brookscorey.hh

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#ifndef DUMUX_MATERIAL_FLUIDMATRIX_BROOKS_COREY_HH
#define DUMUX_MATERIAL_FLUIDMATRIX_BROOKS_COREY_HH
 
#include <cmath>
#include <algorithm>
 
#include <dumux/common/parameters.hh>
#include <dumux/common/optionalscalar.hh>
#include <dumux/material/fluidmatrixinteractions/2p/materiallaw.hh>
 
namespace Dumux::FluidMatrix {
 
class BrooksCorey
{
public:
    template<class Scalar>
    struct Params
    {
        Params(Scalar pcEntry, Scalar lambda)
        : pcEntry_(pcEntry), lambda_(lambda)
        {}
 
        Scalar pcEntry() const{ return pcEntry_; }
        void setPcEntry(Scalar pcEntry){ pcEntry_ = pcEntry; }
 
        Scalar lambda() const { return lambda_; }
        void setLambda(Scalar lambda) { lambda_ = lambda; }
 
        bool operator== (const Params& p) const
        {
            return Dune::FloatCmp::eq(pcEntry(), p.pcEntry(), 1e-6)
                   && Dune::FloatCmp::eq(lambda(), p.lambda(), 1e-6);
        }
 
    private:
        Scalar pcEntry_, lambda_;
    };
 
    template<class Scalar = double>
    static Params<Scalar> makeParams(const std::string& paramGroup)
    {
        const auto pcEntry = getParamFromGroup<Scalar>(paramGroup, "BrooksCoreyPcEntry");
        const auto lambda = getParamFromGroup<Scalar>(paramGroup, "BrooksCoreyLambda");
        return {pcEntry, lambda};
    }
 
    template<class Scalar>
    static Scalar pc(Scalar swe, const Params<Scalar>& params)
    {
        using std::pow;
        using std::clamp;
 
        swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        return params.pcEntry()*pow(swe, -1.0/params.lambda());
    }
 
    template<class Scalar>
    static Scalar swe(Scalar pc, const Params<Scalar>& params)
    {
        using std::pow;
        using std::max;
 
        pc = max(pc, 0.0); // the equation below is undefined for negative pcs
 
        return pow(pc/params.pcEntry(), -params.lambda());
    }
 
    template<class Scalar>
    static Scalar endPointPc(const Params<Scalar>& params)
    { return params.pcEntry(); }
 
    template<class Scalar>
    static Scalar dpc_dswe(Scalar swe, const Params<Scalar>& params)
    {
        using std::pow;
        using std::clamp;
 
        swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        return -params.pcEntry()/params.lambda() * pow(swe, -1.0/params.lambda() - 1.0);
    }
 
    template<class Scalar>
    static Scalar dswe_dpc(Scalar pc, const Params<Scalar>& params)
    {
        using std::pow;
        using std::max;
 
        pc = max(pc, 0.0); // the equation below is undefined for negative pcs
 
        return -params.lambda()/params.pcEntry() * pow(pc/params.pcEntry(), - params.lambda() - 1.0);
    }
 
    template<class Scalar>
    static Scalar krw(Scalar swe, const Params<Scalar>& params)
    {
        using std::pow;
        using std::clamp;
 
        swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        return pow(swe, 2.0/params.lambda() + 3.0);
    }
 
    template<class Scalar>
    static Scalar dkrw_dswe(Scalar swe, const Params<Scalar>& params)
    {
        using std::pow;
        using std::clamp;
 
        swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        return (2.0/params.lambda() + 3.0)*pow(swe, 2.0/params.lambda() + 2.0);
    }
 
    template<class Scalar>
    static Scalar krn(Scalar swe, const Params<Scalar>& params)
    {
        using std::pow;
        using std::clamp;
 
        swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        const Scalar exponent = 2.0/params.lambda() + 1.0;
        const Scalar sne = 1.0 - swe;
        return sne*sne*(1.0 - pow(swe, exponent));
    }
 
    template<class Scalar>
    static Scalar dkrn_dswe(Scalar swe, const Params<Scalar>& params)
    {
        using std::pow;
        using std::clamp;
 
        swe = clamp(swe, 0.0, 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        const auto lambdaInv = 1.0/params.lambda();
        const auto swePow = pow(swe, 2*lambdaInv);
        return 2.0*(swe - 1.0)*(1.0 + (0.5 + lambdaInv)*swePow - (1.5 + lambdaInv)*swePow*swe);
    }
};
 
template <class Scalar>
class BrooksCoreyRegularization
{
public:
    template<class S>
    struct Params
    {
        Params(S pcLowSwe = 0.01) : pcLowSwe_(pcLowSwe) {}
 
        S pcLowSwe() const { return pcLowSwe_; }
        void setPcLowSwe(S pcLowSwe) { pcLowSwe_ = pcLowSwe; }
 
    private:
        S pcLowSwe_ = 0.01;
    };
 
    template<class MaterialLaw>
    void init(const MaterialLaw* m, const std::string& paramGroup)
    {
        pcLowSwe_ = getParamFromGroup<Scalar>(paramGroup, "BrooksCoreyPcLowSweThreshold", 0.01);
        entryPressure_ = getParamFromGroup<Scalar>(paramGroup, "BrooksCoreyPcEntry");
 
        initPcParameters_(m, pcLowSwe_);
    }
 
    template<class MaterialLaw, class BaseParams, class EffToAbsParams>
    void init(const MaterialLaw* m, const BaseParams& bp, const EffToAbsParams& etap, const Params<Scalar>& p)
    {
        pcLowSwe_ = p.pcLowSwe();
        entryPressure_ = bp.pcEntry();
 
        initPcParameters_(m, pcLowSwe_);
    }
 
    bool operator== (const BrooksCoreyRegularization& o) const
    {
        return Dune::FloatCmp::eq(pcLowSwe_, o.pcLowSwe_, 1e-6)
               && Dune::FloatCmp::eq(entryPressure_, o.entryPressure_, 1e-6);
    }
 
    OptionalScalar<Scalar> pc(const Scalar swe) const
    {
        // make sure that the capillary pressure observes a derivative
        // != 0 for 'illegal' saturations. This is favourable for the
        // newton solver (if the derivative is calculated numerically)
        // in order to get the saturation moving to the right
        // direction if it temporarily is in an 'illegal' range.
        if (swe <= pcLowSwe_)
            return pcLowSwePcValue_ + pcDerivativeLowSw_*(swe - pcLowSwe_);
 
        else if (swe >= 1.0)
            return pcDerivativeHighSwEnd_*(swe - 1.0) + entryPressure_;
 
        else
            return {}; // no regularization
    }
 
    OptionalScalar<Scalar> dpc_dswe(const Scalar swe) const
    {
        if (swe <= pcLowSwe_)
            return pcDerivativeLowSw_;
 
        else if (swe >= 1.0)
            return pcDerivativeHighSwEnd_;
 
        else
            return {}; // no regularization
    }
 
    OptionalScalar<Scalar> swe(const Scalar pc) const
    {
        if (pc <= entryPressure_)
            return 1.0 + (pc - entryPressure_)/pcDerivativeHighSwEnd_;
 
        else if (pc >= pcLowSwePcValue_)
            return (pc - pcLowSwePcValue_)/pcDerivativeLowSw_ + pcLowSwe_;
 
        else
            return {}; // no regularization
    }
 
    OptionalScalar<Scalar> dswe_dpc(const Scalar pc) const
    {
        if (pc <= entryPressure_)
            return 1.0/pcDerivativeHighSwEnd_;
 
        else if (pc >= pcLowSwePcValue_)
            return 1.0/pcDerivativeLowSw_;
 
        else
            return {}; // no regularization
    }
 
    OptionalScalar<Scalar> krw(const Scalar swe) const
    {
        if (swe <= 0.0)
            return 0.0;
        else if (swe >= 1.0)
            return 1.0;
        else
            return {}; // no regularization
    }
 
    OptionalScalar<Scalar> dkrw_dswe(const Scalar swe) const
    {
        if (swe <= 0.0)
            return 0.0;
        else if (swe >= 1.0)
            return 0.0;
        else
            return {}; // no regularization
    }
 
    OptionalScalar<Scalar> krn(const Scalar swe) const
    {
        if (swe <= 0.0)
            return 1.0;
        else if (swe >= 1.0)
            return 0.0;
        else
            return {}; // no regularization
    }
 
    OptionalScalar<Scalar> dkrn_dswe(const Scalar swe) const
    {
        if (swe <= 0.0)
            return 0.0;
        else if (swe >= 1.0)
            return 0.0;
        else
            return {}; // no regularization
    }
 
private:
    template<class MaterialLaw>
    void initPcParameters_(const MaterialLaw* m, const Scalar lowSwe)
    {
        const auto lowSw = MaterialLaw::EffToAbs::sweToSw(lowSwe, m->effToAbsParams());
        const auto highSw = MaterialLaw::EffToAbs::sweToSw(1.0, m->effToAbsParams());
        const auto dsw_dswe = MaterialLaw::EffToAbs::dsw_dswe(m->effToAbsParams());
        pcDerivativeLowSw_ = m->template dpc_dsw<false>(lowSw)*dsw_dswe;
        pcDerivativeHighSwEnd_ = m->template dpc_dsw<false>(highSw)*dsw_dswe;
        pcLowSwePcValue_ = m->template pc<false>(lowSw);
    }
 
    Scalar pcLowSwe_;
    Scalar pcLowSwePcValue_;
    Scalar entryPressure_;
    Scalar pcDerivativeLowSw_;
    Scalar pcDerivativeHighSwEnd_;
};
 
template<typename Scalar = double>
using BrooksCoreyDefault = TwoPMaterialLaw<Scalar, BrooksCorey, BrooksCoreyRegularization<Scalar>, TwoPEffToAbsDefaultPolicy>;
 
template<typename Scalar = double>
using BrooksCoreyNoReg = TwoPMaterialLaw<Scalar, BrooksCorey, NoRegularization, TwoPEffToAbsDefaultPolicy>;
 
} // end namespace Dumux::FluidMatrix
 
#endif