ShallowWaterSolver/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
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//
// Description: Lax-Friedrichs Riemann solver.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <ShallowWaterSolver/RiemannSolvers/LaxFriedrichsSolver.h>
 
namespace Nektar
{
 
std::string LaxFriedrichsSolver::solverName =
    SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
        "LaxFriedrichs", LaxFriedrichsSolver::create,
        "LaxFriedrichs Riemann solver");
 
LaxFriedrichsSolver::LaxFriedrichsSolver(
    const LibUtilities::SessionReaderSharedPtr &pSession)
    : NonlinearSWESolver(pSession)
{
}
 
/**
 * @brief Lax-Friedrichs Riemann solver
 *
 * @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 LaxFriedrichsSolver::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);
 
    // Square root of hL and hR.
    NekDouble srL  = sqrt(hL);
    NekDouble srR  = sqrt(hR);
    NekDouble srLR = srL + srR;
 
    // Velocity Roe averages
    NekDouble uRoe = (srL * uL + srR * uR) / srLR;
    NekDouble cRoe = sqrt(0.5 * (cL * cL + cR * cR));
 
    // Minimum and maximum wave speeds
    NekDouble S    = std::max(uRoe + cRoe, std::max(uR + cR, -(uL - cL)));
    NekDouble sign = 1.0;
 
    if (S == -(uL - cL))
    {
        sign = -1.0;
    }
 
    // Lax-Friedrichs Riemann h flux
    hf = 0.5 * ((huL + huR) - sign * S * (hR - hL));
 
    // Lax-Friedrichs Riemann hu flux
    huf =
        0.5 *
        ((hL * uL * uL + 0.5 * g * hL * hL + hR * uR * uR + 0.5 * g * hR * hR) -
         sign * S * (huR - huL));
 
    // Lax-Friedrichs Riemann hv flux
    hvf = 0.5 * ((hL * uL * vL + hR * uR * vR) - sign * S * (hvR - hvL));
}
 
} // namespace Nektar