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).
//
// 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: 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() : CompressibleSolver()
    {
        
    }
    
    /**
     * @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)
    {
        static NekDouble gamma = m_params["gamma"]();
        
        // 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;

        // Left and right pressures
        NekDouble pL = (gamma - 1.0) *
            (EL - 0.5 * (rhouL * uL + rhovL * vL + rhowL * wL));
        NekDouble pR = (gamma - 1.0) *
            (ER - 0.5 * (rhouR * uR + rhovR * vR + rhowR * wR));
        
        // Left and right 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 hRoe = (srL * hL + srR * hR) / srLR;
        NekDouble URoe = (uRoe * uRoe + vRoe * vRoe + wRoe * wRoe);
        NekDouble cRoe = sqrt((gamma - 1.0)*(hRoe - 0.5 * URoe));
        
        // Maximum eigenvalue
        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));
    }
}