SaturationVanGenuchten.cpp

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// SPDX-FileCopyrightText: Copyright (c) OpenGeoSys Community (opengeosys.org)
// SPDX-License-Identifier: BSD-3-Clause
 
#include "SaturationVanGenuchten.h"
 
#include <algorithm>
#include <cmath>
 
#include "MaterialLib/MPL/Medium.h"
 
namespace 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)
    : 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_);
    }
}
 
PropertyDataType SaturationVanGenuchten::value(
    VariableArray const& variable_array,
    ParameterLib::SpatialPosition const& /*pos*/, double const /*t*/,
    double const /*dt*/) const
{
    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_);
}
 
PropertyDataType SaturationVanGenuchten::dValue(
    VariableArray const& variable_array, Variable const variable,
    ParameterLib::SpatialPosition const& /*pos*/, double const /*t*/,
    double const /*dt*/) const
{
    if (variable == Variable::temperature)
    {
        return 0.;
    }
    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_);
}
 
PropertyDataType SaturationVanGenuchten::d2Value(
    VariableArray const& variable_array, Variable const variable1,
    Variable const variable2, ParameterLib::SpatialPosition const& /*pos*/,
    double const /*t*/, double const /*dt*/) const
{
    (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_);
}
}  // namespace MaterialPropertyLib