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CompressibleFlowSolver/RiemannSolvers/HLLCSolver.cpp
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1 ///////////////////////////////////////////////////////////////////////////////
2 //
3 // File: HLLCSolver.cpp
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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: HLLC Riemann solver.
33 //
34 ///////////////////////////////////////////////////////////////////////////////
35 
36 #include <CompressibleFlowSolver/RiemannSolvers/HLLCSolver.h>
37 
38 namespace Nektar
39 {
40  std::string HLLCSolver::solverName =
41  SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
42  "HLLC", HLLCSolver::create, "HLLC Riemann solver");
43 
44  HLLCSolver::HLLCSolver() : CompressibleSolver()
45  {
46 
47  }
48 
49  /**
50  * @brief HLLC Riemann solver
51  *
52  * @param rhoL Density left state.
53  * @param rhoR Density right state.
54  * @param rhouL x-momentum component left state.
55  * @param rhouR x-momentum component right state.
56  * @param rhovL y-momentum component left state.
57  * @param rhovR y-momentum component right state.
58  * @param rhowL z-momentum component left state.
59  * @param rhowR z-momentum component right state.
60  * @param EL Energy left state.
61  * @param ER Energy right state.
62  * @param rhof Computed Riemann flux for density.
63  * @param rhouf Computed Riemann flux for x-momentum component
64  * @param rhovf Computed Riemann flux for y-momentum component
65  * @param rhowf Computed Riemann flux for z-momentum component
66  * @param Ef Computed Riemann flux for energy.
67  */
68  void HLLCSolver::v_PointSolve(
69  NekDouble rhoL, NekDouble rhouL, NekDouble rhovL, NekDouble rhowL, NekDouble EL,
70  NekDouble rhoR, NekDouble rhouR, NekDouble rhovR, NekDouble rhowR, NekDouble ER,
71  NekDouble &rhof, NekDouble &rhouf, NekDouble &rhovf, NekDouble &rhowf, NekDouble &Ef)
72  {
73  static NekDouble gamma = m_params["gamma"]();
74 
75  // Left and Right velocities
76  NekDouble uL = rhouL / rhoL;
77  NekDouble vL = rhovL / rhoL;
78  NekDouble wL = rhowL / rhoL;
79  NekDouble uR = rhouR / rhoR;
80  NekDouble vR = rhovR / rhoR;
81  NekDouble wR = rhowR / rhoR;
82 
83  // Left and right pressure, sound speed and enthalpy.
84  NekDouble pL = (gamma - 1.0) *
85  (EL - 0.5 * (rhouL * uL + rhovL * vL + rhowL * wL));
86  NekDouble pR = (gamma - 1.0) *
87  (ER - 0.5 * (rhouR * uR + rhovR * vR + rhowR * wR));
88  NekDouble cL = sqrt(gamma * pL / rhoL);
89  NekDouble cR = sqrt(gamma * pR / rhoR);
90  NekDouble hL = (EL + pL) / rhoL;
91  NekDouble hR = (ER + pR) / rhoR;
92 
93  // Square root of rhoL and rhoR.
94  NekDouble srL = sqrt(rhoL);
95  NekDouble srR = sqrt(rhoR);
96  NekDouble srLR = srL + srR;
97 
98  // Velocity Roe averages
99  NekDouble uRoe = (srL * uL + srR * uR) / srLR;
100  NekDouble vRoe = (srL * vL + srR * vR) / srLR;
101  NekDouble wRoe = (srL * wL + srR * wR) / srLR;
102  NekDouble hRoe = (srL * hL + srR * hR) / srLR;
103  NekDouble cRoe = sqrt((gamma - 1.0)*(hRoe - 0.5 *
104  (uRoe * uRoe + vRoe * vRoe + wRoe * wRoe)));
105 
106  // Maximum wave speeds
107  NekDouble SL = std::min(uL-cL, uRoe-cRoe);
108  NekDouble SR = std::max(uR+cR, uRoe+cRoe);
109 
110  // HLLC Riemann fluxes (positive case)
111  if (SL >= 0)
112  {
113  rhof = rhouL;
114  rhouf = rhouL * uL + pL;
115  rhovf = rhouL * vL;
116  rhowf = rhouL * wL;
117  Ef = uL * (EL + pL);
118  }
119  // HLLC Riemann fluxes (negative case)
120  else if (SR <= 0)
121  {
122  rhof = rhouR;
123  rhouf = rhouR * uR + pR;
124  rhovf = rhouR * vR;
125  rhowf = rhouR * wR;
126  Ef = uR * (ER + pR);
127  }
128  // HLLC Riemann fluxes (general case (SL < 0 | SR > 0)
129  else
130  {
131  NekDouble SM = (pR - pL + rhouL * (SL - uL) - rhouR * (SR - uR)) /
132  (rhoL * (SL - uL) - rhoR * (SR - uR));
133  NekDouble rhoML = rhoL * (SL - uL) / (SL - SM);
134  NekDouble rhouML = rhoML * SM;
135  NekDouble rhovML = rhoML * vL;
136  NekDouble rhowML = rhoML * wL;
137  NekDouble EML = rhoML * (EL / rhoL +
138  (SM - uL) * (SM + pL / (rhoL * (SL - uL))));
139 
140  NekDouble rhoMR = rhoR * (SR - uR) / (SR - SM);
141  NekDouble rhouMR = rhoMR * SM;
142  NekDouble rhovMR = rhoMR * vR;
143  NekDouble rhowMR = rhoMR * wR;
144  NekDouble EMR = rhoMR * (ER / rhoR +
145  (SM - uR) * (SM + pR / (rhoR * (SR - uR))));
146 
147  if (SL < 0.0 && SM >= 0.0)
148  {
149  rhof = rhouL + SL * (rhoML - rhoL);
150  rhouf = rhouL * uL + pL + SL * (rhouML - rhouL);
151  rhovf = rhouL * vL + SL * (rhovML - rhovL);
152  rhowf = rhouL * wL + SL * (rhowML - rhowL);
153  Ef = uL * (EL + pL) + SL * (EML - EL);
154  }
155  else if(SM < 0.0 && SR > 0.0)
156  {
157  rhof = rhouR + SR * (rhoMR - rhoR);
158  rhouf = rhouR * uR + pR + SR * (rhouMR - rhouR);
159  rhovf = rhouR * vR + SR * (rhovMR - rhovR);
160  rhowf = rhouR * wR + SR * (rhowMR - rhowR);
161  Ef = uR * (ER + pR) + SR * (EMR - ER);
162  }
163  }
164  }
165 
166  void HLLCSolver::v_PointSolveVisc(
167  NekDouble rhoL, NekDouble rhouL, NekDouble rhovL, NekDouble rhowL, NekDouble EL, NekDouble EpsL,
168  NekDouble rhoR, NekDouble rhouR, NekDouble rhovR, NekDouble rhowR, NekDouble ER, NekDouble EpsR,
169  NekDouble &rhof, NekDouble &rhouf, NekDouble &rhovf, NekDouble &rhowf, NekDouble &Ef, NekDouble &Epsf)
170  {
171  static NekDouble gamma = m_params["gamma"]();
172 
173  // Left and Right velocities
174  NekDouble uL = rhouL / rhoL;
175  NekDouble vL = rhovL / rhoL;
176  NekDouble wL = rhowL / rhoL;
177  NekDouble uR = rhouR / rhoR;
178  NekDouble vR = rhovR / rhoR;
179  NekDouble wR = rhowR / rhoR;
180 
181  // Left and right pressure, sound speed and enthalpy.
182  NekDouble pL = (gamma - 1.0) *
183  (EL - 0.5 * (rhouL * uL + rhovL * vL + rhowL * wL));
184  NekDouble pR = (gamma - 1.0) *
185  (ER - 0.5 * (rhouR * uR + rhovR * vR + rhowR * wR));
186  NekDouble cL = sqrt(gamma * pL / rhoL);
187  NekDouble cR = sqrt(gamma * pR / rhoR);
188  NekDouble hL = (EL + pL) / rhoL;
189  NekDouble hR = (ER + pR) / rhoR;
190 
191  // Square root of rhoL and rhoR.
192  NekDouble srL = sqrt(rhoL);
193  NekDouble srR = sqrt(rhoR);
194  NekDouble srLR = srL + srR;
195 
196  // Velocity Roe averages
197  NekDouble uRoe = (srL * uL + srR * uR) / srLR;
198  NekDouble vRoe = (srL * vL + srR * vR) / srLR;
199  NekDouble wRoe = (srL * wL + srR * wR) / srLR;
200  NekDouble hRoe = (srL * hL + srR * hR) / srLR;
201  NekDouble cRoe = sqrt((gamma - 1.0)*(hRoe - 0.5 *
202  (uRoe * uRoe + vRoe * vRoe + wRoe * wRoe)));
203 
204  // Maximum wave speeds
205  NekDouble SL = std::min(uL-cL, uRoe-cRoe);
206  NekDouble SR = std::max(uR+cR, uRoe+cRoe);
207 
208  // HLLC Riemann fluxes (positive case)
209  if (SL >= 0)
210  {
211  rhof = rhouL;
212  rhouf = rhouL * uL + pL;
213  rhovf = rhouL * vL;
214  rhowf = rhouL * wL;
215  Ef = uL * (EL + pL);
216  Epsf = 0.0;
217  }
218  // HLLC Riemann fluxes (negative case)
219  else if (SR <= 0)
220  {
221  rhof = rhouR;
222  rhouf = rhouR * uR + pR;
223  rhovf = rhouR * vR;
224  rhowf = rhouR * wR;
225  Ef = uR * (ER + pR);
226  Epsf = 0.0;
227  }
228  // HLLC Riemann fluxes (general case (SL < 0 | SR > 0)
229  else
230  {
231  NekDouble SM = (pR - pL + rhouL * (SL - uL) - rhouR * (SR - uR)) /
232  (rhoL * (SL - uL) - rhoR * (SR - uR));
233  NekDouble rhoML = rhoL * (SL - uL) / (SL - SM);
234  NekDouble rhouML = rhoML * SM;
235  NekDouble rhovML = rhoML * vL;
236  NekDouble rhowML = rhoML * wL;
237  NekDouble EML = rhoML * (EL / rhoL +
238  (SM - uL) * (SM + pL / (rhoL * (SL - uL))));
239  NekDouble EpsML = EpsL * (SL - uL) / (SL - SM);
240 
241  NekDouble rhoMR = rhoR * (SR - uR) / (SR - SM);
242  NekDouble rhouMR = rhoMR * SM;
243  NekDouble rhovMR = rhoMR * vR;
244  NekDouble rhowMR = rhoMR * wR;
245  NekDouble EMR = rhoMR * (ER / rhoR +
246  (SM - uR) * (SM + pR / (rhoR * (SR - uR))));
247  NekDouble EpsMR = EpsR * (SL - uR) / (SL - SM);
248 
249  if (SL < 0.0 && SM >= 0.0)
250  {
251  rhof = rhouL + SL * (rhoML - rhoL);
252  rhouf = rhouL * uL + pL + SL * (rhouML - rhouL);
253  rhovf = rhouL * vL + SL * (rhovML - rhovL);
254  rhowf = rhouL * wL + SL * (rhowML - rhowL);
255  Ef = uL * (EL + pL) + SL * (EML - EL);
256  Epsf = 0.0 + SL * (EpsML - EpsL);
257  }
258  else if(SM < 0.0 && SR > 0.0)
259  {
260  rhof = rhouR + SR * (rhoMR - rhoR);
261  rhouf = rhouR * uR + pR + SR * (rhouMR - rhouR);
262  rhovf = rhouR * vR + SR * (rhovMR - rhovR);
263  rhowf = rhouR * wR + SR * (rhowMR - rhowR);
264  Ef = uR * (ER + pR) + SR * (EMR - ER);
265  Epsf = 0.0 + SR * (EpsMR - EpsR);
266  }
267  }
268  }
269 }
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