vangenuchten.hh

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#ifndef VAN_GENUCHTEN_HH
#define VAN_GENUCHTEN_HH
 
#include "vangenuchtenparams.hh"
 
#include <algorithm>
#include <cmath>
#include <cassert>
 
namespace Dumux {
 
template <class ScalarT, class ParamsT = VanGenuchtenParams<ScalarT> >
class VanGenuchten
{
public:
    using Params = ParamsT;
    using Scalar = typename Params::Scalar;
 
    static Scalar pc(const Params &params, Scalar swe)
    {
        using std::pow;
        using std::min;
        using std::max;
 
        swe = min(max(swe, 0.0), 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        const Scalar pc = pow(pow(swe, -1.0/params.vgm()) - 1, 1.0/params.vgn())/params.vgAlpha();
        return pc;
    }
 
    static Scalar sw(const Params &params, Scalar pc)
    {
        using std::pow;
        using std::max;
 
        pc = max(pc, 0.0); // the equation below is undefined for negative pcs
 
        const Scalar sw = pow(pow(params.vgAlpha()*pc, params.vgn()) + 1, -params.vgm());
        return sw;
    }
 
    static Scalar endPointPc(const Params &params)
    { return 0.0; }
 
    static Scalar dpc_dswe(const Params &params, Scalar swe)
    {
        using std::pow;
        using std::min;
        using std::max;
 
        swe = min(max(swe, 0.0), 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        const Scalar powSwe = pow(swe, -1/params.vgm());
        return - 1.0/params.vgAlpha() * pow(powSwe - 1, 1.0/params.vgn() - 1)/params.vgn()
                                      * powSwe/swe/params.vgm();
    }
 
    static Scalar dswe_dpc(const Params &params, Scalar pc)
    {
        using std::pow;
        using std::max;
 
        pc = max(pc, 0.0); // the equation below is undefined for negative pcs
 
        const Scalar powAlphaPc = pow(params.vgAlpha()*pc, params.vgn());
        return -pow(powAlphaPc + 1, -params.vgm()-1)*params.vgm()*powAlphaPc/pc*params.vgn();
    }
 
    static Scalar krw(const Params &params, Scalar swe)
    {
        using std::pow;
        using std::sqrt;
        using std::min;
        using std::max;
 
        swe = min(max(swe, 0.0), 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        const Scalar r = 1.0 - pow(1.0 - pow(swe, 1.0/params.vgm()), params.vgm());
        return sqrt(swe)*r*r;
    }
 
    static Scalar dkrw_dswe(const Params &params, Scalar swe)
    {
        using std::pow;
        using std::sqrt;
        using std::min;
        using std::max;
 
        swe = min(max(swe, 0.0), 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        const Scalar x = 1.0 - pow(swe, 1.0/params.vgm());
        const Scalar xToM = pow(x, params.vgm());
        return (1.0 - xToM)/sqrt(swe) * ( (1.0 - xToM)/2 + 2*xToM*(1.0-x)/x );
    }
 
    static Scalar krn(const Params &params, Scalar swe)
    {
        using std::pow;
        using std::min;
        using std::max;
 
        swe = min(max(swe, 0.0), 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        return pow(1 - swe, 1.0/3) * pow(1 - pow(swe, 1.0/params.vgm()), 2*params.vgm());
    }
 
    static Scalar dkrn_dswe(const Params &params, Scalar swe)
    {
        using std::pow;
        using std::min;
        using std::max;
 
        swe = min(max(swe, 0.0), 1.0); // the equation below is only defined for 0.0 <= sw <= 1.0
 
        const Scalar x = pow(swe, 1.0/params.vgm());
        return -pow(1.0 - x, 2*params.vgm()) * pow(1.0 - swe, -2.0/3) * (1.0/3 + 2*x/swe);
    }
 
};
 
} // end namespace Dumux
 
#endif