CompressibleFlowSolver/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.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <CompressibleFlowSolver/RiemannSolvers/HLLCSolver.h>
 
namespace Nektar
{
std::string HLLCSolver::solverName =
    SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
        "HLLC", HLLCSolver::create, "HLLC Riemann solver");
 
HLLCSolver::HLLCSolver(const LibUtilities::SessionReaderSharedPtr &pSession)
    : CompressibleSolver(pSession)
{
}
 
/**
 * @brief HLLC Riemann solver
 *
 * @param rhoL      Density left state.
 * @param rhoR      Density right state.
 * @param rhouL     x-momentum component left state.
 * @param rhouR     x-momentum component right state.
 * @param rhovL     y-momentum component left state.
 * @param rhovR     y-momentum component right state.
 * @param rhowL     z-momentum component left state.
 * @param rhowR     z-momentum component right state.
 * @param EL        Energy left state.
 * @param ER        Energy right state.
 * @param rhof      Computed Riemann flux for density.
 * @param rhouf     Computed Riemann flux for x-momentum component
 * @param rhovf     Computed Riemann flux for y-momentum component
 * @param rhowf     Computed Riemann flux for z-momentum component
 * @param Ef        Computed Riemann flux for energy.
 */
void HLLCSolver::v_PointSolve(NekDouble rhoL, NekDouble rhouL, NekDouble rhovL,
                              NekDouble rhowL, NekDouble EL, NekDouble rhoR,
                              NekDouble rhouR, NekDouble rhovR, NekDouble rhowR,
                              NekDouble ER, NekDouble &rhof, NekDouble &rhouf,
                              NekDouble &rhovf, NekDouble &rhowf, NekDouble &Ef)
{
    // Left and Right velocities
    NekDouble uL = rhouL / rhoL;
    NekDouble vL = rhovL / rhoL;
    NekDouble wL = rhowL / rhoL;
    NekDouble uR = rhouR / rhoR;
    NekDouble vR = rhovR / rhoR;
    NekDouble wR = rhowR / rhoR;
 
    // Internal energy (per unit mass)
    NekDouble eL = (EL - 0.5 * (rhouL * uL + rhovL * vL + rhowL * wL)) / rhoL;
    NekDouble eR = (ER - 0.5 * (rhouR * uR + rhovR * vR + rhowR * wR)) / rhoR;
    // Pressure
    NekDouble pL = m_eos->GetPressure(rhoL, eL);
    NekDouble pR = m_eos->GetPressure(rhoR, eR);
    // Speed of sound
    NekDouble cL = m_eos->GetSoundSpeed(rhoL, eL);
    NekDouble cR = m_eos->GetSoundSpeed(rhoR, eR);
 
    // Left and right total enthalpy
    NekDouble HL = (EL + pL) / rhoL;
    NekDouble HR = (ER + pR) / rhoR;
 
    // Square root of rhoL and rhoR.
    NekDouble srL  = sqrt(rhoL);
    NekDouble srR  = sqrt(rhoR);
    NekDouble srLR = srL + srR;
 
    // Roe average state
    NekDouble uRoe  = (srL * uL + srR * uR) / srLR;
    NekDouble vRoe  = (srL * vL + srR * vR) / srLR;
    NekDouble wRoe  = (srL * wL + srR * wR) / srLR;
    NekDouble URoe2 = uRoe * uRoe + vRoe * vRoe + wRoe * wRoe;
    NekDouble HRoe  = (srL * HL + srR * HR) / srLR;
    NekDouble cRoe  = GetRoeSoundSpeed(rhoL, pL, eL, HL, srL, rhoR, pR, eR, HR,
                                      srR, HRoe, URoe2, srLR);
 
    // Maximum wave speeds
    NekDouble SL = std::min(uL - cL, uRoe - cRoe);
    NekDouble SR = std::max(uR + cR, uRoe + cRoe);
 
    // HLLC Riemann fluxes (positive case)
    if (SL >= 0)
    {
        rhof  = rhouL;
        rhouf = rhouL * uL + pL;
        rhovf = rhouL * vL;
        rhowf = rhouL * wL;
        Ef    = uL * (EL + pL);
    }
    // HLLC Riemann fluxes (negative case)
    else if (SR <= 0)
    {
        rhof  = rhouR;
        rhouf = rhouR * uR + pR;
        rhovf = rhouR * vR;
        rhowf = rhouR * wR;
        Ef    = uR * (ER + pR);
    }
    // HLLC Riemann fluxes (general case (SL < 0 | SR > 0)
    else
    {
        NekDouble SM = (pR - pL + rhouL * (SL - uL) - rhouR * (SR - uR)) /
                       (rhoL * (SL - uL) - rhoR * (SR - uR));
        NekDouble rhoML  = rhoL * (SL - uL) / (SL - SM);
        NekDouble rhouML = rhoML * SM;
        NekDouble rhovML = rhoML * vL;
        NekDouble rhowML = rhoML * wL;
        NekDouble EML =
            rhoML * (EL / rhoL + (SM - uL) * (SM + pL / (rhoL * (SL - uL))));
 
        NekDouble rhoMR  = rhoR * (SR - uR) / (SR - SM);
        NekDouble rhouMR = rhoMR * SM;
        NekDouble rhovMR = rhoMR * vR;
        NekDouble rhowMR = rhoMR * wR;
        NekDouble EMR =
            rhoMR * (ER / rhoR + (SM - uR) * (SM + pR / (rhoR * (SR - uR))));
 
        if (SL < 0.0 && SM >= 0.0)
        {
            rhof  = rhouL + SL * (rhoML - rhoL);
            rhouf = rhouL * uL + pL + SL * (rhouML - rhouL);
            rhovf = rhouL * vL + SL * (rhovML - rhovL);
            rhowf = rhouL * wL + SL * (rhowML - rhowL);
            Ef    = uL * (EL + pL) + SL * (EML - EL);
        }
        else if (SM < 0.0 && SR > 0.0)
        {
            rhof  = rhouR + SR * (rhoMR - rhoR);
            rhouf = rhouR * uR + pR + SR * (rhouMR - rhouR);
            rhovf = rhouR * vR + SR * (rhovMR - rhovR);
            rhowf = rhouR * wR + SR * (rhowMR - rhowR);
            Ef    = uR * (ER + pR) + SR * (EMR - ER);
        }
    }
}
} // namespace Nektar