CompressibleFlowSolver/RiemannSolvers/LaxFriedrichsSolver.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: LaxFriedrichsSolver.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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//
// Description: LaxFriedrichs Riemann solver.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <CompressibleFlowSolver/RiemannSolvers/LaxFriedrichsSolver.h>
 
namespace Nektar
{
std::string LaxFriedrichsSolver::solverName =
    SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
        "LaxFriedrichs", LaxFriedrichsSolver::create,
        "Lax-Friedrichs Riemann solver");
 
LaxFriedrichsSolver::LaxFriedrichsSolver(
    const LibUtilities::SessionReaderSharedPtr &pSession)
    : CompressibleSolver(pSession)
{
}
 
/**
 * @brief Lax-Friedrichs 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 LaxFriedrichsSolver::v_PointSolve(double rhoL, double rhouL, double rhovL,
                                       double rhowL, double EL, double rhoR,
                                       double rhouR, double rhovR, double rhowR,
                                       double ER, double &rhof, double &rhouf,
                                       double &rhovf, double &rhowf, double &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);
 
    // 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 eigenvalue
    NekDouble URoe = fabs(uRoe) + cRoe;
 
    // Lax-Friedrichs flux formula
    rhof  = 0.5 * (rhouL + rhouR - URoe * (rhoR - rhoL));
    rhouf = 0.5 * (pL + rhouL * uL + pR + rhouR * uR - URoe * (rhouR - rhouL));
    rhovf = 0.5 * (rhouL * vL + rhouR * vR - URoe * (rhovR - rhovL));
    rhowf = 0.5 * (rhouL * wL + rhouR * wR - URoe * (rhowR - rhowL));
    Ef    = 0.5 * (uL * (EL + pL) + uR * (ER + pR) - URoe * (ER - EL));
}
} // namespace Nektar