ShallowWaterSolver/RiemannSolvers/HLLCSolver.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: HLLCSolver.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// License for the specific language governing rights and limitations under
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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// DEALINGS IN THE SOFTWARE.
//
// Description: HLLC Riemann solver for the Nonlinear Shallow Water Equations.
//
///////////////////////////////////////////////////////////////////////////////

#include <ShallowWaterSolver/RiemannSolvers/HLLCSolver.h>

namespace Nektar
{
    std::string HLLCSolver::solverName =
        SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
            "HLLC",
            HLLCSolver::create,
            "HLLC Riemann solver");

    HLLCSolver::HLLCSolver() : NonlinearSWESolver()
    {

    }

    /**
     * @brief HLLC Riemann solver for the Nonlinear Shallow Water Equations
     *
     * @param hL      Water depth left state.
     * @param hR      Water depth right state.  
     * @param huL     x-momentum component left state.  
     * @param huR     x-momentum component right state.  
     * @param hvL     y-momentum component left state.  
     * @param hvR     y-momentum component right state.  
     * @param hf      Computed Riemann flux for density.
     * @param huf     Computed Riemann flux for x-momentum component 
     * @param hvf     Computed Riemann flux for y-momentum component 
     */
    void HLLCSolver::v_PointSolve(
        double  hL, double  huL, double  hvL,
        double  hR, double  huR, double  hvR,
        double &hf, double &huf, double &hvf)
    {        
        static NekDouble g = m_params["gravity"]();
        
        // Left and Right velocities
        NekDouble uL = huL / hL;
        NekDouble vL = hvL / hL;
    NekDouble uR = huR / hR;
        NekDouble vR = hvR / hR;
      

        // Left and right wave speeds
    NekDouble cL = sqrt(g * hL);
    NekDouble cR = sqrt(g * hR);
    
    // the two-rarefaction wave assumption
    NekDouble hC,huC,hvC,SL,SR,hstar,ustar,Sstar;
    hstar = 0.5*(cL + cR) + 0.25*(uL - uR);
    hstar *= hstar;
    hstar *= (1.0/g);
    ustar = 0.5*(uL + uR) + cL - cR;

    
    // Compute SL
    if (hstar > hL)
      SL = uL - cL * sqrt(0.5*((hstar*hstar + hstar*hL)/(hL*hL)));
    else
      SL = uL - cL;
    
    // Compute SR
    if (hstar > hR)
      SR = uR + cR * sqrt(0.5*((hstar*hstar + hstar*hR)/(hR*hR)));
    else
      SR = uR + cR;
    
    if (fabs(hR*(uR-SR)-hL*(uL-SL)) <= 1.0e-10)
      Sstar = ustar;
    else
      Sstar = (SL*hR*(uR-SR)-SR*hL*(uL-SL))/(hR*(uR-SR)-hL*(uL-SL));
    
    if (SL >= 0)
      {
        hf  = hL * uL;
        huf  = uL * uL * hL + 0.5 * g * hL * hL;
        hvf  = hL * uL * vL;
      }
    else if (SR <= 0)
      {
        hf  = hR * uR;
        huf  = uR * uR * hR + 0.5 * g * hR * hR;
        hvf  = hR * uR *vR;
      }
    else if ((SL < 0) && (Sstar >= 0))
      {
        hC  = hL * ((SL - uL) / (SL - Sstar));
        huC = hC * Sstar;
        hvC = hC * vL;
        
        hf = hL*uL + SL * (hC - hL);
        huf = (uL*uL*hL+0.5*g*hL*hL) + SL * (huC - hL*uL);
        hvf = (uL*vL*hL) + SL * (hvC - hL*vL);
      }
    else if ((SR > 0) && (Sstar <= 0))
      {
        hC  = hR * ((SR - uR) / (SR - Sstar));
        huC = hC * Sstar;
        hvC = hC * vR;
        
        hf = hR*uR + SR * (hC - hR);
        huf = (uR*uR*hR+0.5*g*hR*hR) + SR * (huC - hR*uR);
        hvf = (uR*vR*hR) + SR * (hvC - hR*vR);
      }
    else
      {
        ASSERTL0(false,"Error in HLLC solver -- non physical combination of SR, SL and Sstar");
      }
    }
}