UpwindSolver.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: UpwindSolver.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.
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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//
// Description: Upwind Riemann solver.
//
///////////////////////////////////////////////////////////////////////////////
 
#include <SolverUtils/RiemannSolvers/UpwindSolver.h>
 
namespace Nektar::SolverUtils
{
std::string UpwindSolver::solverName =
    GetRiemannSolverFactory().RegisterCreatorFunction(
        "Upwind", UpwindSolver::create, "Upwind solver");
 
/**
 * @class UpwindSolver
 *
 * @brief Upwind scheme Riemann solver.
 *
 * 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.
 */
UpwindSolver::UpwindSolver(const LibUtilities::SessionReaderSharedPtr &pSession)
    : RiemannSolver(pSession)
{
}
 
/**
 * @brief Implementation of the upwind 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 UpwindSolver::v_Solve([[maybe_unused]] 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)
{
    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] = traceVel[j] * tmp[i][j];
        }
    }
}
} // namespace Nektar::SolverUtils