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UpwindLDGSolver.cpp
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1 ///////////////////////////////////////////////////////////////////////////////
2 //
3 // File: UpwindLDGSolver.cpp
4 //
5 // For more information, please see: http://www.nektar.info
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7 // The MIT License
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9 // Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
10 // Department of Aeronautics, Imperial College London (UK), and Scientific
11 // Computing and Imaging Institute, University of Utah (USA).
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31 //
32 // Description: Upwind Riemann solver for LDG.
33 //
34 ///////////////////////////////////////////////////////////////////////////////
35 
37 
38 namespace Nektar
39 {
40  namespace SolverUtils
41  {
43  RegisterCreatorFunction("UpwindLDG", UpwindLDGSolver::create, "Upwind LDG solver");
44 
45  /**
46  * @class UpwindLDGSolver
47  *
48  * @brief Upwind scheme Riemann solver for LDG.
49  *
50  * The upwind solver determines the flux based upon an advection
51  * velocity \f$\mathbf{V}\f$ and trace normal \f$\mathbf{n}\f$. In
52  * particular, the flux for each component of the velocity field is
53  * deterined by:
54  *
55  * \f[ \mathbf{f}(u^+,u^-) = \begin{cases} \mathbf{V}u^+, &
56  * \mathbf{V}\cdot\mathbf{n} \geq 0,\\ \mathbf{V}u^-, &
57  * \mathbf{V}\cdot\mathbf{n} < 0.\end{cases} \f]
58  *
59  * Here the superscript + and - denotes forwards and backwards spaces
60  * respectively.
61  */
62 
63  /**
64  * @brief Default constructor.
65  */
68  {
69  }
70 
71  /**
72  * @brief Implementation of the upwind LDG solver.
73  *
74  * The upwind solver assumes that a scalar field Vn is defined, which
75  * corresponds with the dot product \f$\mathbf{V}\cdot\mathbf{n}\f$,
76  * where \f$\mathbf{V}\f$ is the advection velocity and \f$\mathbf{n}\f$
77  * defines the normal of a vertex, edge or face at each quadrature point
78  * of the trace space.
79  *
80  * @param Fwd Forwards trace space.
81  * @param Bwd Backwards trace space.
82  * @param flux Resulting flux.
83  */
85  const int nDim,
86  const Array<OneD, const Array<OneD, NekDouble> > &Fwd,
87  const Array<OneD, const Array<OneD, NekDouble> > &Bwd,
88  Array<OneD, Array<OneD, NekDouble> > &flux)
89  {
90  ASSERTL1(CheckScalars("Vn"), "Vn not defined.");
91  const Array<OneD, NekDouble> &traceVel = m_scalars["Vn"]();
92 
93  for (int j = 0; j < traceVel.num_elements(); ++j)
94  {
95  const Array<OneD, const Array<OneD, NekDouble> > &tmp =
96  traceVel[j] >= 0 ? Fwd : Bwd;
97  for (int i = 0; i < Fwd.num_elements(); ++i)
98  {
99  flux[i][j] = tmp[i][j];
100  }
101  }
102  }
103  }
104 }