regularizedbrookscorey.hh

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#ifndef REGULARIZED_BROOKS_COREY_HH
#define REGULARIZED_BROOKS_COREY_HH
 
#include "brookscorey.hh"
#include "regularizedbrookscoreyparams.hh"
 
#include <dumux/common/spline.hh>
 
namespace Dumux {

template <class ScalarT, class ParamsT = RegularizedBrooksCoreyParams<ScalarT> >
class RegularizedBrooksCorey
{
    using BrooksCorey = Dumux::BrooksCorey<ScalarT, ParamsT>;
 
public:
    using Params = ParamsT;
    using Scalar = typename Params::Scalar;

    static Scalar pc(const Params &params, Scalar swe)
    {
        const Scalar sThres = params.thresholdSw();
 
        // make sure that the capilary pressure observes a
        // derivative != 0 for 'illegal' saturations. This is
        // required for example by newton solvers (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 <= sThres) {
            Scalar m = BrooksCorey::dpc_dswe(params, sThres);
            Scalar pcsweLow = BrooksCorey::pc(params, sThres);
            return pcsweLow + m*(swe - sThres);
        }
        else if (swe > 1.0) {
            Scalar m = BrooksCorey::dpc_dswe(params, 1.0);
            Scalar pcsweHigh = BrooksCorey::pc(params, 1.0);
            return pcsweHigh + m*(swe - 1.0);
        }
 
        // if the effective saturation is in an 'reasonable'
        // range, we use the real Brooks-Corey law...
        return BrooksCorey::pc(params, swe);
    }

    static Scalar sw(const Params &params, Scalar pc)
    {
        const Scalar sThres = params.thresholdSw();
 
        // calculate the saturation which corrosponds to the
        // saturation in the non-regularized version of
        // the Brooks-Corey law
        Scalar swe = BrooksCorey::sw(params, pc);
 
        // make sure that the capilary pressure observes a
        // derivative != 0 for 'illegal' saturations. This is
        // required for example by newton solvers (if the
        // derivative calculated numerically) in order to get the
        // saturation moving to the right direction if it
        // temporarily is in an 'illegal' range.
        if (swe <= sThres) {
            // invert the low saturation regularization of pc()
            Scalar m = BrooksCorey::dpc_dswe(params, sThres);
            Scalar pcsweLow = BrooksCorey::pc(params, sThres);
            return sThres + (pc - pcsweLow)/m;
        }
        else if (swe > 1.0) {
            Scalar m = BrooksCorey::dpc_dswe(params, 1.0);
            Scalar pcsweHigh = BrooksCorey::pc(params, 1.0);
            return 1.0 + (pc - pcsweHigh)/m;
        }
 
        return BrooksCorey::sw(params, pc);
    }

    static Scalar endPointPc(const Params &params)
    { return params.pe(); }

    static Scalar dpc_dswe(const Params &params, Scalar swe)
    {
        const Scalar sThres = params.thresholdSw();
 
        // derivative of the regualarization
        if (swe <= sThres) {
            // calculate the slope of the straight line used in pc()
            Scalar m = BrooksCorey::dpc_dswe(params, sThres);
            return m;
        }
        else if (swe > 1.0) {
            // calculate the slope of the straight line used in pc()
            Scalar m = BrooksCorey::dpc_dswe(params, 1.0);
            return m;
        }
 
        return BrooksCorey::dpc_dswe(params, swe);
    }

    static Scalar dswe_dpc(const Params &params, Scalar pc)
    {
        const Scalar sThres = params.thresholdSw();
 
        //instead of return value = inf, return a very large number
        if (params.pe() == 0.0)
        {
            return 1e100;
        }
 
        // calculate the saturation which corresponds to the
        // saturation in the non-regularized version of the
        // Brooks-Corey law
        Scalar swe;
        if (pc < 0)
            swe = 1.5; // make sure we regularize below
        else
            swe = BrooksCorey::sw(params, pc);
 
        // derivative of the regularization
        if (swe <= sThres) {
            // calculate the slope of the straight line used in pc()
            Scalar m = BrooksCorey::dpc_dswe(params, sThres);
            return 1/m;
        }
        else if (swe > 1.0) {
            // calculate the slope of the straight line used in pc()
            Scalar m = BrooksCorey::dpc_dswe(params, 1.0);
            return 1/m;
        }
        return 1.0/BrooksCorey::dpc_dswe(params, swe);
    }

    static Scalar krw(const Params &params, Scalar swe)
    {
        if (swe <= 0.0)
            return 0.0;
        else if (swe >= 1.0)
            return 1.0;
 
        return BrooksCorey::krw(params, swe);
    }

    static Scalar krn(const Params &params, Scalar swe)
    {
        if (swe >= 1.0)
            return 0.0;
        else if (swe <= 0.0)
            return 1.0;
 
        return BrooksCorey::krn(params, swe);
    }
};
} // end namespace Dumux
 
#endif