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).
//
// 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
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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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(const LibUtilities::SessionReaderSharedPtr &pSession)
    : NonlinearSWESolver(pSession)
{
}
 
/**
 * @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(NekDouble hL, NekDouble huL, NekDouble hvL,
                              NekDouble hR, NekDouble huR, NekDouble hvR,
                              NekDouble &hf, NekDouble &huf, NekDouble &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
    {
        NEKERROR(ErrorUtil::efatal,
                 "Error in HLLC solver -- non physical combination of "
                 "SR, SL and Sstar");
    }
}
 
} // namespace Nektar