regularizedparkervangen3p.hh

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#ifndef REGULARIZED_PARKERVANGEN_3P_HH
#define REGULARIZED_PARKERVANGEN_3P_HH
 
#include "parkervangen3p.hh"
#include "regularizedparkervangen3pparams.hh"
 
#include <dumux/common/spline.hh>
 
namespace Dumux {
 
template <class ScalarT, class ParamsT = RegularizedParkerVanGen3PParams<ScalarT> >
class RegularizedParkerVanGen3P
{
    using ParkerVanGen3P = Dumux::ParkerVanGen3P<ScalarT, ParamsT>;
 
public:
    using Params = ParamsT;
    using Scalar = typename Params::Scalar;
 
    static Scalar pc(const Params &params, Scalar sw)
    {
        return ParkerVanGen3P::pc(params, sw);
    }
 
    static Scalar pcgw(const Params &params, Scalar swe)
    {
        //if specified, a constant value is used for regularization
        if(params.constRegularization())
        {
            if(swe < 0.0)
                swe = 0.0;
            if(swe > 1.0)
                swe = 1.0;
        }
 
        // retrieve the low and the high threshold saturations for the
        // unregularized capillary pressure curve from the parameters
        const Scalar swThLow = params.pcLowS();
        const Scalar swThHigh = params.pcHighS();
 
        // 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 < swThLow)
        {
            const Scalar mLow = ParkerVanGen3P::dpcgw_dswe(params, swThLow);
            return ParkerVanGen3P::pcgw(params, swThLow) + mLow*(swe - swThLow);
        }
        else if (swe > swThHigh)
        {
            Scalar yTh = ParkerVanGen3P::pcgw(params, swThHigh);
            Scalar m1 = (0.0 - yTh)/(1.0 - swThHigh)*2;
 
            if (swe < 1.0) {
                // use spline between threshold swe and 1.0
                Scalar mTh = ParkerVanGen3P::dpcgw_dswe(params, swThHigh);
                Spline<Scalar> sp(swThHigh, 1.0, // x0, x1
                                  yTh, 0, // y0, y1
                                  mTh, m1); // m0, m1
                return sp.eval(swe);
            }
            else {
                // straight line for swe > 1.0
                return m1*(swe - 1.0) + 0.0;
            }
        }
 
        // if the effective saturation is in an 'reasonable'
        // range, we use the real van genuchten law...
        return ParkerVanGen3P::pcgw(params, swe);
    }
 
    static Scalar pcnw(const Params &params, Scalar swe)
    {
        //if specified, a constant value is used for regularization
        if(params.constRegularization())
        {
            if(swe < 0.0)
                swe = 0.0;
            if(swe > 1.0)
                swe = 1.0;
        }
 
        // retrieve the low and the high threshold saturations for the
        // unregularized capillary pressure curve from the parameters
        const Scalar swThLow = params.pcLowS();
        const Scalar swThHigh = params.pcHighS();
 
        // 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 < swThLow)
        {
            const Scalar mLow = ParkerVanGen3P::dpcnw_dswe(params, swThLow);
            return ParkerVanGen3P::pcnw(params, swThLow) + mLow*(swe - swThLow);
        }
        else if (swe > swThHigh)
        {
            Scalar yTh = ParkerVanGen3P::pcnw(params, swThHigh);
            Scalar m1 = (0.0 - yTh)/(1.0 - swThHigh)*2;
 
            if (swe < 1.0) {
                // use spline between threshold swe and 1.0
                Scalar mTh = ParkerVanGen3P::dpcnw_dswe(params, swThHigh);
                Spline<Scalar> sp(swThHigh, 1.0, // x0, x1
                                  yTh, 0, // y0, y1
                                  mTh, m1); // m0, m1
                return sp.eval(swe);
            }
            else {
                // straight line for swe > 1.0
                return m1*(swe - 1.0) + 0.0;
            }
        }
 
        // if the effective saturation is in an 'reasonable'
        // range, we use the real van genuchten law...
        return ParkerVanGen3P::pcnw(params, swe);
    }
 
    static Scalar pcgn(const Params &params, Scalar ste)
    {
        //if specified, a constant value is used for regularization
        if(params.constRegularization())
        {
            if(ste < 0.0)
                ste = 0.0;
            if(ste > 1.0)
                ste = 1.0;
        }
 
        // retrieve the low and the high threshold saturations for the
        // unregularized capillary pressure curve from the parameters
        const Scalar swThLow = params.pcLowS();
        const Scalar swThHigh = params.pcHighS();
 
        // 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 (ste < swThLow)
        {
            const Scalar mLow = ParkerVanGen3P::dpcgn_dste(params, swThLow);
            return ParkerVanGen3P::pcgn(params, swThLow) + mLow*(ste - swThLow);
        }
        else if (ste > swThHigh)
        {
            Scalar yTh = ParkerVanGen3P::pcgn(params, swThHigh);
            Scalar m1 = (0.0 - yTh)/(1.0 - swThHigh)*2;
 
            if (ste < 1.0) {
                // use spline between threshold swe and 1.0
                Scalar mTh = ParkerVanGen3P::dpcgn_dste(params, swThHigh);
                Spline<Scalar> sp(swThHigh, 1.0, // x0, x1
                                  yTh, 0, // y0, y1
                                  mTh, m1); // m0, m1
                return sp.eval(ste);
            }
            else {
                // straight line for swe > 1.0
                return m1*(ste - 1.0) + 0.0;
            }
        }
 
        // if the effective saturation is in an 'reasonable'
        // range, we use the real van genuchten law...
        return ParkerVanGen3P::pcgn(params, ste);
    }
 
    static Scalar pcAlpha(const Params &params, Scalar sne)
    {
        return ParkerVanGen3P::pcAlpha(params, sne);
    }
 
    static Scalar sw(const Params &params, Scalar pc)
    {
        return ParkerVanGen3P::sw(params, pc);
    }
 
    static Scalar dpc_dswe(const Params &params, Scalar swe)
    {
        return ParkerVanGen3P::dpc_dswe(params, swe);
    }
 
    static Scalar dswe_dpc(const Params &params, Scalar pc)
    {
        return ParkerVanGen3P::dswe_dpc(params, pc);
    }
 
    static Scalar krw(const Params &params,  const Scalar swe)
    {
        //use regularization
        if(swe > 1.0) return 1.0;
        if(swe < 0.0) return 0.0;
 
        //or use actual material law
        return ParkerVanGen3P::krw(params, swe);
    }
 
    static Scalar krn(const Params &params, Scalar swe, Scalar sn, Scalar ste)
    {
        using std::max;
        using std::min;
        swe = max(min(swe, 1.0), 0.0);
        ste = max(min(ste, 1.0), 0.0);
 
        if(ste - swe <= 0.0)
            return 0.0;
 
        //or use actual material law
        return ParkerVanGen3P::krn(params, swe, sn, ste);
    }
 
 
    static Scalar krg(const Params &params, const Scalar ste)
    {
        //return 0 if there is no gas
        if(ste > 1.0)
            return 0.0;
 
        // use linear regularization for very high gas saturations
        // to avoid a kink in the curve and to maintain a slope for
        // the Newton solver
        const Scalar threshold = 1e-3;
        if(ste <= threshold)
        {
            const Scalar mSwr = ParkerVanGen3P::dkrg_dste(params, threshold);
            const Scalar ySwr = ParkerVanGen3P::krg(params, threshold);
            return ySwr + mSwr*(ste - threshold);
        }
 
        // For very low gas saturations:
        // We use a scaling factor that decreases the gas phase permeability quite fast a very low gas phase
        // saturations, thus making that phase virtually immobile.
        // This prevents numerical issues related to the degeneration of the gas phase mass balance for the 3p3c model
        // at very low gas phase saturations.
 
        //get the absolute gas phase saturation
        const Scalar st = ste*(1 - params.swr()) + params.swr();
        const Scalar sg = 1.0 - st;
        using std::max;
        const Scalar scalFact = (sg > 0.1) ? 1.0 : max(0.0,
                                                      (sg - params.sgr())/(0.1 - params.sgr()));
 
        //or use actual material law
        return scalFact * ParkerVanGen3P::krg(params, ste);
    }
 
    static Scalar kr(const Params &params, const int phaseIdx, const Scalar swe, const Scalar sn, const Scalar ste)
    {
        switch (phaseIdx)
        {
        case 0:
            return krw(params, swe);
        case 1:
            return krn(params, swe, sn, ste);
        case 2:
            return krg(params, ste);
        }
        DUNE_THROW(Dune::InvalidStateException,
                   "Invalid phase index ");
    }
 
   static Scalar bulkDensTimesAdsorpCoeff (const Params &params)
   {
      return ParkerVanGen3P::bulkDensTimesAdsorpCoeff(params);
   }
 
};
} // end namespace Dumux
 
#endif