\text{max}}$ are the residual and the maximum saturations. The (pressure) exponent $m \in (0,1)$ and the pressure scaling parameter $p_b$ (it is equal to $\rho g/\alpha$ in original publication) are given by the user. The scaling parameter $p_b$ is given in same units as pressure.

Another (saturaton) exponent $n$ is usually set to $n = 1 / (1 - m)$.

The saturation is computed from the capillary pressure as follows:

\[S(p_c)= \begin{cases} S_{\text{max}} & \text{for $p_c \leq 0$, and}\\ \left( \left(\frac{p_c}{p_b}\right)^{\frac{1}{1-m}} +1\right)^{-m} (S_{\text{max}}-S_r) +S_r& \text{for $p_c > 0$.} \end{cases} \]

The result is then clamped between the residual and maximum liquid saturations.

Definition at line 45 of file SaturationVanGenuchten.h.

#include <SaturationVanGenuchten.h>

Inheritance diagram for MaterialPropertyLib::SaturationVanGenuchten:

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Collaboration diagram for MaterialPropertyLib::SaturationVanGenuchten:

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Public Member Functions
	SaturationVanGenuchten (std::string name, double const residual_liquid_saturation, double const residual_gas_saturation, double const pressure_exponent, double const saturation_exponent, double const p_b)

void	checkScale () const override

PropertyDataType	value (VariableArray const &variable_array, ParameterLib::SpatialPosition const &, double const, double const) const override

PropertyDataType	dValue (VariableArray const &variable_array, Variable const variable, ParameterLib::SpatialPosition const &, double const, double const) const override

PropertyDataType	d2Value (VariableArray const &variable_array, Variable const variable1, Variable const variable2, ParameterLib::SpatialPosition const &, double const, double const) const override
	Default implementation: 2nd derivative of any constant property is zero.

Public Member Functions inherited from MaterialPropertyLib::Property
virtual	~Property ()

virtual PropertyDataType	initialValue (ParameterLib::SpatialPosition const &pos, double const t) const

virtual PropertyDataType	value () const

virtual PropertyDataType	value (VariableArray const &variable_array, VariableArray const &variable_array_prev, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

virtual PropertyDataType	dValue (VariableArray const &variable_array, VariableArray const &variable_array_prev, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

virtual void	setProperties (std::vector< std::unique_ptr< Phase > > const &phases)
	Default implementation:

void	setScale (std::variant< Medium , Phase , Component * > scale)

template<typename T >
T	initialValue (ParameterLib::SpatialPosition const &pos, double const t) const

template<typename T >
T	value () const

template<typename T >
T	value (VariableArray const &variable_array, VariableArray const &variable_array_prev, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	value (VariableArray const &variable_array, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	dValue (VariableArray const &variable_array, VariableArray const &variable_array_prev, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	dValue (VariableArray const &variable_array, Variable const variable, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

template<typename T >
T	d2Value (VariableArray const &variable_array, Variable const &variable1, Variable const &variable2, ParameterLib::SpatialPosition const &pos, double const t, double const dt) const

Private Attributes
double const	S_L_res_

double const	S_L_max_

double const	m_

double const	n_

double const	p_b_

Additional Inherited Members
Protected Attributes inherited from MaterialPropertyLib::Property
std::string	name_

PropertyDataType	value_
	The single value of a property.

PropertyDataType	dvalue_

std::variant< Medium , Phase , Component * >	scale_

Constructor & Destructor Documentation

◆ SaturationVanGenuchten()

MaterialPropertyLib::SaturationVanGenuchten::SaturationVanGenuchten	(	std::string	name,
		double const	residual_liquid_saturation,
		double const	residual_gas_saturation,
		double const	pressure_exponent,
		double const	saturation_exponent,
		double const	p_b )

Definition at line 20 of file SaturationVanGenuchten.cpp.

    : S_L_res_(residual_liquid_saturation),
      S_L_max_(1. - residual_gas_saturation),
      m_(pressure_exponent),
      n_(saturation_exponent),
      p_b_(p_b)
{
    name_ = std::move(name);
 
    if (!(m_ > 0 && m_ < 1))
    {
        OGS_FATAL(
            "The pressure exponent value m = {:g} of van Genuchten saturation "
            "model, is out of its range of (0, 1)",
            m_);
    }
 
    if (n_ < 1)
    {
        OGS_FATAL(
            "The saturation exponent value n = {:g} of van Genuchten "
            "saturation model, is out of its range of [1, +inf)",
            n_);
    }
}

References m_, n_, MaterialPropertyLib::name, MaterialPropertyLib::Property::name_, and OGS_FATAL.

Member Function Documentation

◆ checkScale()

void MaterialPropertyLib::SaturationVanGenuchten::checkScale ( ) const

inlineoverridevirtual

Reimplemented from MaterialPropertyLib::Property.

Definition at line 55 of file SaturationVanGenuchten.h.

    {
        if (!std::holds_alternative<Medium*>(scale_))
        {
            OGS_FATAL(
                "The property 'SaturationVanGenuchten' is implemented on the "
                "'media' scale only.");
        }
    }

References OGS_FATAL, and MaterialPropertyLib::Property::scale_.

◆ d2Value()

PropertyDataType MaterialPropertyLib::SaturationVanGenuchten::d2Value	(	VariableArray const &	variable_array,
		Variable const	variable1,
		Variable const	variable2,
		ParameterLib::SpatialPosition const &	pos,
		double const	t,
		double const	dt ) const

overridevirtual

Default implementation: 2nd derivative of any constant property is zero.

This virtual method will compute the second derivative of a property with respect to the given variables pv1 and pv2.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 107 of file SaturationVanGenuchten.cpp.

{
    (void)variable1;
    (void)variable2;
    assert((variable1 == Variable::capillary_pressure) &&
           (variable2 == Variable::capillary_pressure) &&
           "SaturationVanGenuchten::d2Value is implemented for  derivatives "
           "with respect to capillary pressure only.");
 
    const double p_cap = variable_array.capillary_pressure;
 
    if (p_cap <= 0)
    {
        return 0.;
    }
 
    double const p = p_cap / p_b_;
    double const p_to_n = std::pow(p, n_);
 
    double const S_eff = std::pow(p_to_n + 1., -m_);
    double const S = S_eff * S_L_max_ - S_eff * S_L_res_ + S_L_res_;
 
    if (S < S_L_res_ || S > S_L_max_)
    {
        return 0.;
    }
 
    double const d2S_eff_dp_cap2 =
        m_ * n_ * n_ * p_to_n * S_eff * (p_to_n - m_) /
        ((p_cap * p_to_n + p_cap) * (p_cap * p_to_n + p_cap));
    return d2S_eff_dp_cap2 * (S_L_max_ - S_L_res_);
}

References MaterialPropertyLib::capillary_pressure, MaterialPropertyLib::VariableArray::capillary_pressure, m_, n_, p_b_, S_L_max_, and S_L_res_.

◆ dValue()

PropertyDataType MaterialPropertyLib::SaturationVanGenuchten::dValue	(	VariableArray const &	variable_array,
		Variable const	variable,
		ParameterLib::SpatialPosition const &	pos,
		double const	t,
		double const	dt ) const

overridevirtual

This virtual method will compute the property derivative value based on the variables that are passed as arguments with the default implementation using empty variables array for the previous time step.

The default implementation of this method only returns the property value derivative without altering it.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 72 of file SaturationVanGenuchten.cpp.

{
    if (variable != Variable::capillary_pressure)
    {
        OGS_FATAL(
            "SaturationVanGenuchten::dValue is implemented for derivatives "
            "with respect to capillary pressure only.");
    }
 
    const double p_cap = variable_array.capillary_pressure;
 
    if (p_cap <= 0)
    {
        return 0.;
    }
 
    double const p = p_cap / p_b_;
    double const p_to_n = std::pow(p, n_);
 
    double const S_eff = std::pow(p_to_n + 1., -m_);
    double const S = S_eff * S_L_max_ - S_eff * S_L_res_ + S_L_res_;
 
    if (S < S_L_res_ || S > S_L_max_)
    {
        return 0.;
    }
 
    double const dS_eff_dp_cap =
        -m_ * n_ * p_to_n * S_eff / (p_cap * (p_to_n + 1.));
    return dS_eff_dp_cap * (S_L_max_ - S_L_res_);
}

References MaterialPropertyLib::capillary_pressure, MaterialPropertyLib::VariableArray::capillary_pressure, m_, n_, OGS_FATAL, p_b_, S_L_max_, and S_L_res_.

◆ value()

PropertyDataType MaterialPropertyLib::SaturationVanGenuchten::value	(	VariableArray const &	variable_array,
		ParameterLib::SpatialPosition const &	,
		double const	,
		double const	) const

overridevirtual

Those methods override the base class implementations and actually compute and set the property values_ and dValues_.

Reimplemented from MaterialPropertyLib::Property.

Definition at line 52 of file SaturationVanGenuchten.cpp.

{
    const double p_cap = variable_array.capillary_pressure;
 
    if (p_cap <= 0)
    {
        return S_L_max_;
    }
 
    double const p = p_cap / p_b_;
    double const p_to_n = std::pow(p, n_);
 
    double const S_eff = std::pow(p_to_n + 1., -m_);
    double const S = S_eff * S_L_max_ - S_eff * S_L_res_ + S_L_res_;
    return std::clamp(S, S_L_res_, S_L_max_);
}

References MaterialPropertyLib::VariableArray::capillary_pressure, m_, n_, p_b_, S_L_max_, and S_L_res_.

Member Data Documentation

◆ m_

double const MaterialPropertyLib::SaturationVanGenuchten::m_

private

Definition at line 85 of file SaturationVanGenuchten.h.

Referenced by SaturationVanGenuchten(), d2Value(), dValue(), and value().

◆ n_

double const MaterialPropertyLib::SaturationVanGenuchten::n_

private

Definition at line 86 of file SaturationVanGenuchten.h.

Referenced by SaturationVanGenuchten(), d2Value(), dValue(), and value().

◆ p_b_

double const MaterialPropertyLib::SaturationVanGenuchten::p_b_

private

Definition at line 87 of file SaturationVanGenuchten.h.

Referenced by d2Value(), dValue(), and value().

◆ S_L_max_

double const MaterialPropertyLib::SaturationVanGenuchten::S_L_max_

private

Definition at line 84 of file SaturationVanGenuchten.h.

Referenced by d2Value(), dValue(), and value().

◆ S_L_res_

double const MaterialPropertyLib::SaturationVanGenuchten::S_L_res_

private

Definition at line 83 of file SaturationVanGenuchten.h.

Referenced by d2Value(), dValue(), and value().

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

MaterialLib/MPL/Properties/CapillaryPressureSaturation/SaturationVanGenuchten.h
MaterialLib/MPL/Properties/CapillaryPressureSaturation/SaturationVanGenuchten.cpp

Detailed Description

Public Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ SaturationVanGenuchten()

Member Function Documentation

◆ checkScale()

◆ d2Value()

◆ dValue()

◆ value()

Member Data Documentation

◆ m_

◆ n_

◆ p_b_

◆ S_L_max_

◆ S_L_res_