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CompressibleFlowSolver/RiemannSolvers/LaxFriedrichsSolver.cpp
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1 ///////////////////////////////////////////////////////////////////////////////
2 //
3 // File: LaxFriedrichsSolver.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: Lax-Friedrichs Riemann solver.
33 //
34 ///////////////////////////////////////////////////////////////////////////////
35 
36 #include <CompressibleFlowSolver/RiemannSolvers/LaxFriedrichsSolver.h>
37 
38 namespace Nektar
39 {
40  std::string LaxFriedrichsSolver::solverName =
41  SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
42  "LaxFriedrichs", LaxFriedrichsSolver::create,
43  "Lax-Friedrichs Riemann solver");
44 
45  LaxFriedrichsSolver::LaxFriedrichsSolver() : CompressibleSolver()
46  {
47 
48  }
49 
50  /**
51  * @brief Lax-Friedrichs Riemann solver
52  *
53  * @param rhoL Density left state.
54  * @param rhoR Density right state.
55  * @param rhouL x-momentum component left state.
56  * @param rhouR x-momentum component right state.
57  * @param rhovL y-momentum component left state.
58  * @param rhovR y-momentum component right state.
59  * @param rhowL z-momentum component left state.
60  * @param rhowR z-momentum component right state.
61  * @param EL Energy left state.
62  * @param ER Energy right state.
63  * @param rhof Computed Riemann flux for density.
64  * @param rhouf Computed Riemann flux for x-momentum component
65  * @param rhovf Computed Riemann flux for y-momentum component
66  * @param rhowf Computed Riemann flux for z-momentum component
67  * @param Ef Computed Riemann flux for energy.
68  */
69  void LaxFriedrichsSolver::v_PointSolve(
70  NekDouble rhoL, NekDouble rhouL, NekDouble rhovL, NekDouble rhowL, NekDouble EL,
71  NekDouble rhoR, NekDouble rhouR, NekDouble rhovR, NekDouble rhowR, NekDouble ER,
72  NekDouble &rhof, NekDouble &rhouf, NekDouble &rhovf, NekDouble &rhowf, NekDouble &Ef)
73  {
74  static NekDouble gamma = m_params["gamma"]();
75 
76  // Left and right velocities
77  NekDouble uL = rhouL / rhoL;
78  NekDouble vL = rhovL / rhoL;
79  NekDouble wL = rhowL / rhoL;
80  NekDouble uR = rhouR / rhoR;
81  NekDouble vR = rhovR / rhoR;
82  NekDouble wR = rhowR / rhoR;
83 
84  // Left and right pressures
85  NekDouble pL = (gamma - 1.0) *
86  (EL - 0.5 * (rhouL*uL + rhovL*vL + rhowL*wL));
87 
88  NekDouble pR = (gamma - 1.0) *
89  (ER - 0.5 * (rhouR*uR + rhovR*vR + rhowR*wR));
90 
91  // Left and right speeds of sound
92  NekDouble cL = sqrt(gamma * pL / rhoL);
93  NekDouble cR = sqrt(gamma * pR / rhoR);
94 
95  // Left and right entalpies
96  NekDouble hL = (EL + pL) / rhoL;
97  NekDouble hR = (ER + pR) / rhoR;
98 
99  // Square root of rhoL and rhoR.
100  NekDouble srL = sqrt(rhoL);
101  NekDouble srR = sqrt(rhoR);
102  NekDouble srLR = srL + srR;
103 
104  // Velocity Roe averages
105  NekDouble uRoe = (srL * uL + srR * uR) / srLR;
106  NekDouble vRoe = (srL * vL + srR * vR) / srLR;
107  NekDouble wRoe = (srL * wL + srR * wR) / srLR;
108  NekDouble hRoe = (srL * hL + srR * hR) / srLR;
109  NekDouble cRoe = sqrt((gamma - 1.0)*(hRoe - 0.5 *
110  (uRoe * uRoe + vRoe * vRoe + wRoe * wRoe)));
111 
112  // Minimum and maximum wave speeds
113  NekDouble S = std::max(uRoe+cRoe, std::max(uR+cR, -uL+cL));
114  NekDouble sign = 1.0;
115 
116  if(S == -uL+cL)
117  {
118  sign = -1.0;
119  }
120 
121  // Lax-Friedrichs Riemann rho flux
122  rhof = 0.5 * ((rhouL + rhouR) - sign * S * (rhoR -rhoL));
123 
124  // Lax-Friedrichs Riemann rhou flux
125  rhouf = 0.5 * ((rhoL * uL * uL + pL + rhoR * uR * uR + pR) -
126  sign * S * (rhouR - rhouL));
127 
128  // Lax-Friedrichs Riemann rhov flux
129  rhovf = 0.5 * ((rhoL * uL * vL + rhoR * uR * vR) -
130  sign * S * (rhovR - rhovL));
131 
132  // Lax-Friedrichs Riemann rhow flux
133  rhowf = 0.5 * ((rhoL * uL * wL + rhoR * uR * wR) -
134  sign * S * (rhowR - rhowL));
135 
136  // Lax-Friedrichs Riemann E flux
137  Ef = 0.5 * ((uL * (EL + pL) + uR * (ER + pR)) -
138  sign * S * (ER - EL));
139  }
140 
141  void LaxFriedrichsSolver::v_PointSolveVisc(
142  NekDouble rhoL, NekDouble rhouL, NekDouble rhovL, NekDouble rhowL, NekDouble EL, NekDouble EpsL,
143  NekDouble rhoR, NekDouble rhouR, NekDouble rhovR, NekDouble rhowR, NekDouble ER, NekDouble EpsR,
144  NekDouble &rhof, NekDouble &rhouf, NekDouble &rhovf, NekDouble &rhowf, NekDouble &Ef, NekDouble &Epsf)
145  {
146  static NekDouble gamma = m_params["gamma"]();
147 
148  // Left and right velocities
149  NekDouble uL = rhouL / rhoL;
150  NekDouble vL = rhovL / rhoL;
151  NekDouble wL = rhowL / rhoL;
152  NekDouble uR = rhouR / rhoR;
153  NekDouble vR = rhovR / rhoR;
154  NekDouble wR = rhowR / rhoR;
155 
156  // Left and right pressures
157  NekDouble pL = (gamma - 1.0) *
158  (EL - 0.5 * (rhouL*uL + rhovL*vL + rhowL*wL));
159 
160  NekDouble pR = (gamma - 1.0) *
161  (ER - 0.5 * (rhouR*uR + rhovR*vR + rhowR*wR));
162 
163  // Left and right speeds of sound
164  NekDouble cL = sqrt(gamma * pL / rhoL);
165  NekDouble cR = sqrt(gamma * pR / rhoR);
166 
167  // Left and right entalpies
168  NekDouble hL = (EL + pL) / rhoL;
169  NekDouble hR = (ER + pR) / rhoR;
170 
171  // Square root of rhoL and rhoR.
172  NekDouble srL = sqrt(rhoL);
173  NekDouble srR = sqrt(rhoR);
174  NekDouble srLR = srL + srR;
175 
176  // Velocity Roe averages
177  NekDouble uRoe = (srL * uL + srR * uR) / srLR;
178  NekDouble vRoe = (srL * vL + srR * vR) / srLR;
179  NekDouble wRoe = (srL * wL + srR * wR) / srLR;
180  NekDouble hRoe = (srL * hL + srR * hR) / srLR;
181  NekDouble cRoe = sqrt((gamma - 1.0)*(hRoe - 0.5 *
182  (uRoe * uRoe + vRoe * vRoe + wRoe * wRoe)));
183 
184  // Minimum and maximum wave speeds
185  NekDouble S = std::max(uRoe+cRoe, std::max(uR+cR, -uL+cL));
186  NekDouble sign = 1.0;
187 
188  if(S == -uL+cL)
189  {
190  sign = -1.0;
191  }
192 
193  // Lax-Friedrichs Riemann rho flux
194  rhof = 0.5 * ((rhouL + rhouR) - sign * S * (rhoR -rhoL));
195 
196  // Lax-Friedrichs Riemann rhou flux
197  rhouf = 0.5 * ((rhoL * uL * uL + pL + rhoR * uR * uR + pR) -
198  sign * S * (rhouR - rhouL));
199 
200  // Lax-Friedrichs Riemann rhov flux
201  rhovf = 0.5 * ((rhoL * uL * vL + rhoR * uR * vR) -
202  sign * S * (rhovR - rhovL));
203 
204  // Lax-Friedrichs Riemann rhow flux
205  rhowf = 0.5 * ((rhoL * uL * wL + rhoR * uR * wR) -
206  sign * S * (rhowR - rhowL));
207 
208  // Lax-Friedrichs Riemann E flux
209  Ef = 0.5 * ((uL * (EL + pL) + uR * (ER + pR)) -
210  sign * S * (ER - EL));
211 
212  Epsf = 0.5 * ((EpsL + EpsR) -
213  sign * S * (EpsR - EpsL));
214  }
215 
216 }
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