Line data Source code
1 : //
2 : // This implements the Riemann Roe solver.
3 : //
4 : // Notation and algorithm follow the presentation in Section 5.3.3
5 : // of *Computational Gasdynamics* by Culbert B. Laney (page 88)
6 : //
7 : // This solver uses an optional entropy fix
8 : // Option 1: chimeracfd method https://chimeracfd.com/programming/gryphon/fluxroe.html
9 : // Option 2: Eq. 4.3.67 in *Computational Fluid Dynamics for Engineers and Scientists* by Sreenivas Jayanti
10 : //
11 :
12 : #ifndef SOLVER_LOCAL_RIEMANN_ROE_H
13 : #define SOLVER_LOCAL_RIEMANN_ROE_H
14 :
15 : #include "IO/ParmParse.H"
16 : #include "Solver/Local/Riemann/Riemann.H"
17 :
18 : /// A bunch of solvers
19 : namespace Solver
20 : {
21 : /// Local solvers
22 : namespace Local
23 : {
24 :
25 : namespace Riemann
26 : {
27 :
28 : /// Roe Riemann Solver based on Gas Dynamics - Culbert B. Laney
29 : class Roe : public Riemann
30 : {
31 : public:
32 :
33 :
34 : static constexpr const char* name = "roe";
35 6 : Roe (IO::ParmParse &pp, std::string name)
36 30 : {pp_queryclass(name,*this);}
37 : Roe (IO::ParmParse &pp)
38 : {pp_queryclass(*this);}
39 2 : Roe ()
40 2 : {
41 2 : IO::ParmParse pp;
42 6 : pp_queryclass(*this);
43 2 : }
44 :
45 : int verbose = 0;
46 : int entropy_fix = 0;
47 : int lowmach = 0;
48 : Set::Scalar phi = NAN;
49 :
50 8 : static void Parse(Roe & value, IO::ParmParse & pp)
51 : {
52 : // enable to dump diagnostic data if the roe solver fails
53 48 : pp.query_default("verbose", value.verbose, 1);
54 : // apply entropy fix if tru
55 48 : pp.query_default("entropy_fix", value.entropy_fix, false);
56 :
57 : // Apply the lowmach fix descripte in Rieper 2010
58 : // "A low-Mach number fix for Roe’s approximate Riemann solver"
59 40 : pp.query_default("lowmach",value.lowmach,false);
60 :
61 :
62 8 : if (value.entropy_fix == 1)
63 4 : Util::Warning(INFO,"The entropy fix is experimental and should be used with caution");
64 7 : else if (value.entropy_fix == 2)
65 4 : Util::Warning(INFO,"The entropy fix is experimental and should be used with caution. Has previously caused errors with FlowDrivenCavity regression test");
66 8 : }
67 :
68 36556816 : virtual Flux Solve(State lo, State hi, Set::Scalar gamma, Set::Scalar p_ref, Set::Scalar small) override
69 : {
70 36556816 : Set::Scalar rho_L = lo.rho , rho_R = hi.rho;
71 36556816 : Set::Scalar Mn_L = lo.M_normal , Mn_R = hi.M_normal ;
72 36556816 : Set::Scalar Mt_L = lo.M_tangent , Mt_R = hi.M_tangent ;
73 36556816 : Set::Scalar E_L = lo.E , E_R = hi.E ;
74 :
75 : // Ensure no negative densities
76 36556816 : rho_L = std::max(0.0,rho_L);
77 36556816 : rho_R = std::max(0.0,rho_R);
78 :
79 : // STEP 1: Compute fluid primitives
80 36556816 : Set::Scalar ke_L = 0.5 * (Mn_L * Mn_L /*+ Mt_L * Mt_L*/) / (rho_L+small); // KE per unit volume
81 36556816 : Set::Scalar ue_L = E_L - ke_L; // IE per unit volume
82 36556816 : Set::Scalar p_L = (gamma - 1.0) * ue_L + p_ref; // pressure
83 36556816 : Set::Scalar h_TL = (ke_L + ue_L + p_L) / (rho_L+small); // specific stagnation enthalpy (per unit mass)
84 :
85 36556816 : Set::Scalar ke_R = 0.5 * (Mn_R * Mn_R /*+ Mt_R * Mt_R*/) / (rho_R+small);
86 36556816 : Set::Scalar ue_R = E_R - ke_R;
87 36556816 : Set::Scalar p_R = (gamma - 1.0) * ue_R + p_ref;
88 36556816 : Set::Scalar h_TR = (ke_R + ue_R + p_R) / (rho_R+small);
89 :
90 36556816 : Set::Scalar u_L = Mn_L/(rho_L+small), u_R = Mn_R/(rho_R+small);
91 36556816 : Set::Scalar v_L = Mt_L/(rho_L+small), v_R = Mt_R/(rho_R+small);
92 :
93 : //
94 : // STEP 2: Compute Roe-averaged quantities
95 : //
96 36556816 : Set::Scalar rho_RL = std::sqrt(rho_L * rho_R);
97 36556816 : Set::Scalar u_RL = (std::sqrt(rho_L) * u_L + std::sqrt(rho_R) * u_R ) / (std::sqrt(rho_L) + std::sqrt(rho_R) + small);
98 36556816 : Set::Scalar h_RL = (std::sqrt(rho_L) * h_TL + std::sqrt(rho_R) * h_TR) / (std::sqrt(rho_L) + std::sqrt(rho_R) + small);
99 36556816 : Set::Scalar a_RL_sq = std::max(0.0,(gamma - 1.0) * (h_RL - 0.5 * u_RL * u_RL));
100 :
101 :
102 : #ifdef AMREX_DEBUG
103 : if (verbose && ((a_RL_sq<0) || (a_RL_sq!=a_RL_sq)))
104 : {
105 : Util::Message(INFO, "sound speed ", a_RL_sq);
106 :
107 : Util::Message(INFO, "mixed rho ", lo.rho, " ", hi.rho);
108 : Util::Message(INFO, "mixed Mn ", lo.M_normal, " ", hi.M_normal);
109 : Util::Message(INFO, "mixed Mt ", lo.M_tangent, " ", hi.M_tangent);
110 : Util::Message(INFO, "mixed E ", lo.E, " ", hi.E);
111 :
112 : Util::Message(INFO, "fluid rho ", rho_L, " ", rho_R);
113 : Util::Message(INFO, "fluid Mn ", Mn_L, " ", Mn_R);
114 : Util::Message(INFO, "fluid Mt ", Mt_L, " ", Mt_R);
115 : Util::Message(INFO, "fluid E ", E_L, " ", E_R);
116 :
117 : Util::Message(INFO, "fluid rho ", rho_L, " ", rho_R);
118 : Util::Message(INFO, "fluid u ", u_L, " ", u_R);
119 : Util::Message(INFO, "fluid v ", v_L, " ", v_R);
120 : Util::Message(INFO, "fluid p ", p_L, " ", p_R);
121 : }
122 : Util::AssertException(INFO,TEST(a_RL_sq==a_RL_sq)," a_RL_sq is nan/inf; (a_RL_sq=", a_RL_sq,")");
123 : Util::AssertException(INFO,TEST(a_RL_sq>=0), " a_RL_sq is negative; (a_RL_sq=(",a_RL_sq,")");
124 : #endif
125 :
126 36556816 : Set::Scalar a_RL = std::sqrt(a_RL_sq) + small;
127 :
128 : //
129 : // STEP 3: Compute Roe-averaged wave speeds
130 : //
131 36556816 : Set::Scalar lambda1 = u_RL; // 5.53a
132 36556816 : Set::Scalar lambda2 = u_RL + a_RL; // 5.53b
133 36556816 : Set::Scalar lambda3 = u_RL - a_RL; // 5.53c
134 :
135 : //
136 : // STEP 4: Compute wave strengths
137 : //
138 36556816 : Set::Scalar deltarho= rho_R - rho_L;
139 36556816 : Set::Scalar deltap = p_R - p_L;
140 36556816 : Set::Scalar deltau = u_R - u_L;
141 :
142 36556816 : if (lowmach)
143 : {
144 0 : Set::Scalar v_RL = (std::sqrt(rho_L) * v_L + std::sqrt(rho_R) * v_R ) /
145 0 : (std::sqrt(rho_L) + std::sqrt(rho_R) + small);
146 0 : Set::Scalar Ma = (std::abs(u_RL) + std::abs(v_RL)) / (a_RL + small);
147 0 : Ma = std::min(Ma, 1.0);
148 0 : deltau *= Ma;
149 : }
150 :
151 36556816 : Set::Scalar deltav1 = deltarho - deltap / (a_RL_sq + small); // 5.54a
152 36556816 : Set::Scalar deltav2 = deltau + deltap / (rho_RL * a_RL + small); // 5.54b
153 36556816 : Set::Scalar deltav3 = deltau - deltap / (rho_RL * a_RL + small); // 5.54c
154 :
155 : //
156 : // STEP 5: Compute the right eigenvectors
157 : //
158 36556816 : Set::Scalar r11 = 1.0;
159 36556816 : Set::Scalar r12 = u_RL;
160 36556816 : Set::Scalar r13 = 0.5*u_RL*u_RL;
161 36556816 : Set::Scalar r21 = 0.5*rho_RL/a_RL;
162 36556816 : Set::Scalar r22 = 0.5*rho_RL/a_RL * ( u_RL + a_RL );
163 36556816 : Set::Scalar r23 = 0.5*rho_RL/a_RL * ( h_RL + a_RL*u_RL );
164 36556816 : Set::Scalar r31 = -0.5*rho_RL/a_RL;
165 36556816 : Set::Scalar r32 = -0.5*rho_RL/a_RL * ( u_RL - a_RL );
166 36556816 : Set::Scalar r33 = -0.5*rho_RL/a_RL * ( h_RL - a_RL*u_RL );
167 :
168 : //
169 : // STEP 6: Compute solution - not needed since fluxes will be computed in STEP 7
170 : //
171 :
172 : //
173 : // ROE ENTROPY FIX (Source cited in header comments)
174 : //
175 36556816 : if (entropy_fix == 1) { // chimeracfd
176 8192000 : lambda1 = fabs(lambda1);
177 8192000 : lambda2 = fabs(lambda2);
178 8192000 : lambda3 = fabs(lambda3);
179 8192000 : if ( lambda1 < deltau ) lambda1 = 0.5*(lambda1*lambda1 + deltau*deltau)/deltau;
180 8192000 : if ( lambda2 < deltau ) lambda2 = 0.5*(lambda2*lambda2 + deltau*deltau)/deltau;
181 8192000 : if ( lambda3 < deltau ) lambda3 = 0.5*(lambda3*lambda3 + deltau*deltau)/deltau;
182 : }
183 28364816 : else if (entropy_fix == 2) { // Jayanti
184 8192000 : Set::Scalar a_L = std::sqrt(gamma * p_L / (rho_L + small)); // sound speed
185 8192000 : Set::Scalar a_R = std::sqrt(gamma * p_R / (rho_R + small));
186 8192000 : Set::Scalar lambda1_L = u_L; Set::Scalar lambda1_R = u_R; // eigenvalues
187 8192000 : Set::Scalar lambda2_L = u_L + a_L; Set::Scalar lambda2_R = u_R + a_R;
188 8192000 : Set::Scalar lambda3_L = u_L - a_L; Set::Scalar lambda3_R = u_R - a_R;
189 8192000 : Set::Scalar fix1 = std::max(0.0, std::max(lambda1 - lambda1_L, lambda1_R - lambda1));
190 8192000 : Set::Scalar fix2 = std::max(0.0, std::max(lambda2 - lambda2_L, lambda2_R - lambda2));
191 8192000 : Set::Scalar fix3 = std::max(0.0, std::max(lambda3 - lambda3_L, lambda3_R - lambda3));
192 8192000 : if ( lambda1 < fix1 ) lambda1 = fix1;
193 8192000 : if ( lambda2 < fix2 ) lambda2 = fix2;
194 8192000 : if ( lambda3 < fix3 ) lambda3 = fix3;
195 : }
196 :
197 : //
198 : // STEP 7: Compute fluxes
199 : //
200 36556816 : Flux fl;
201 :
202 36556816 : fl.mass = (0.5*(rho_L*u_L + rho_R*u_R) - 0.5*(
203 36556816 : r11*fabs(lambda1)*deltav1 +
204 36556816 : r21*fabs(lambda2)*deltav2 +
205 36556816 : r31*fabs(lambda3)*deltav3)
206 : );
207 :
208 36556816 : if (fl.mass != fl.mass)
209 : {
210 0 : if (verbose)
211 : {
212 0 : Util::ParallelMessage(INFO,"hi ", hi);
213 0 : Util::ParallelMessage(INFO,"lo ", lo);
214 0 : Util::ParallelMessage(INFO,"rho_R ", rho_R);
215 0 : Util::ParallelMessage(INFO,"rho_L ", rho_L);
216 0 : Util::ParallelMessage(INFO,"rho_RL ", rho_RL);
217 0 : Util::ParallelMessage(INFO,"u_R ", u_R);
218 0 : Util::ParallelMessage(INFO,"u_L ", u_L);
219 0 : Util::ParallelMessage(INFO,"u_RL ", u_RL);
220 0 : Util::ParallelMessage(INFO,"a_RL ", a_RL);
221 0 : Util::ParallelMessage(INFO,"lambda1 ", lambda1);
222 0 : Util::ParallelMessage(INFO,"lambda2 ", lambda2);
223 0 : Util::ParallelMessage(INFO,"lambda3 ", lambda3);
224 0 : Util::ParallelMessage(INFO,"deltav1 ", deltav1);
225 0 : Util::ParallelMessage(INFO,"deltav2 ", deltav2);
226 0 : Util::ParallelMessage(INFO,"deltav3 ", deltav3);
227 : }
228 0 : Util::Exception(INFO);
229 : }
230 :
231 :
232 36556816 : fl.momentum_normal = ( 0.5*(rho_L*u_L*u_L + p_L + rho_R*u_R*u_R + p_R) - 0.5*(
233 36556816 : r12*fabs(lambda1)*deltav1 +
234 36556816 : r22*fabs(lambda2)*deltav2 +
235 36556816 : r32*fabs(lambda3)*deltav3)
236 : );
237 :
238 :
239 36556816 : fl.energy = ( 0.5*(u_L*(ke_L + p_L + ue_L) + u_R*(ke_R + p_R + ue_R)) - 0.5*
240 : (
241 36556816 : r13*fabs(lambda1)*deltav1 +
242 36556816 : r23*fabs(lambda2)*deltav2 +
243 36556816 : r33*fabs(lambda3)*deltav3)
244 : );
245 :
246 : //
247 : // (Update the tangential momentum flux)
248 : //
249 36556816 : fl.momentum_tangent = 0.5 * (rho_L * u_L * v_L + rho_R * u_R * v_R);
250 :
251 73113632 : return fl;
252 : }
253 :
254 :
255 2 : static int Test()
256 : {
257 2 : Roe solver;
258 :
259 :
260 2 : int failed = 0;
261 :
262 2 : Set::Scalar gamma = 1.4;
263 2 : Set::Scalar pref = 10.0;
264 2 : Set::Scalar small = 1E-10;
265 :
266 : // Test 1: Tangential Velocity Difference - No Normal Flux
267 : try {
268 2 : State left (1.0, 1.0, 0.0, 1.0);
269 2 : State center(1.0, 1.0, 1.0, 1.0);
270 2 : State right (1.0, 1.0, 2.0, 1.0);
271 2 : Flux fluxlo = solver.Solve(center, right, gamma, pref, small);
272 2 : Flux fluxhi = solver.Solve(left, center, gamma, pref, small);
273 :
274 2 : if (fabs(fluxhi.mass - fluxlo.mass) > 1E-10
275 2 : || fabs(fluxhi.momentum_normal - fluxlo.momentum_normal) > 1E-10
276 2 : || fabs(fluxhi.energy - fluxlo.energy) > 1E-10) {
277 0 : Util::Warning(INFO, "left: ",left);
278 0 : Util::Warning(INFO, "center: ",center);
279 0 : Util::Warning(INFO, "right: ",right);
280 0 : Util::Warning(INFO, "Fluxlo: ",fluxlo);
281 0 : Util::Warning(INFO, "Fluxhi: ",fluxhi);
282 0 : Util::Exception(INFO, "Tangential velocity difference incorrectly affecting normal flux.");
283 : }
284 4 : Util::Test::SubMessage("Test 1: Tangential velocity should induce no normal flux",0);
285 0 : } catch (const std::runtime_error& e)
286 : {
287 0 : failed++;
288 0 : Util::Test::SubMessage("Test 1: Tangential velocity should induce no normal flux",1);
289 0 : }
290 :
291 : // Test 2: Pure Transverse Velocity Difference
292 : try {
293 2 : State left (1.0, 0.0, 0.0, 1.0);
294 2 : State center(1.0, 0.0, 1.0, 1.0);
295 2 : State right (1.0, 0.0, 2.0, 1.0);
296 2 : Flux fluxlo = solver.Solve(left, center, gamma, pref, small);
297 2 : Flux fluxhi = solver.Solve(center, right, gamma, pref, small);
298 2 : if (fabs(fluxhi.mass - fluxlo.mass) > 1E-10
299 2 : || fabs(fluxhi.momentum_normal - fluxlo.momentum_normal) > 1E-10
300 2 : || fabs(fluxhi.energy - fluxlo.energy) > 1E-10) {
301 0 : Util::Warning(INFO, "left: ",left);
302 0 : Util::Warning(INFO, "center: ",center);
303 0 : Util::Warning(INFO, "right: ",right);
304 0 : Util::Warning(INFO, "Fluxhi: ",fluxhi);
305 0 : Util::Warning(INFO, "Fluxlo: ",fluxlo);
306 0 : Util::Exception(INFO, "Pure transverse velocity difference affecting normal flux.");
307 : }
308 4 : Util::Test::SubMessage("Test 2: Pure transverse velocity difference",0);
309 0 : } catch (const std::runtime_error& e)
310 : {
311 0 : failed++;
312 0 : Util::Test::SubMessage("Test 2: Pure transverse velocity difference",1);
313 0 : }
314 :
315 : // Test 3: Symmetry Test (no flux across identical states)
316 : try {
317 2 : State left(1.0, 0.0, 0.0, 1.0);
318 2 : State center(1.0, 0.0, 0.0, 1.0);
319 2 : State right(1.0, 0.0, 0.0, 1.0);
320 2 : Flux fluxhi = solver.Solve(center, right, gamma, pref, small);
321 2 : Flux fluxlo = solver.Solve(left, center, gamma, pref, small);
322 2 : if (fabs(fluxhi.mass - fluxlo.mass) > 1E-10 // no change in mass flux
323 2 : || fabs(fluxhi.momentum_normal - fluxlo.momentum_normal) > 1E-10 // no change in momentum flux
324 2 : || fabs(fluxhi.momentum_tangent) > 1E-10 // zero tangent flux
325 2 : || fabs(fluxlo.momentum_tangent) > 1E-10 // zero tangent flux
326 2 : || fabs(fluxhi.energy-fluxlo.energy) > 1E-10 // no change in energy flux
327 : ) {
328 0 : Util::Warning(INFO, "left: ",left);
329 0 : Util::Warning(INFO, "right: ",right);
330 0 : Util::Warning(INFO, "Fluxhi: ",fluxhi);
331 0 : Util::Warning(INFO, "Fluxlo: ",fluxlo);
332 0 : Util::Exception(INFO, "Symmetric states should result in zero flux.");
333 : }
334 4 : Util::Test::SubMessage("Test 3: Constant states induces no flux difference",0);
335 0 : } catch (const std::runtime_error& e)
336 : {
337 0 : failed++;
338 0 : Util::Test::SubMessage("Test 3: Constant states induces no flux difference",1);
339 0 : }
340 :
341 : // Test 4: Uniform Flow Test (no flux across uniform flow)
342 : try {
343 2 : State left (1.0, 1.0, 0.5, 1.0);
344 2 : State center(1.0, 1.0, 0.5, 1.0);
345 2 : State right (1.0, 1.0, 0.5, 1.0);
346 2 : Flux fluxhi = solver.Solve(center, right, gamma, pref, small);
347 2 : Flux fluxlo = solver.Solve(left, center, gamma, pref, small);
348 2 : if (fabs(fluxhi.mass - fluxlo.mass) > 1E-10 ||
349 2 : fabs(fluxhi.momentum_normal - fluxlo.momentum_normal) > 1E-10 ||
350 2 : fabs(fluxhi.energy - fluxlo.energy) > 1E-10) {
351 0 : Util::Warning(INFO, "left: ",left);
352 0 : Util::Warning(INFO, "center: ",center);
353 0 : Util::Warning(INFO, "right: ",right);
354 0 : Util::Warning(INFO, "Fluxlo: ",fluxlo);
355 0 : Util::Warning(INFO, "Fluxhi: ",fluxhi);
356 0 : Util::Exception(INFO, "Uniform flow should result in no flux.");
357 : }
358 4 : Util::Test::SubMessage("Test 4: Uniform flow should maintain constant flux",0);
359 0 : } catch (const std::runtime_error& e)
360 : {
361 0 : failed++;
362 0 : Util::Test::SubMessage("Test 4: Uniform flow should maintain constant flux",1);
363 0 : }
364 :
365 2 : return failed;
366 2 : }
367 : };
368 : }
369 : }
370 : }
371 :
372 : #endif
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