RichardsSeffRSC.C

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//  Rogers-Stallybrass-Clements version of effective saturation as a function of CAPILLARY pressure,
//  and derivs wrt that capillary pressure.
//  valid for residual saturations = 0, and viscosityOil = 2*viscosityWater.  (the "2" is important
//  here!).
// C Rogers, MP Stallybrass and DL Clements "On two phase filtration under gravity and with boundary
// infiltration: application of a Backlund transformation" Nonlinear Analysis Theory Methods and
// Applications 7 (1983) 785--799.
//
#include "RichardsSeffRSC.h"
 
Real
RichardsSeffRSC::seff(Real pc, Real shift, Real scale)
{
  Real x = (pc - shift) / scale;
  Real ex = std::exp(x);
  return std::pow(1 + ex, -0.5);
}
 
Real
RichardsSeffRSC::dseff(Real pc, Real shift, Real scale)
{
  Real x = (pc - shift) / scale;
  Real ex = std::exp(x);
  return -0.5 * ex * std::pow(1 + ex, -1.5) / scale;
}
 
Real
RichardsSeffRSC::d2seff(Real pc, Real shift, Real scale)
{
  Real x = (pc - shift) / scale;
  Real ex = std::exp(x);
  return (0.75 * ex * ex * std::pow(1 + ex, -2.5) - 0.5 * ex * std::pow(1 + ex, -1.5)) / scale /
         scale;
}