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LinearHLLSolver.cpp
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1 ///////////////////////////////////////////////////////////////////////////////
2 //
3 // File: LinearHLLSolver.cpp
4 //
5 // For more information, please see: http://www.nektar.info
6 //
7 // The MIT License
8 //
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).
12 //
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31 //
32 // Description: HLL Riemann solver for the Linear Shallow Water Equations.
33 // Only valid for constant depth
34 //
35 ///////////////////////////////////////////////////////////////////////////////
36 
38 
39 namespace Nektar
40 {
41  std::string LinearHLLSolver::solverName =
43  "LinearHLL",
45  "Linear HLL Riemann solver");
46 
48  {
49 
50  }
51 
52  /**
53  * @brief HLL Riemann solver for the linear Shallow Water Equations
54  *
55  * @param etaL Free surface elevation left state.
56  * @param etaR Free surface elevation right state.
57  * @param uL x-velocity left state.
58  * @param uR x-velocity right state.
59  * @param vL y-velocity left state.
60  * @param vR y-velocity right state.
61  * @param dL still water depth component left state.
62  * @param dR still water depth component right state.
63  * @param etaf Computed Riemann flux for continuity.
64  * @param uf Computed Riemann flux for x-momentum component
65  * @param vf Computed Riemann flux for y-momentum component
66  */
68  double etaL, double uL, double vL, double dL,
69  double etaR, double uR, double vR, double dR,
70  double &etaf, double &uf, double &vf)
71  {
72  static NekDouble g = m_params["gravity"]();
73 
74  if (dL != dR)
75  {
76  ASSERTL0(false,"not constant depth in LinearHLL");
77  }
78 
79  // Left and right wave speeds
80  NekDouble cL = sqrt(g * dL);
81  NekDouble cR = sqrt(g * dR);
82 
83  NekDouble SL = uL - cL;
84  NekDouble SR = uR + cR;
85 
86  if (SL >= 0)
87  {
88  etaf = dL * uL;
89  uf = g * etaL;
90  vf = 0.0;
91  }
92  else if (SR <= 0)
93  {
94  etaf = dR * uR;
95  uf = g * etaR;
96  vf = 0.0;
97  }
98  else
99  {
100  etaf = (SR * dL * uL - SL * dR * uR +
101  SL * SR * (etaR - etaL)) / (SR - SL);
102  uf = (SR * g * etaL - SL * g * etaR +
103  SL * SR * (uR - uL)) / (SR - SL);
104  vf = (SL * SR * (vR - vL)) / (SR - SL);
105  }
106  }
107 }