Nektar++
Static Public Member Functions | Static Public Attributes | Protected Member Functions | List of all members
Nektar::ExactSolverToro Class Reference

#include <ExactSolverToro.h>

Inheritance diagram for Nektar::ExactSolverToro:
[legend]

Static Public Member Functions

static RiemannSolverSharedPtr create (const LibUtilities::SessionReaderSharedPtr &pSession)
 

Static Public Attributes

static std::string solverName
 

Protected Member Functions

 ExactSolverToro (const LibUtilities::SessionReaderSharedPtr &pSession)
 
void v_PointSolve (NekDouble rhoL, NekDouble rhouL, NekDouble rhovL, NekDouble rhowL, NekDouble EL, NekDouble rhoR, NekDouble rhouR, NekDouble rhovR, NekDouble rhowR, NekDouble ER, NekDouble &rhof, NekDouble &rhouf, NekDouble &rhovf, NekDouble &rhowf, NekDouble &Ef) override
 Exact Riemann solver for the Euler equations. More...
 
- Protected Member Functions inherited from Nektar::CompressibleSolver
 CompressibleSolver (const LibUtilities::SessionReaderSharedPtr &pSession)
 Session ctor. More...
 
 CompressibleSolver ()
 Programmatic ctor. More...
 
void v_Solve (const int nDim, const Array< OneD, const Array< OneD, ND > > &Fwd, const Array< OneD, const Array< OneD, ND > > &Bwd, Array< OneD, Array< OneD, ND > > &flux) override
 
virtual void v_ArraySolve (const Array< OneD, const Array< OneD, ND > > &Fwd, const Array< OneD, const Array< OneD, ND > > &Bwd, Array< OneD, Array< OneD, ND > > &flux)
 
virtual void v_PointSolve (ND rhoL, ND rhouL, ND rhovL, ND rhowL, ND EL, ND rhoR, ND rhouR, ND rhovR, ND rhowR, ND ER, ND &rhof, ND &rhouf, ND &rhovf, ND &rhowf, ND &Ef)
 
ND GetRoeSoundSpeed (ND rhoL, ND pL, ND eL, ND HL, ND srL, ND rhoR, ND pR, ND eR, ND HR, ND srR, ND HRoe, ND URoe2, ND srLR)
 
- Protected Member Functions inherited from Nektar::SolverUtils::RiemannSolver
SOLVER_UTILS_EXPORT RiemannSolver ()
 
SOLVER_UTILS_EXPORT RiemannSolver (const LibUtilities::SessionReaderSharedPtr &pSession)
 
virtual SOLVER_UTILS_EXPORT ~RiemannSolver ()
 
virtual void v_Solve (const int nDim, const Array< OneD, const Array< OneD, NekDouble > > &Fwd, const Array< OneD, const Array< OneD, NekDouble > > &Bwd, Array< OneD, Array< OneD, NekDouble > > &flux)=0
 
SOLVER_UTILS_EXPORT void GenerateRotationMatrices (const Array< OneD, const Array< OneD, NekDouble > > &normals)
 Generate rotation matrices for 3D expansions. More...
 
void FromToRotation (Array< OneD, const NekDouble > &from, Array< OneD, const NekDouble > &to, NekDouble *mat)
 A function for creating a rotation matrix that rotates a vector from into another vector to. More...
 
SOLVER_UTILS_EXPORT void rotateToNormal (const Array< OneD, const Array< OneD, NekDouble > > &inarray, const Array< OneD, const Array< OneD, NekDouble > > &normals, const Array< OneD, const Array< OneD, NekDouble > > &vecLocs, Array< OneD, Array< OneD, NekDouble > > &outarray)
 Rotate a vector field to trace normal. More...
 
SOLVER_UTILS_EXPORT void rotateFromNormal (const Array< OneD, const Array< OneD, NekDouble > > &inarray, const Array< OneD, const Array< OneD, NekDouble > > &normals, const Array< OneD, const Array< OneD, NekDouble > > &vecLocs, Array< OneD, Array< OneD, NekDouble > > &outarray)
 Rotate a vector field from trace normal. More...
 
SOLVER_UTILS_EXPORT bool CheckScalars (std::string name)
 Determine whether a scalar has been defined in m_scalars. More...
 
SOLVER_UTILS_EXPORT bool CheckVectors (std::string name)
 Determine whether a vector has been defined in m_vectors. More...
 
SOLVER_UTILS_EXPORT bool CheckParams (std::string name)
 Determine whether a parameter has been defined in m_params. More...
 
SOLVER_UTILS_EXPORT bool CheckAuxScal (std::string name)
 Determine whether a scalar has been defined in m_auxScal. More...
 
SOLVER_UTILS_EXPORT bool CheckAuxVec (std::string name)
 Determine whether a vector has been defined in m_auxVec. More...
 
virtual SOLVER_UTILS_EXPORT void v_CalcFluxJacobian (const int nDim, const Array< OneD, const Array< OneD, NekDouble > > &Fwd, const Array< OneD, const Array< OneD, NekDouble > > &Bwd, const Array< OneD, const Array< OneD, NekDouble > > &normals, DNekBlkMatSharedPtr &FJac, DNekBlkMatSharedPtr &BJac)
 

Additional Inherited Members

- Public Member Functions inherited from Nektar::SolverUtils::RiemannSolver
SOLVER_UTILS_EXPORT void Solve (const int nDim, const Array< OneD, const Array< OneD, NekDouble > > &Fwd, const Array< OneD, const Array< OneD, NekDouble > > &Bwd, Array< OneD, Array< OneD, NekDouble > > &flux)
 Perform the Riemann solve given the forwards and backwards spaces. More...
 
template<typename FuncPointerT , typename ObjectPointerT >
void SetScalar (std::string name, FuncPointerT func, ObjectPointerT obj)
 
void SetScalar (std::string name, RSScalarFuncType fp)
 
template<typename FuncPointerT , typename ObjectPointerT >
void SetVector (std::string name, FuncPointerT func, ObjectPointerT obj)
 
void SetVector (std::string name, RSVecFuncType fp)
 
template<typename FuncPointerT , typename ObjectPointerT >
void SetParam (std::string name, FuncPointerT func, ObjectPointerT obj)
 
void SetParam (std::string name, RSParamFuncType fp)
 
template<typename FuncPointerT , typename ObjectPointerT >
void SetAuxScal (std::string name, FuncPointerT func, ObjectPointerT obj)
 
template<typename FuncPointerT , typename ObjectPointerT >
void SetAuxVec (std::string name, FuncPointerT func, ObjectPointerT obj)
 
void SetAuxVec (std::string name, RSVecFuncType fp)
 
std::map< std::string, RSScalarFuncType > & GetScalars ()
 
std::map< std::string, RSVecFuncType > & GetVectors ()
 
std::map< std::string, RSParamFuncType > & GetParams ()
 
SOLVER_UTILS_EXPORT void CalcFluxJacobian (const int nDim, const Array< OneD, const Array< OneD, NekDouble > > &Fwd, const Array< OneD, const Array< OneD, NekDouble > > &Bwd, DNekBlkMatSharedPtr &FJac, DNekBlkMatSharedPtr &BJac)
 Calculate the flux jacobian of Fwd and Bwd. More...
 
- Public Attributes inherited from Nektar::SolverUtils::RiemannSolver
int m_spacedim
 
- Protected Types inherited from Nektar::CompressibleSolver
using ND = NekDouble
 
- Protected Attributes inherited from Nektar::CompressibleSolver
bool m_pointSolve
 
EquationOfStateSharedPtr m_eos
 
bool m_idealGas
 
- Protected Attributes inherited from Nektar::SolverUtils::RiemannSolver
bool m_requiresRotation
 Indicates whether the Riemann solver requires a rotation to be applied to the velocity fields. More...
 
std::map< std::string, RSScalarFuncType > m_scalars
 Map of scalar function types. More...
 
std::map< std::string, RSVecFuncType > m_vectors
 Map of vector function types. More...
 
std::map< std::string, RSParamFuncType > m_params
 Map of parameter function types. More...
 
std::map< std::string, RSScalarFuncType > m_auxScal
 Map of auxiliary scalar function types. More...
 
std::map< std::string, RSVecFuncType > m_auxVec
 Map of auxiliary vector function types. More...
 
Array< OneD, Array< OneD, NekDouble > > m_rotMat
 Rotation matrices for each trace quadrature point. More...
 
Array< OneD, Array< OneD, Array< OneD, NekDouble > > > m_rotStorage
 Rotation storage. More...
 

Detailed Description

Definition at line 42 of file ExactSolverToro.h.

Constructor & Destructor Documentation

◆ ExactSolverToro()

Nektar::ExactSolverToro::ExactSolverToro ( const LibUtilities::SessionReaderSharedPtr &  pSession)
protected

Definition at line 46 of file ExactSolverToro.cpp.

48 : CompressibleSolver(pSession)
49{
50}
Nektar::CompressibleSolver::CompressibleSolver
CompressibleSolver()
Programmatic ctor.
Definition: CompressibleSolver.cpp:54

Referenced by create().

Member Function Documentation

◆ create()

static RiemannSolverSharedPtr Nektar::ExactSolverToro::create ( const LibUtilities::SessionReaderSharedPtr &  pSession)
inlinestatic

Definition at line 45 of file ExactSolverToro.h.

47 {
48 return RiemannSolverSharedPtr(new ExactSolverToro(pSession));
49 }
Nektar::ExactSolverToro::ExactSolverToro
ExactSolverToro(const LibUtilities::SessionReaderSharedPtr &pSession)
Definition: ExactSolverToro.cpp:46
Nektar::SolverUtils::RiemannSolverSharedPtr
std::shared_ptr< RiemannSolver > RiemannSolverSharedPtr
A shared pointer to an EquationSystem object.
Definition: RiemannSolver.h:195

References ExactSolverToro().

◆ v_PointSolve()

void Nektar::ExactSolverToro::v_PointSolve ( NekDouble  rhoL,
NekDouble  rhouL,
NekDouble  rhovL,
NekDouble  rhowL,
NekDouble  EL,
NekDouble  rhoR,
NekDouble  rhouR,
NekDouble  rhovR,
NekDouble  rhowR,
NekDouble  ER,
NekDouble &  rhof,
NekDouble &  rhouf,
NekDouble &  rhovf,
NekDouble &  rhowf,
NekDouble &  Ef 
)
overrideprotectedvirtual

Exact Riemann solver for the Euler equations.

This algorithm is transcribed from:

"Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction", E. F. Toro (3rd edition, 2009).

The full Fortran 77 routine can be found at the end of chapter 4 (section 4.9). This transcription is essentially the functions STARPU and SAMPLE glued together, and variable names are kept mostly the same. See the preceding chapter which explains the derivation of the solver. The routines PREFUN and GUESSP are kept separate and are reproduced above.

Parameters
rhoLDensity left state.
rhoRDensity right state.
rhouLx-momentum component left state.
rhouRx-momentum component right state.
rhovLy-momentum component left state.
rhovRy-momentum component right state.
rhowLz-momentum component left state.
rhowRz-momentum component right state.
ELEnergy left state.
EREnergy right state.
rhofComputed Riemann flux for density.
rhoufComputed Riemann flux for x-momentum component
rhovfComputed Riemann flux for y-momentum component
rhowfComputed Riemann flux for z-momentum component
EfComputed Riemann flux for energy.

Reimplemented from Nektar::CompressibleSolver.

Definition at line 168 of file ExactSolverToro.cpp.

173{
174 static NekDouble gamma = m_params["gamma"]();
175
176 // Left and right variables.
177 NekDouble uL = rhouL / rhoL;
178 NekDouble vL = rhovL / rhoL;
179 NekDouble wL = rhowL / rhoL;
180 NekDouble uR = rhouR / rhoR;
181 NekDouble vR = rhovR / rhoR;
182 NekDouble wR = rhowR / rhoR;
183
184 // Left and right pressure.
185 NekDouble pL =
186 (gamma - 1.0) * (EL - 0.5 * (rhouL * uL + rhovL * vL + rhowL * wL));
187 NekDouble pR =
188 (gamma - 1.0) * (ER - 0.5 * (rhouR * uR + rhovR * vR + rhowR * wR));
189
190 // Compute gammas.
191 NekDouble g[] = {gamma,
192 (gamma - 1.0) / (2.0 * gamma),
193 (gamma + 1.0) / (2.0 * gamma),
194 2.0 * gamma / (gamma - 1.0),
195 2.0 / (gamma - 1.0),
196 2.0 / (gamma + 1.0),
197 (gamma - 1.0) / (gamma + 1.0),
198 0.5 * (gamma - 1.0),
199 gamma - 1.0};
200
201 // Compute sound speeds.
202 NekDouble cL = sqrt(gamma * pL / rhoL);
203 NekDouble cR = sqrt(gamma * pR / rhoR);
204
205 ASSERTL0(g[4] * (cL + cR) > (uR - uL),
206 "Vacuum is generated by given data.");
207
208 // Guess initial pressure.
209 NekDouble pOld = guessp(g, rhoL, uL, pL, cL, rhoR, uR, pR, cR);
210 NekDouble uDiff = uR - uL;
211 NekDouble p, fL, fR, fLd, fRd, change;
212 int k;
213
214 // Newton-Raphson iteration for pressure in star region.
215 for (k = 0; k < NRITER; ++k)
216 {
217 prefun(g, pOld, rhoL, pL, cL, fL, fLd);
218 prefun(g, pOld, rhoR, pR, cR, fR, fRd);
219 p = pOld - (fL + fR + uDiff) / (fLd + fRd);
220 change = 2 * fabs((p - pOld) / (p + pOld));
221
222 if (change <= TOL)
223 {
224 break;
225 }
226
227 if (p < 0.0)
228 {
229 p = TOL;
230 }
231
232 pOld = p;
233 }
234
235 ASSERTL0(k < NRITER, "Divergence in Newton-Raphson scheme");
236
237 // Compute velocity in star region.
238 NekDouble u = 0.5 * (uL + uR + fR - fL);
239
240 // -- SAMPLE ROUTINE --
241 // The variable S aligns with the Fortran parameter S of the SAMPLE
242 // routine, but is hard-coded as 0 (and should be optimised out by the
243 // compiler). Since we are using a Godunov scheme we pick this as 0 (see
244 // chapter 6 of Toro 2009).
245 const NekDouble S = 0.0;
246
247 // Computed primitive variables.
248 NekDouble outRho, outU, outV, outW, outP;
249
250 if (S <= u)
251 {
252 if (p <= pL)
253 {
254 // Left rarefaction
255 NekDouble shL = uL - cL;
256 if (S <= shL)
257 {
258 // Sampled point is left data state.
259 outRho = rhoL;
260 outU = uL;
261 outV = vL;
262 outW = wL;
263 outP = pL;
264 }
265 else
266 {
267 NekDouble cmL = cL * pow(p / pL, g[1]);
268 NekDouble stL = u - cmL;
269
270 if (S > stL)
271 {
272 // Sampled point is star left state
273 outRho = rhoL * pow(p / pL, 1.0 / gamma);
274 outU = u;
275 outV = vL;
276 outW = wL;
277 outP = p;
278 }
279 else
280 {
281 // Sampled point is inside left fan
282 NekDouble c = g[5] * (cL + g[7] * (uL - S));
283 outRho = rhoL * pow(c / cL, g[4]);
284 outU = g[5] * (cL + g[7] * uL + S);
285 outV = vL;
286 outW = wL;
287 outP = pL * pow(c / cL, g[3]);
288 }
289 }
290 }
291 else
292 {
293 // Left shock
294 NekDouble pmL = p / pL;
295 NekDouble SL = uL - cL * sqrt(g[2] * pmL + g[1]);
296 if (S <= SL)
297 {
298 // Sampled point is left data state
299 outRho = rhoL;
300 outU = uL;
301 outV = vL;
302 outW = wL;
303 outP = pL;
304 }
305 else
306 {
307 // Sampled point is star left state
308 outRho = rhoL * (pmL + g[6]) / (pmL * g[6] + 1.0);
309 outU = u;
310 outV = vL;
311 outW = wL;
312 outP = p;
313 }
314 }
315 }
316 else
317 {
318 if (p > pR)
319 {
320 // Right shock
321 NekDouble pmR = p / pR;
322 NekDouble SR = uR + cR * sqrt(g[2] * pmR + g[1]);
323 if (S >= SR)
324 {
325 // Sampled point is right data state
326 outRho = rhoR;
327 outU = uR;
328 outV = vR;
329 outW = wR;
330 outP = pR;
331 }
332 else
333 {
334 // Sampled point is star right state
335 outRho = rhoR * (pmR + g[6]) / (pmR * g[6] + 1.0);
336 outU = u;
337 outV = vR;
338 outW = wR;
339 outP = p;
340 }
341 }
342 else
343 {
344 // Right rarefaction
345 NekDouble shR = uR + cR;
346
347 if (S >= shR)
348 {
349 // Sampled point is right data state
350 outRho = rhoR;
351 outU = uR;
352 outV = vR;
353 outW = wR;
354 outP = pR;
355 }
356 else
357 {
358 NekDouble cmR = cR * pow(p / pR, g[1]);
359 NekDouble stR = u + cmR;
360
361 if (S <= stR)
362 {
363 // Sampled point is star right state
364 outRho = rhoR * pow(p / pR, 1.0 / gamma);
365 outU = u;
366 outV = vR;
367 outW = wR;
368 outP = p;
369 }
370 else
371 {
372 // Sampled point is inside left fan
373 NekDouble c = g[5] * (cR - g[7] * (uR - S));
374 outRho = rhoR * pow(c / cR, g[4]);
375 outU = g[5] * (-cR + g[7] * uR + S);
376 outV = vR;
377 outW = wR;
378 outP = pR * pow(c / cR, g[3]);
379 }
380 }
381 }
382 }
383
384 // Transform computed primitive variables to fluxes.
385 rhof = outRho * outU;
386 rhouf = outP + outRho * outU * outU;
387 rhovf = outRho * outU * outV;
388 rhowf = outRho * outU * outW;
389 Ef = outU *
390 (outP / (gamma - 1.0) +
391 0.5 * outRho * (outU * outU + outV * outV + outW * outW) + outP);
392}
ASSERTL0
#define ASSERTL0(condition, msg)
Definition: ErrorUtil.hpp:208
TOL
#define TOL
Definition: ExactSolverToro.cpp:37
NRITER
#define NRITER
Definition: ExactSolverToro.cpp:38
Nektar::SolverUtils::RiemannSolver::m_params
std::map< std::string, RSParamFuncType > m_params
Map of parameter function types.
Definition: RiemannSolver.h:146
CellMLToNektar.cellml_metadata.p
p
Definition: cellml_metadata.py:350
Nektar::guessp
NekDouble guessp(NekDouble g[], NekDouble rhoL, NekDouble uL, NekDouble pL, NekDouble cL, NekDouble rhoR, NekDouble uR, NekDouble pR, NekDouble cR)
Use either PVRS, two-rarefaction or two-shock Riemann solvers to calculate an initial pressure for th...
Definition: ExactSolverToro.cpp:67
Nektar::prefun
void prefun(NekDouble *g, NekDouble p, NekDouble dk, NekDouble pk, NekDouble ck, NekDouble &f, NekDouble &fd)
Evaluate pressure functions fL and fR in Newton iteration of Riemann solver (see equation 4....
Definition: ExactSolverToro.cpp:117
Nektar::NekDouble
double NekDouble
Definition: NektarUnivTypeDefs.hpp:43
tinysimd::sqrt
scalarT< T > sqrt(scalarT< T > in)
Definition: scalar.hpp:294

References ASSERTL0, Nektar::guessp(), Nektar::SolverUtils::RiemannSolver::m_params, NRITER, CellMLToNektar.cellml_metadata::p, Nektar::prefun(), tinysimd::sqrt(), and TOL.

Member Data Documentation

◆ solverName

std::string Nektar::ExactSolverToro::solverName
static
Initial value:
=
SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
"ExactToro", ExactSolverToro::create, "Exact Riemann solver")
Nektar::ExactSolverToro::create
static RiemannSolverSharedPtr create(const LibUtilities::SessionReaderSharedPtr &pSession)
Definition: ExactSolverToro.h:45
Nektar::LibUtilities::NekFactory::RegisterCreatorFunction
tKey RegisterCreatorFunction(tKey idKey, CreatorFunction classCreator, std::string pDesc="")
Register a class with the factory.
Definition: NekFactory.hpp:197
Nektar::SolverUtils::GetRiemannSolverFactory
RiemannSolverFactory & GetRiemannSolverFactory()
Definition: RiemannSolver.cpp:63

Definition at line 51 of file ExactSolverToro.h.

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