UpwindLDGSolver.cpp

Go to the documentation of this file.

///////////////////////////////////////////////////////////////////////////////
//
// File: UpwindLDGSolver.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
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Upwind Riemann solver for LDG.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <boost/core/ignore_unused.hpp>
 
#include <SolverUtils/RiemannSolvers/UpwindLDGSolver.h>
 
namespace Nektar
{
namespace SolverUtils
{
std::string UpwindLDGSolver::solverName =
    GetRiemannSolverFactory().RegisterCreatorFunction(
        "UpwindLDG", UpwindLDGSolver::create, "Upwind LDG solver");
 
/**
 * @class UpwindLDGSolver
 *
 * @brief Upwind scheme Riemann solver for LDG.
 *
 * The upwind solver determines the flux based upon an advection
 * velocity \f$\mathbf{V}\f$ and trace normal \f$\mathbf{n}\f$. In
 * particular, the flux for each component of the velocity field is
 * deterined by:
 *
 * \f[ \mathbf{f}(u^+,u^-) = \begin{cases} \mathbf{V}u^+, &
 * \mathbf{V}\cdot\mathbf{n} \geq 0,\\ \mathbf{V}u^-, &
 * \mathbf{V}\cdot\mathbf{n} < 0.\end{cases} \f]
 *
 * Here the superscript + and - denotes forwards and backwards spaces
 * respectively.
 */
 
/**
 * @brief Default constructor.
 */
UpwindLDGSolver::UpwindLDGSolver(
    const LibUtilities::SessionReaderSharedPtr &pSession)
    : RiemannSolver(pSession)
{
}
 
/**
 * @brief Implementation of the upwind LDG solver.
 *
 * The upwind solver assumes that a scalar field Vn is defined, which
 * corresponds with the dot product \f$\mathbf{V}\cdot\mathbf{n}\f$,
 * where \f$\mathbf{V}\f$ is the advection velocity and \f$\mathbf{n}\f$
 * defines the normal of a vertex, edge or face at each quadrature point
 * of the trace space.
 *
 * @param Fwd   Forwards trace space.
 * @param Bwd   Backwards trace space.
 * @param flux  Resulting flux.
 */
void UpwindLDGSolver::v_Solve(
    const int nDim, const Array<OneD, const Array<OneD, NekDouble>> &Fwd,
    const Array<OneD, const Array<OneD, NekDouble>> &Bwd,
    Array<OneD, Array<OneD, NekDouble>> &flux)
{
    boost::ignore_unused(nDim);
 
    ASSERTL1(CheckScalars("Vn"), "Vn not defined.");
    const Array<OneD, NekDouble> &traceVel = m_scalars["Vn"]();
 
    for (int j = 0; j < traceVel.size(); ++j)
    {
        const Array<OneD, const Array<OneD, NekDouble>> &tmp =
            traceVel[j] >= 0 ? Fwd : Bwd;
        for (int i = 0; i < Fwd.size(); ++i)
        {
            flux[i][j] = tmp[i][j];
        }
    }
}
} // namespace SolverUtils
} // namespace Nektar