xref: /libCEED/examples/fluids/navierstokes.c (revision 40c555b91eb7f2e7ad2125ad71591663283771c3)
1 // Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
2 // the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
3 // reserved. See files LICENSE and NOTICE for details.
4 //
5 // This file is part of CEED, a collection of benchmarks, miniapps, software
6 // libraries and APIs for efficient high-order finite element and spectral
7 // element discretizations for exascale applications. For more information and
8 // source code availability see http://github.com/ceed.
9 //
10 // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
11 // a collaborative effort of two U.S. Department of Energy organizations (Office
12 // of Science and the National Nuclear Security Administration) responsible for
13 // the planning and preparation of a capable exascale ecosystem, including
14 // software, applications, hardware, advanced system engineering and early
15 // testbed platforms, in support of the nation's exascale computing imperative.
16 
17 //                        libCEED + PETSc Example: Navier-Stokes
18 //
19 // This example demonstrates a simple usage of libCEED with PETSc to solve a
20 // Navier-Stokes problem.
21 //
22 // The code is intentionally "raw", using only low-level communication
23 // primitives.
24 //
25 // Build with:
26 //
27 //     make [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>] navierstokes
28 //
29 // Sample runs:
30 //
31 //     ./navierstokes -ceed /cpu/self -problem density_current -degree 1
32 //     ./navierstokes -ceed /gpu/occa -problem advection -degree 1
33 //
34 //TESTARGS -ceed {ceed_resource} -test -degree 1
35 
36 /// @file
37 /// Navier-Stokes example using PETSc
38 
39 const char help[] = "Solve Navier-Stokes using PETSc and libCEED\n";
40 
41 #include <petscts.h>
42 #include <petscdmplex.h>
43 #include <ceed.h>
44 #include <stdbool.h>
45 #include <petscsys.h>
46 #include "common.h"
47 #include "advection.h"
48 #include "advection2d.h"
49 #include "densitycurrent.h"
50 
51 // Problem Options
52 typedef enum {
53   NS_DENSITY_CURRENT = 0,
54   NS_ADVECTION = 1,
55   NS_ADVECTION2D = 2,
56 } problemType;
57 static const char *const problemTypes[] = {
58   "density_current",
59   "advection",
60   "advection2d",
61   "problemType","NS_",0
62 };
63 
64 typedef enum {
65   STAB_NONE = 0,
66   STAB_SU = 1,   // Streamline Upwind
67   STAB_SUPG = 2, // Streamline Upwind Petrov-Galerkin
68 } StabilizationType;
69 static const char *const StabilizationTypes[] = {
70   "NONE",
71   "SU",
72   "SUPG",
73   "StabilizationType", "STAB_", NULL
74 };
75 
76 // Problem specific data
77 typedef struct {
78   CeedInt dim, qdatasize;
79   CeedQFunctionUser setup, ics, apply_rhs, apply_ifunction;
80   PetscErrorCode (*bc)(PetscInt, PetscReal, const PetscReal[], PetscInt,
81                        PetscScalar[], void *);
82   const char *setup_loc, *ics_loc, *apply_rhs_loc, *apply_ifunction_loc;
83   const bool non_zero_time;
84 } problemData;
85 
86 problemData problemOptions[] = {
87   [NS_DENSITY_CURRENT] = {
88     .dim                 = 3,
89     .qdatasize           = 10,
90     .setup               = Setup,
91     .setup_loc           = Setup_loc,
92     .ics                 = ICsDC,
93     .ics_loc             = ICsDC_loc,
94     .apply_rhs           = DC,
95     .apply_rhs_loc       = DC_loc,
96     .apply_ifunction     = IFunction_DC,
97     .apply_ifunction_loc = IFunction_DC_loc,
98     .bc                  = Exact_DC,
99     .non_zero_time       = false,
100   },
101   [NS_ADVECTION] = {
102     .dim                 = 3,
103     .qdatasize           = 10,
104     .setup               = Setup,
105     .setup_loc           = Setup_loc,
106     .ics                 = ICsAdvection,
107     .ics_loc             = ICsAdvection_loc,
108     .apply_rhs           = Advection,
109     .apply_rhs_loc       = Advection_loc,
110     .apply_ifunction     = IFunction_Advection,
111     .apply_ifunction_loc = IFunction_Advection_loc,
112     .bc                  = Exact_Advection,
113     .non_zero_time       = false,
114   },
115   [NS_ADVECTION2D] = {
116     .dim                 = 2,
117     .qdatasize           = 5,
118     .setup               = Setup2d,
119     .setup_loc           = Setup2d_loc,
120     .ics                 = ICsAdvection2d,
121     .ics_loc             = ICsAdvection2d_loc,
122     .apply_rhs           = Advection2d,
123     .apply_rhs_loc       = Advection2d_loc,
124     .apply_ifunction     = IFunction_Advection2d,
125     .apply_ifunction_loc = IFunction_Advection2d_loc,
126     .bc                  = Exact_Advection2d,
127     .non_zero_time       = true,
128   },
129 };
130 
131 // PETSc user data
132 typedef struct User_ *User;
133 typedef struct Units_ *Units;
134 
135 struct User_ {
136   MPI_Comm comm;
137   PetscInt outputfreq;
138   DM dm;
139   DM dmviz;
140   Mat interpviz;
141   Ceed ceed;
142   Units units;
143   CeedVector qceed, qdotceed, gceed;
144   CeedOperator op_rhs, op_ifunction;
145   Vec M;
146   char outputfolder[PETSC_MAX_PATH_LEN];
147   PetscInt contsteps;
148 };
149 
150 struct Units_ {
151   // fundamental units
152   PetscScalar meter;
153   PetscScalar kilogram;
154   PetscScalar second;
155   PetscScalar Kelvin;
156   // derived units
157   PetscScalar Pascal;
158   PetscScalar JperkgK;
159   PetscScalar mpersquareds;
160   PetscScalar WpermK;
161   PetscScalar kgpercubicm;
162   PetscScalar kgpersquaredms;
163   PetscScalar Joulepercubicm;
164 };
165 
166 typedef struct SimpleBC_ *SimpleBC;
167 struct SimpleBC_ {
168   PetscInt nwall, nslip[3];
169   PetscInt walls[10], slips[3][10];
170 };
171 
172 // Essential BC dofs are encoded in closure indices as -(i+1).
173 static PetscInt Involute(PetscInt i) {
174   return i >= 0 ? i : -(i+1);
175 }
176 
177 // Utility function to create local CEED restriction
178 static PetscErrorCode CreateRestrictionFromPlex(Ceed ceed, DM dm, CeedInt P,
179     CeedElemRestriction *Erestrict) {
180 
181   PetscSection   section;
182   PetscInt       c, cStart, cEnd, Nelem, Ndof, *erestrict, eoffset, nfields, dim;
183   PetscErrorCode ierr;
184   Vec Uloc;
185 
186   PetscFunctionBeginUser;
187   ierr = DMGetDimension(dm, &dim); CHKERRQ(ierr);
188   ierr = DMGetLocalSection(dm,&section); CHKERRQ(ierr);
189   ierr = PetscSectionGetNumFields(section, &nfields); CHKERRQ(ierr);
190   PetscInt ncomp[nfields], fieldoff[nfields+1];
191   fieldoff[0] = 0;
192   for (PetscInt f=0; f<nfields; f++) {
193     ierr = PetscSectionGetFieldComponents(section, f, &ncomp[f]); CHKERRQ(ierr);
194     fieldoff[f+1] = fieldoff[f] + ncomp[f];
195   }
196 
197   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd); CHKERRQ(ierr);
198   Nelem = cEnd - cStart;
199   ierr = PetscMalloc1(Nelem*PetscPowInt(P, dim), &erestrict); CHKERRQ(ierr);
200   for (c=cStart,eoffset=0; c<cEnd; c++) {
201     PetscInt numindices, *indices, nnodes;
202     ierr = DMPlexGetClosureIndices(dm, section, section, c, &numindices,
203                                    &indices, NULL); CHKERRQ(ierr);
204     if (numindices % fieldoff[nfields]) SETERRQ1(PETSC_COMM_SELF,
205           PETSC_ERR_ARG_INCOMP, "Number of closure indices not compatible with Cell %D",
206           c);
207     nnodes = numindices / fieldoff[nfields];
208     for (PetscInt i=0; i<nnodes; i++) {
209       // Check that indices are blocked by node and thus can be coalesced as a single field with
210       // fieldoff[nfields] = sum(ncomp) components.
211       for (PetscInt f=0; f<nfields; f++) {
212         for (PetscInt j=0; j<ncomp[f]; j++) {
213           if (Involute(indices[fieldoff[f]*nnodes + i*ncomp[f] + j])
214               != Involute(indices[i*ncomp[0]]) + fieldoff[f] + j)
215             SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,
216                      "Cell %D closure indices not interlaced for node %D field %D component %D",
217                      c, i, f, j);
218         }
219       }
220       // Essential boundary conditions are encoded as -(loc+1), but we don't care so we decode.
221       PetscInt loc = Involute(indices[i*ncomp[0]]);
222       erestrict[eoffset++] = loc / fieldoff[nfields];
223     }
224     ierr = DMPlexRestoreClosureIndices(dm, section, section, c, &numindices,
225                                        &indices, NULL); CHKERRQ(ierr);
226   }
227   if (eoffset != Nelem*PetscPowInt(P, dim)) SETERRQ3(PETSC_COMM_SELF,
228         PETSC_ERR_LIB, "ElemRestriction of size (%D,%D) initialized %D nodes", Nelem,
229         PetscPowInt(P, dim),eoffset);
230   ierr = DMGetLocalVector(dm, &Uloc); CHKERRQ(ierr);
231   ierr = VecGetLocalSize(Uloc, &Ndof); CHKERRQ(ierr);
232   ierr = DMRestoreLocalVector(dm, &Uloc); CHKERRQ(ierr);
233   CeedElemRestrictionCreate(ceed, CEED_INTERLACED, Nelem, PetscPowInt(P, dim),
234                             Ndof/fieldoff[nfields], fieldoff[nfields],
235                             CEED_MEM_HOST, CEED_COPY_VALUES, erestrict, Erestrict);
236   ierr = PetscFree(erestrict); CHKERRQ(ierr);
237   PetscFunctionReturn(0);
238 }
239 
240 static int CreateVectorFromPetscVec(Ceed ceed, Vec p, CeedVector *v) {
241   PetscErrorCode ierr;
242   PetscInt m;
243 
244   PetscFunctionBeginUser;
245   ierr = VecGetLocalSize(p, &m); CHKERRQ(ierr);
246   ierr = CeedVectorCreate(ceed, m, v); CHKERRQ(ierr);
247   PetscFunctionReturn(0);
248 }
249 
250 static int VectorPlacePetscVec(CeedVector c, Vec p) {
251   PetscErrorCode ierr;
252   PetscInt mceed,mpetsc;
253   PetscScalar *a;
254 
255   PetscFunctionBeginUser;
256   ierr = CeedVectorGetLength(c, &mceed); CHKERRQ(ierr);
257   ierr = VecGetLocalSize(p, &mpetsc); CHKERRQ(ierr);
258   if (mceed != mpetsc) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,
259                                   "Cannot place PETSc Vec of length %D in CeedVector of length %D",
260                                   mpetsc, mceed);
261   ierr = VecGetArray(p, &a); CHKERRQ(ierr);
262   CeedVectorSetArray(c, CEED_MEM_HOST, CEED_USE_POINTER, a);
263   PetscFunctionReturn(0);
264 }
265 
266 static PetscErrorCode DMPlexInsertBoundaryValues_NS(DM dm,
267     PetscBool insertEssential, Vec Qloc, PetscReal time, Vec faceGeomFVM,
268     Vec cellGeomFVM, Vec gradFVM) {
269   PetscErrorCode ierr;
270   Vec Qbc;
271 
272   PetscFunctionBegin;
273   ierr = DMGetNamedLocalVector(dm, "Qbc", &Qbc); CHKERRQ(ierr);
274   ierr = VecAXPY(Qloc, 1., Qbc); CHKERRQ(ierr);
275   ierr = DMRestoreNamedLocalVector(dm, "Qbc", &Qbc); CHKERRQ(ierr);
276   PetscFunctionReturn(0);
277 }
278 
279 // This is the RHS of the ODE, given as u_t = G(t,u)
280 // This function takes in a state vector Q and writes into G
281 static PetscErrorCode RHS_NS(TS ts, PetscReal t, Vec Q, Vec G, void *userData) {
282   PetscErrorCode ierr;
283   User user = *(User *)userData;
284   PetscScalar *q, *g;
285   Vec Qloc, Gloc;
286 
287   // Global-to-local
288   PetscFunctionBeginUser;
289   ierr = DMGetLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
290   ierr = DMGetLocalVector(user->dm, &Gloc); CHKERRQ(ierr);
291   ierr = VecZeroEntries(Qloc); CHKERRQ(ierr);
292   ierr = DMGlobalToLocal(user->dm, Q, INSERT_VALUES, Qloc); CHKERRQ(ierr);
293   ierr = DMPlexInsertBoundaryValues(user->dm, PETSC_TRUE, Qloc, 0.0,
294                                     NULL, NULL, NULL); CHKERRQ(ierr);
295   ierr = VecZeroEntries(Gloc); CHKERRQ(ierr);
296 
297   // Ceed Vectors
298   ierr = VecGetArrayRead(Qloc, (const PetscScalar **)&q); CHKERRQ(ierr);
299   ierr = VecGetArray(Gloc, &g); CHKERRQ(ierr);
300   CeedVectorSetArray(user->qceed, CEED_MEM_HOST, CEED_USE_POINTER, q);
301   CeedVectorSetArray(user->gceed, CEED_MEM_HOST, CEED_USE_POINTER, g);
302 
303   // Apply CEED operator
304   CeedOperatorApply(user->op_rhs, user->qceed, user->gceed,
305                     CEED_REQUEST_IMMEDIATE);
306 
307   // Restore vectors
308   ierr = VecRestoreArrayRead(Qloc, (const PetscScalar **)&q); CHKERRQ(ierr);
309   ierr = VecRestoreArray(Gloc, &g); CHKERRQ(ierr);
310 
311   ierr = VecZeroEntries(G); CHKERRQ(ierr);
312   ierr = DMLocalToGlobal(user->dm, Gloc, ADD_VALUES, G); CHKERRQ(ierr);
313 
314   // Inverse of the lumped mass matrix
315   ierr = VecPointwiseMult(G, G, user->M); // M is Minv
316   CHKERRQ(ierr);
317 
318   ierr = DMRestoreLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
319   ierr = DMRestoreLocalVector(user->dm, &Gloc); CHKERRQ(ierr);
320   PetscFunctionReturn(0);
321 }
322 
323 static PetscErrorCode IFunction_NS(TS ts, PetscReal t, Vec Q, Vec Qdot, Vec G,
324                                    void *userData) {
325   PetscErrorCode ierr;
326   User user = *(User *)userData;
327   const PetscScalar *q, *qdot;
328   PetscScalar *g;
329   Vec Qloc, Qdotloc, Gloc;
330 
331   // Global-to-local
332   PetscFunctionBeginUser;
333   ierr = DMGetLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
334   ierr = DMGetLocalVector(user->dm, &Qdotloc); CHKERRQ(ierr);
335   ierr = DMGetLocalVector(user->dm, &Gloc); CHKERRQ(ierr);
336   ierr = VecZeroEntries(Qloc); CHKERRQ(ierr);
337   ierr = DMGlobalToLocal(user->dm, Q, INSERT_VALUES, Qloc); CHKERRQ(ierr);
338   ierr = DMPlexInsertBoundaryValues(user->dm, PETSC_TRUE, Qloc, 0.0,
339                                     NULL, NULL, NULL); CHKERRQ(ierr);
340   ierr = VecZeroEntries(Qdotloc); CHKERRQ(ierr);
341   ierr = DMGlobalToLocal(user->dm, Qdot, INSERT_VALUES, Qdotloc); CHKERRQ(ierr);
342   ierr = VecZeroEntries(Gloc); CHKERRQ(ierr);
343 
344   // Ceed Vectors
345   ierr = VecGetArrayRead(Qloc, &q); CHKERRQ(ierr);
346   ierr = VecGetArrayRead(Qdotloc, &qdot); CHKERRQ(ierr);
347   ierr = VecGetArray(Gloc, &g); CHKERRQ(ierr);
348   CeedVectorSetArray(user->qceed, CEED_MEM_HOST, CEED_USE_POINTER,
349                      (PetscScalar *)q);
350   CeedVectorSetArray(user->qdotceed, CEED_MEM_HOST, CEED_USE_POINTER,
351                      (PetscScalar *)qdot);
352   CeedVectorSetArray(user->gceed, CEED_MEM_HOST, CEED_USE_POINTER, g);
353 
354   // Apply CEED operator
355   CeedOperatorApply(user->op_ifunction, user->qceed, user->gceed,
356                     CEED_REQUEST_IMMEDIATE);
357 
358   // Restore vectors
359   ierr = VecRestoreArrayRead(Qloc, &q); CHKERRQ(ierr);
360   ierr = VecRestoreArrayRead(Qdotloc, &qdot); CHKERRQ(ierr);
361   ierr = VecRestoreArray(Gloc, &g); CHKERRQ(ierr);
362 
363   ierr = VecZeroEntries(G); CHKERRQ(ierr);
364   ierr = DMLocalToGlobal(user->dm, Gloc, ADD_VALUES, G); CHKERRQ(ierr);
365 
366   ierr = DMRestoreLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
367   ierr = DMRestoreLocalVector(user->dm, &Qdotloc); CHKERRQ(ierr);
368   ierr = DMRestoreLocalVector(user->dm, &Gloc); CHKERRQ(ierr);
369   PetscFunctionReturn(0);
370 }
371 
372 // User provided TS Monitor
373 static PetscErrorCode TSMonitor_NS(TS ts, PetscInt stepno, PetscReal time,
374                                    Vec Q, void *ctx) {
375   User user = ctx;
376   Vec Qloc;
377   char filepath[PETSC_MAX_PATH_LEN];
378   PetscViewer viewer;
379   PetscErrorCode ierr;
380 
381   // Set up output
382   PetscFunctionBeginUser;
383   // Print every 'outputfreq' steps
384   if (stepno % user->outputfreq != 0)
385     PetscFunctionReturn(0);
386   ierr = DMGetLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
387   ierr = PetscObjectSetName((PetscObject)Qloc, "StateVec"); CHKERRQ(ierr);
388   ierr = VecZeroEntries(Qloc); CHKERRQ(ierr);
389   ierr = DMGlobalToLocal(user->dm, Q, INSERT_VALUES, Qloc); CHKERRQ(ierr);
390 
391   // Output
392   ierr = PetscSNPrintf(filepath, sizeof filepath, "%s/ns-%03D.vtu",
393                        user->outputfolder, stepno + user->contsteps);
394   CHKERRQ(ierr);
395   ierr = PetscViewerVTKOpen(PetscObjectComm((PetscObject)Q), filepath,
396                             FILE_MODE_WRITE, &viewer); CHKERRQ(ierr);
397   ierr = VecView(Qloc, viewer); CHKERRQ(ierr);
398   if (user->dmviz) {
399     Vec Qrefined, Qrefined_loc;
400     char filepath_refined[PETSC_MAX_PATH_LEN];
401     PetscViewer viewer_refined;
402 
403     ierr = DMGetGlobalVector(user->dmviz, &Qrefined); CHKERRQ(ierr);
404     ierr = DMGetLocalVector(user->dmviz, &Qrefined_loc); CHKERRQ(ierr);
405     ierr = PetscObjectSetName((PetscObject)Qrefined_loc, "Refined");
406     CHKERRQ(ierr);
407     ierr = MatInterpolate(user->interpviz, Q, Qrefined); CHKERRQ(ierr);
408     ierr = VecZeroEntries(Qrefined_loc); CHKERRQ(ierr);
409     ierr = DMGlobalToLocal(user->dmviz, Qrefined, INSERT_VALUES, Qrefined_loc);
410     CHKERRQ(ierr);
411     ierr = PetscSNPrintf(filepath_refined, sizeof filepath_refined,
412                          "%s/nsrefined-%03D.vtu",
413                          user->outputfolder, stepno + user->contsteps);
414     CHKERRQ(ierr);
415     ierr = PetscViewerVTKOpen(PetscObjectComm((PetscObject)Qrefined),
416                               filepath_refined,
417                               FILE_MODE_WRITE, &viewer_refined); CHKERRQ(ierr);
418     ierr = VecView(Qrefined_loc, viewer_refined); CHKERRQ(ierr);
419     ierr = DMRestoreLocalVector(user->dmviz, &Qrefined_loc); CHKERRQ(ierr);
420     ierr = DMRestoreGlobalVector(user->dmviz, &Qrefined); CHKERRQ(ierr);
421     ierr = PetscViewerDestroy(&viewer_refined); CHKERRQ(ierr);
422   }
423   ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
424   ierr = DMRestoreLocalVector(user->dm, &Qloc); CHKERRQ(ierr);
425 
426   // Save data in a binary file for continuation of simulations
427   ierr = PetscSNPrintf(filepath, sizeof filepath, "%s/ns-solution.bin",
428                        user->outputfolder); CHKERRQ(ierr);
429   ierr = PetscViewerBinaryOpen(user->comm, filepath, FILE_MODE_WRITE, &viewer);
430   CHKERRQ(ierr);
431   ierr = VecView(Q, viewer); CHKERRQ(ierr);
432   ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
433 
434   // Save time stamp
435   // Dimensionalize time back
436   time /= user->units->second;
437   ierr = PetscSNPrintf(filepath, sizeof filepath, "%s/ns-time.bin",
438                        user->outputfolder); CHKERRQ(ierr);
439   ierr = PetscViewerBinaryOpen(user->comm, filepath, FILE_MODE_WRITE, &viewer);
440   CHKERRQ(ierr);
441   #if PETSC_VERSION_GE(3,13,0)
442   ierr = PetscViewerBinaryWrite(viewer, &time, 1, PETSC_REAL);
443   #else
444   ierr = PetscViewerBinaryWrite(viewer, &time, 1, PETSC_REAL, true);
445   #endif
446   CHKERRQ(ierr);
447   ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
448 
449   PetscFunctionReturn(0);
450 }
451 
452 static PetscErrorCode ICs_FixMultiplicity(CeedOperator op_ics,
453     CeedVector xcorners, CeedVector q0ceed, DM dm, Vec Qloc, Vec Q,
454     CeedElemRestriction restrictq, SetupContext ctxSetup, CeedScalar time) {
455   PetscErrorCode ierr;
456   CeedVector multlvec;
457   Vec Multiplicity, MultiplicityLoc;
458 
459   ctxSetup->time = time;
460   ierr = VecZeroEntries(Qloc); CHKERRQ(ierr);
461   ierr = VectorPlacePetscVec(q0ceed, Qloc); CHKERRQ(ierr);
462   CeedOperatorApply(op_ics, xcorners, q0ceed, CEED_REQUEST_IMMEDIATE);
463   ierr = VecZeroEntries(Q); CHKERRQ(ierr);
464   ierr = DMLocalToGlobal(dm, Qloc, ADD_VALUES, Q); CHKERRQ(ierr);
465 
466   // Fix multiplicity for output of ICs
467   ierr = DMGetLocalVector(dm, &MultiplicityLoc); CHKERRQ(ierr);
468   CeedElemRestrictionCreateVector(restrictq, &multlvec, NULL);
469   ierr = VectorPlacePetscVec(multlvec, MultiplicityLoc); CHKERRQ(ierr);
470   CeedElemRestrictionGetMultiplicity(restrictq, multlvec);
471   CeedVectorDestroy(&multlvec);
472   ierr = DMGetGlobalVector(dm, &Multiplicity); CHKERRQ(ierr);
473   ierr = VecZeroEntries(Multiplicity); CHKERRQ(ierr);
474   ierr = DMLocalToGlobal(dm, MultiplicityLoc, ADD_VALUES, Multiplicity);
475   CHKERRQ(ierr);
476   ierr = VecPointwiseDivide(Q, Q, Multiplicity); CHKERRQ(ierr);
477   ierr = VecPointwiseDivide(Qloc, Qloc, MultiplicityLoc); CHKERRQ(ierr);
478   ierr = DMRestoreLocalVector(dm, &MultiplicityLoc); CHKERRQ(ierr);
479   ierr = DMRestoreGlobalVector(dm, &Multiplicity); CHKERRQ(ierr);
480 
481   PetscFunctionReturn(0);
482 }
483 
484 static PetscErrorCode ComputeLumpedMassMatrix(Ceed ceed, DM dm,
485     CeedElemRestriction restrictq, CeedBasis basisq,
486     CeedElemRestriction restrictqdi, CeedVector qdata, Vec M) {
487   PetscErrorCode ierr;
488   CeedQFunction qf_mass;
489   CeedOperator op_mass;
490   CeedVector mceed;
491   Vec Mloc;
492   CeedInt ncompq, qdatasize;
493 
494   PetscFunctionBeginUser;
495   CeedElemRestrictionGetNumComponents(restrictq, &ncompq);
496   CeedElemRestrictionGetNumComponents(restrictqdi, &qdatasize);
497   // Create the Q-function that defines the action of the mass operator
498   CeedQFunctionCreateInterior(ceed, 1, Mass, Mass_loc, &qf_mass);
499   CeedQFunctionAddInput(qf_mass, "q", ncompq, CEED_EVAL_INTERP);
500   CeedQFunctionAddInput(qf_mass, "qdata", qdatasize, CEED_EVAL_NONE);
501   CeedQFunctionAddOutput(qf_mass, "v", ncompq, CEED_EVAL_INTERP);
502 
503   // Create the mass operator
504   CeedOperatorCreate(ceed, qf_mass, NULL, NULL, &op_mass);
505   CeedOperatorSetField(op_mass, "q", restrictq, basisq, CEED_VECTOR_ACTIVE);
506   CeedOperatorSetField(op_mass, "qdata", restrictqdi,
507                        CEED_BASIS_COLLOCATED, qdata);
508   CeedOperatorSetField(op_mass, "v", restrictq, basisq, CEED_VECTOR_ACTIVE);
509 
510   ierr = DMGetLocalVector(dm, &Mloc); CHKERRQ(ierr);
511   ierr = VecZeroEntries(Mloc); CHKERRQ(ierr);
512   CeedElemRestrictionCreateVector(restrictq, &mceed, NULL);
513   ierr = VectorPlacePetscVec(mceed, Mloc); CHKERRQ(ierr);
514 
515   {
516     // Compute a lumped mass matrix
517     CeedVector onesvec;
518     CeedElemRestrictionCreateVector(restrictq, &onesvec, NULL);
519     CeedVectorSetValue(onesvec, 1.0);
520     CeedOperatorApply(op_mass, onesvec, mceed, CEED_REQUEST_IMMEDIATE);
521     CeedVectorDestroy(&onesvec);
522     CeedOperatorDestroy(&op_mass);
523     CeedVectorDestroy(&mceed);
524   }
525   CeedQFunctionDestroy(&qf_mass);
526 
527   ierr = VecZeroEntries(M); CHKERRQ(ierr);
528   ierr = DMLocalToGlobal(dm, Mloc, ADD_VALUES, M); CHKERRQ(ierr);
529   ierr = DMRestoreLocalVector(dm, &Mloc); CHKERRQ(ierr);
530 
531   // Invert diagonally lumped mass vector for RHS function
532   ierr = VecReciprocal(M); CHKERRQ(ierr);
533   PetscFunctionReturn(0);
534 }
535 
536 PetscErrorCode SetUpDM(DM dm, problemData *problem, PetscInt degree,
537                        SimpleBC bc, void *ctxSetup) {
538   PetscErrorCode ierr;
539 
540   PetscFunctionBeginUser;
541   {
542     // Configure the finite element space and boundary conditions
543     PetscFE fe;
544     PetscSpace fespace;
545     PetscInt ncompq = 5;
546     ierr = PetscFECreateLagrange(PETSC_COMM_SELF, problem->dim, ncompq,
547                                  PETSC_FALSE, degree, PETSC_DECIDE,
548                                  &fe);
549     ierr = PetscObjectSetName((PetscObject)fe, "Q"); CHKERRQ(ierr);
550     ierr = DMAddField(dm,NULL,(PetscObject)fe); CHKERRQ(ierr);
551     ierr = DMCreateDS(dm); CHKERRQ(ierr);
552     // Wall boundary conditions are zero energy density and zero flux for
553     //   velocity in advection/advection2d, and zero velocity and zero flux
554     //   for mass density and energy density in density_current
555     {
556       if (problem->bc == Exact_Advection || problem->bc == Exact_Advection2d) {
557         PetscInt comps[1] = {4};
558         ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", "Face Sets", 0,
559                              1, comps, (void(*)(void))problem->bc,
560                              bc->nwall, bc->walls, ctxSetup); CHKERRQ(ierr);
561       } else if (problem->bc == Exact_DC) {
562         PetscInt comps[3] = {1, 2, 3};
563         ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", "Face Sets", 0,
564                              3, comps, (void(*)(void))problem->bc,
565                              bc->nwall, bc->walls, ctxSetup); CHKERRQ(ierr);
566       }
567     }
568     {
569       PetscInt comps[1] = {1};
570       ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "slipx", "Face Sets", 0,
571                            1, comps, (void(*)(void))NULL, bc->nslip[0],
572                            bc->slips[0], ctxSetup); CHKERRQ(ierr);
573       comps[0] = 2;
574       ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "slipy", "Face Sets", 0,
575                            1, comps, (void(*)(void))NULL, bc->nslip[1],
576                            bc->slips[1], ctxSetup); CHKERRQ(ierr);
577       comps[0] = 3;
578       ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "slipz", "Face Sets", 0,
579                            1, comps, (void(*)(void))NULL, bc->nslip[2],
580                            bc->slips[2], ctxSetup); CHKERRQ(ierr);
581     }
582     ierr = DMPlexSetClosurePermutationTensor(dm,PETSC_DETERMINE,NULL);
583     CHKERRQ(ierr);
584     ierr = PetscFEGetBasisSpace(fe, &fespace); CHKERRQ(ierr);
585     ierr = PetscFEDestroy(&fe); CHKERRQ(ierr);
586   }
587   {
588     // Empty name for conserved field (because there is only one field)
589     PetscSection section;
590     ierr = DMGetLocalSection(dm, &section); CHKERRQ(ierr);
591     ierr = PetscSectionSetFieldName(section, 0, ""); CHKERRQ(ierr);
592     ierr = PetscSectionSetComponentName(section, 0, 0, "Density");
593     CHKERRQ(ierr);
594     ierr = PetscSectionSetComponentName(section, 0, 1, "MomentumX");
595     CHKERRQ(ierr);
596     ierr = PetscSectionSetComponentName(section, 0, 2, "MomentumY");
597     CHKERRQ(ierr);
598     ierr = PetscSectionSetComponentName(section, 0, 3, "MomentumZ");
599     CHKERRQ(ierr);
600     ierr = PetscSectionSetComponentName(section, 0, 4, "EnergyDensity");
601     CHKERRQ(ierr);
602   }
603   PetscFunctionReturn(0);
604 }
605 
606 int main(int argc, char **argv) {
607   PetscInt ierr;
608   MPI_Comm comm;
609   DM dm, dmcoord, dmviz;
610   Mat interpviz;
611   TS ts;
612   TSAdapt adapt;
613   User user;
614   Units units;
615   char ceedresource[4096] = "/cpu/self";
616   PetscInt cStart, cEnd, localNelem, lnodes, steps;
617   const PetscInt ncompq = 5;
618   PetscMPIInt rank;
619   PetscScalar ftime;
620   Vec Q, Qloc, Xloc;
621   Ceed ceed;
622   CeedInt numP, numQ;
623   CeedVector xcorners, qdata, q0ceed;
624   CeedBasis basisx, basisxc, basisq;
625   CeedElemRestriction restrictx, restrictxcoord, restrictq, restrictqdi;
626   CeedQFunction qf_setup, qf_ics, qf_rhs, qf_ifunction;
627   CeedOperator op_setup, op_ics;
628   CeedScalar Rd;
629   PetscScalar WpermK, Pascal, JperkgK, mpersquareds, kgpercubicm,
630               kgpersquaredms, Joulepercubicm;
631   problemType problemChoice;
632   problemData *problem = NULL;
633   StabilizationType stab;
634   PetscBool   test, implicit;
635   PetscInt    viz_refine = 0;
636   struct SimpleBC_ bc = {
637     .nwall = 6,
638     .walls = {1,2,3,4,5,6},
639   };
640   double start, cpu_time_used;
641 
642   // Create the libCEED contexts
643   PetscScalar meter     = 1e-2;     // 1 meter in scaled length units
644   PetscScalar second    = 1e-2;     // 1 second in scaled time units
645   PetscScalar kilogram  = 1e-6;     // 1 kilogram in scaled mass units
646   PetscScalar Kelvin    = 1;        // 1 Kelvin in scaled temperature units
647   CeedScalar theta0     = 300.;     // K
648   CeedScalar thetaC     = -15.;     // K
649   CeedScalar P0         = 1.e5;     // Pa
650   CeedScalar N          = 0.01;     // 1/s
651   CeedScalar cv         = 717.;     // J/(kg K)
652   CeedScalar cp         = 1004.;    // J/(kg K)
653   CeedScalar g          = 9.81;     // m/s^2
654   CeedScalar lambda     = -2./3.;   // -
655   CeedScalar mu         = 75.;      // Pa s, dynamic viscosity
656   // mu = 75 is not physical for air, but is good for numerical stability
657   CeedScalar k          = 0.02638;  // W/(m K)
658   CeedScalar CtauS      = 0.;       // dimensionless
659   CeedScalar strong_form = 0.;      // [0,1]
660   PetscScalar lx        = 8000.;    // m
661   PetscScalar ly        = 8000.;    // m
662   PetscScalar lz        = 4000.;    // m
663   CeedScalar rc         = 1000.;    // m (Radius of bubble)
664   PetscScalar resx      = 1000.;    // m (resolution in x)
665   PetscScalar resy      = 1000.;    // m (resolution in y)
666   PetscScalar resz      = 1000.;    // m (resolution in z)
667   PetscInt outputfreq   = 10;       // -
668   PetscInt contsteps    = 0;        // -
669   PetscInt degree       = 1;        // -
670   PetscInt qextra       = 2;        // -
671   DMBoundaryType periodicity[] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,
672                                   DM_BOUNDARY_NONE
673                                  };
674   PetscReal center[3], dc_axis[3] = {0, 0, 0};
675 
676   ierr = PetscInitialize(&argc, &argv, NULL, help);
677   if (ierr) return ierr;
678 
679   // Allocate PETSc context
680   ierr = PetscCalloc1(1, &user); CHKERRQ(ierr);
681   ierr = PetscMalloc1(1, &units); CHKERRQ(ierr);
682 
683   // Parse command line options
684   comm = PETSC_COMM_WORLD;
685   ierr = PetscOptionsBegin(comm, NULL, "Navier-Stokes in PETSc with libCEED",
686                            NULL); CHKERRQ(ierr);
687   ierr = PetscOptionsString("-ceed", "CEED resource specifier",
688                             NULL, ceedresource, ceedresource,
689                             sizeof(ceedresource), NULL); CHKERRQ(ierr);
690   ierr = PetscOptionsBool("-test", "Run in test mode",
691                           NULL, test=PETSC_FALSE, &test, NULL); CHKERRQ(ierr);
692   problemChoice = NS_DENSITY_CURRENT;
693   ierr = PetscOptionsEnum("-problem", "Problem to solve", NULL,
694                           problemTypes, (PetscEnum)problemChoice,
695                           (PetscEnum *)&problemChoice, NULL); CHKERRQ(ierr);
696   problem = &problemOptions[problemChoice];
697   ierr = PetscOptionsEnum("-stab", "Stabilization method", NULL,
698                           StabilizationTypes, (PetscEnum)(stab = STAB_NONE),
699                           (PetscEnum *)&stab, NULL); CHKERRQ(ierr);
700   ierr = PetscOptionsBool("-implicit", "Use implicit (IFunction) formulation",
701                           NULL, implicit=PETSC_FALSE, &implicit, NULL);
702   CHKERRQ(ierr);
703   if (!implicit && stab != STAB_NONE) {
704     ierr = PetscPrintf(comm, "Warning! Use -stab only with -implicit\n");
705     CHKERRQ(ierr);
706   }
707   {
708     PetscInt len;
709     PetscBool flg;
710     ierr = PetscOptionsIntArray("-bc_wall",
711                                 "Use wall boundary conditions on this list of faces",
712                                 NULL, bc.walls,
713                                 (len = sizeof(bc.walls) / sizeof(bc.walls[0]),
714                                  &len), &flg); CHKERRQ(ierr);
715     if (flg) bc.nwall = len;
716     for (PetscInt j=0; j<3; j++) {
717       const char *flags[3] = {"-bc_slip_x", "-bc_slip_y", "-bc_slip_z"};
718       ierr = PetscOptionsIntArray(flags[j],
719                                   "Use slip boundary conditions on this list of faces",
720                                   NULL, bc.slips[j],
721                                   (len = sizeof(bc.slips[j]) / sizeof(bc.slips[j][0]),
722                                    &len), &flg);
723       CHKERRQ(ierr);
724       if (flg) bc.nslip[j] = len;
725     }
726   }
727   ierr = PetscOptionsInt("-viz_refine",
728                          "Regular refinement levels for visualization",
729                          NULL, viz_refine, &viz_refine, NULL);
730   CHKERRQ(ierr);
731   ierr = PetscOptionsScalar("-units_meter", "1 meter in scaled length units",
732                             NULL, meter, &meter, NULL); CHKERRQ(ierr);
733   meter = fabs(meter);
734   ierr = PetscOptionsScalar("-units_second","1 second in scaled time units",
735                             NULL, second, &second, NULL); CHKERRQ(ierr);
736   second = fabs(second);
737   ierr = PetscOptionsScalar("-units_kilogram","1 kilogram in scaled mass units",
738                             NULL, kilogram, &kilogram, NULL); CHKERRQ(ierr);
739   kilogram = fabs(kilogram);
740   ierr = PetscOptionsScalar("-units_Kelvin",
741                             "1 Kelvin in scaled temperature units",
742                             NULL, Kelvin, &Kelvin, NULL); CHKERRQ(ierr);
743   Kelvin = fabs(Kelvin);
744   ierr = PetscOptionsScalar("-theta0", "Reference potential temperature",
745                             NULL, theta0, &theta0, NULL); CHKERRQ(ierr);
746   ierr = PetscOptionsScalar("-thetaC", "Perturbation of potential temperature",
747                             NULL, thetaC, &thetaC, NULL); CHKERRQ(ierr);
748   ierr = PetscOptionsScalar("-P0", "Atmospheric pressure",
749                             NULL, P0, &P0, NULL); CHKERRQ(ierr);
750   ierr = PetscOptionsScalar("-N", "Brunt-Vaisala frequency",
751                             NULL, N, &N, NULL); CHKERRQ(ierr);
752   ierr = PetscOptionsScalar("-cv", "Heat capacity at constant volume",
753                             NULL, cv, &cv, NULL); CHKERRQ(ierr);
754   ierr = PetscOptionsScalar("-cp", "Heat capacity at constant pressure",
755                             NULL, cp, &cp, NULL); CHKERRQ(ierr);
756   ierr = PetscOptionsScalar("-g", "Gravitational acceleration",
757                             NULL, g, &g, NULL); CHKERRQ(ierr);
758   ierr = PetscOptionsScalar("-lambda",
759                             "Stokes hypothesis second viscosity coefficient",
760                             NULL, lambda, &lambda, NULL); CHKERRQ(ierr);
761   ierr = PetscOptionsScalar("-mu", "Shear dynamic viscosity coefficient",
762                             NULL, mu, &mu, NULL); CHKERRQ(ierr);
763   ierr = PetscOptionsScalar("-k", "Thermal conductivity",
764                             NULL, k, &k, NULL); CHKERRQ(ierr);
765   ierr = PetscOptionsScalar("-CtauS",
766                             "Scale coefficient for tau (nondimensional)",
767                             NULL, CtauS, &CtauS, NULL); CHKERRQ(ierr);
768   if (stab == STAB_NONE && CtauS != 0) {
769     ierr = PetscPrintf(comm, "Warning! Use -CtauS only with -stab su or -stab supg\n");
770     CHKERRQ(ierr);
771   }
772   ierr = PetscOptionsScalar("-strong_form",
773                             "Strong (1) or weak/integrated by parts (0) advection residual",
774                             NULL, strong_form, &strong_form, NULL);
775   CHKERRQ(ierr);
776   ierr = PetscOptionsScalar("-lx", "Length scale in x direction",
777                             NULL, lx, &lx, NULL); CHKERRQ(ierr);
778   ierr = PetscOptionsScalar("-ly", "Length scale in y direction",
779                             NULL, ly, &ly, NULL); CHKERRQ(ierr);
780   ierr = PetscOptionsScalar("-lz", "Length scale in z direction",
781                             NULL, lz, &lz, NULL); CHKERRQ(ierr);
782   ierr = PetscOptionsScalar("-rc", "Characteristic radius of thermal bubble",
783                             NULL, rc, &rc, NULL); CHKERRQ(ierr);
784   ierr = PetscOptionsScalar("-resx","Target resolution in x",
785                             NULL, resx, &resx, NULL); CHKERRQ(ierr);
786   ierr = PetscOptionsScalar("-resy","Target resolution in y",
787                             NULL, resy, &resy, NULL); CHKERRQ(ierr);
788   ierr = PetscOptionsScalar("-resz","Target resolution in z",
789                             NULL, resz, &resz, NULL); CHKERRQ(ierr);
790   PetscInt n = problem->dim;
791   ierr = PetscOptionsEnumArray("-periodicity", "Periodicity per direction",
792                                NULL, DMBoundaryTypes, (PetscEnum *)periodicity,
793                                &n, NULL); CHKERRQ(ierr);
794   n = problem->dim;
795   center[0] = 0.5 * lx;
796   center[1] = 0.5 * ly;
797   center[2] = 0.5 * lz;
798   ierr = PetscOptionsRealArray("-center", "Location of bubble center",
799                                NULL, center, &n, NULL); CHKERRQ(ierr);
800   n = problem->dim;
801   ierr = PetscOptionsRealArray("-dc_axis",
802                                "Axis of density current cylindrical anomaly, or {0,0,0} for spherically symmetric",
803                                NULL, dc_axis, &n, NULL); CHKERRQ(ierr);
804   {
805     PetscReal norm = PetscSqrtReal(PetscSqr(dc_axis[0]) +
806                                    PetscSqr(dc_axis[1]) + PetscSqr(dc_axis[2]));
807     if (norm > 0) {
808       for (int i=0; i<3; i++) dc_axis[i] /= norm;
809     }
810   }
811   ierr = PetscOptionsInt("-output_freq",
812                          "Frequency of output, in number of steps",
813                          NULL, outputfreq, &outputfreq, NULL); CHKERRQ(ierr);
814   ierr = PetscOptionsInt("-continue", "Continue from previous solution",
815                          NULL, contsteps, &contsteps, NULL); CHKERRQ(ierr);
816   ierr = PetscOptionsInt("-degree", "Polynomial degree of finite elements",
817                          NULL, degree, &degree, NULL); CHKERRQ(ierr);
818   ierr = PetscOptionsInt("-qextra", "Number of extra quadrature points",
819                          NULL, qextra, &qextra, NULL); CHKERRQ(ierr);
820   PetscStrncpy(user->outputfolder, ".", 2);
821   ierr = PetscOptionsString("-of", "Output folder",
822                             NULL, user->outputfolder, user->outputfolder,
823                             sizeof(user->outputfolder), NULL); CHKERRQ(ierr);
824   ierr = PetscOptionsEnd(); CHKERRQ(ierr);
825 
826   // Define derived units
827   Pascal = kilogram / (meter * PetscSqr(second));
828   JperkgK =  PetscSqr(meter) / (PetscSqr(second) * Kelvin);
829   mpersquareds = meter / PetscSqr(second);
830   WpermK = kilogram * meter / (pow(second,3) * Kelvin);
831   kgpercubicm = kilogram / pow(meter,3);
832   kgpersquaredms = kilogram / (PetscSqr(meter) * second);
833   Joulepercubicm = kilogram / (meter * PetscSqr(second));
834 
835   // Scale variables to desired units
836   theta0 *= Kelvin;
837   thetaC *= Kelvin;
838   P0 *= Pascal;
839   N *= (1./second);
840   cv *= JperkgK;
841   cp *= JperkgK;
842   Rd = cp - cv;
843   g *= mpersquareds;
844   mu *= Pascal * second;
845   k *= WpermK;
846   lx = fabs(lx) * meter;
847   ly = fabs(ly) * meter;
848   lz = fabs(lz) * meter;
849   rc = fabs(rc) * meter;
850   resx = fabs(resx) * meter;
851   resy = fabs(resy) * meter;
852   resz = fabs(resz) * meter;
853   for (int i=0; i<3; i++) center[i] *= meter;
854 
855   const CeedInt dim = problem->dim, ncompx = problem->dim,
856                 qdatasize = problem->qdatasize;
857   // Set up the libCEED context
858   struct SetupContext_ ctxSetup =  {
859     .theta0 = theta0,
860     .thetaC = thetaC,
861     .P0 = P0,
862     .N = N,
863     .cv = cv,
864     .cp = cp,
865     .Rd = Rd,
866     .g = g,
867     .rc = rc,
868     .lx = lx,
869     .ly = ly,
870     .lz = lz,
871     .periodicity0 = periodicity[0],
872     .periodicity1 = periodicity[1],
873     .periodicity2 = periodicity[2],
874     .center[0] = center[0],
875     .center[1] = center[1],
876     .center[2] = center[2],
877     .dc_axis[0] = dc_axis[0],
878     .dc_axis[1] = dc_axis[1],
879     .dc_axis[2] = dc_axis[2],
880     .time = 0,
881   };
882 
883   // Create the mesh
884   {
885     const PetscReal scale[3] = {lx, ly, lz};
886     ierr = DMPlexCreateBoxMesh(comm, dim, PETSC_FALSE, NULL, NULL, scale,
887                                periodicity, PETSC_TRUE, &dm);
888     CHKERRQ(ierr);
889   }
890 
891   // Distribute the mesh over processes
892   {
893     DM               dmDist = NULL;
894     PetscPartitioner part;
895 
896     ierr = DMPlexGetPartitioner(dm, &part); CHKERRQ(ierr);
897     ierr = PetscPartitionerSetFromOptions(part); CHKERRQ(ierr);
898     ierr = DMPlexDistribute(dm, 0, NULL, &dmDist); CHKERRQ(ierr);
899     if (dmDist) {
900       ierr = DMDestroy(&dm); CHKERRQ(ierr);
901       dm  = dmDist;
902     }
903   }
904   ierr = DMViewFromOptions(dm, NULL, "-dm_view"); CHKERRQ(ierr);
905 
906   // Setup DM
907   ierr = DMLocalizeCoordinates(dm); CHKERRQ(ierr);
908   ierr = DMSetFromOptions(dm); CHKERRQ(ierr);
909   ierr = SetUpDM(dm, problem, degree, &bc, &ctxSetup); CHKERRQ(ierr);
910 
911   // Print FEM space information
912   if (!test) {
913     ierr = PetscPrintf(PETSC_COMM_WORLD,
914                        "Degree of FEM space: %D\n",
915                        degree); CHKERRQ(ierr);
916   }
917 
918   // Refine DM for high-order viz
919   dmviz = NULL;
920   interpviz = NULL;
921   if (viz_refine) {
922     DM dmhierarchy[viz_refine+1];
923 
924     ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE); CHKERRQ(ierr);
925     dmhierarchy[0] = dm;
926     for (PetscInt i = 0, d = degree; i < viz_refine; i++) {
927       Mat interp_next;
928 
929       ierr = DMRefine(dmhierarchy[i], MPI_COMM_NULL, &dmhierarchy[i+1]);
930       CHKERRQ(ierr);
931       ierr = DMSetCoarseDM(dmhierarchy[i+1], dmhierarchy[i]); CHKERRQ(ierr);
932       d = (d + 1) / 2;
933       if (i + 1 == viz_refine) d = 1;
934       ierr = SetUpDM(dmhierarchy[i+1], problem, d, &bc, &ctxSetup); CHKERRQ(ierr);
935       ierr = DMCreateInterpolation(dmhierarchy[i], dmhierarchy[i+1],
936                                    &interp_next, NULL); CHKERRQ(ierr);
937       if (!i) interpviz = interp_next;
938       else {
939         Mat C;
940         ierr = MatMatMult(interp_next, interpviz, MAT_INITIAL_MATRIX,
941                           PETSC_DECIDE, &C); CHKERRQ(ierr);
942         ierr = MatDestroy(&interp_next); CHKERRQ(ierr);
943         ierr = MatDestroy(&interpviz); CHKERRQ(ierr);
944         interpviz = C;
945       }
946     }
947     for (PetscInt i=1; i<viz_refine; i++) {
948       ierr = DMDestroy(&dmhierarchy[i]); CHKERRQ(ierr);
949     }
950     dmviz = dmhierarchy[viz_refine];
951   }
952   ierr = DMCreateGlobalVector(dm, &Q); CHKERRQ(ierr);
953   ierr = DMGetLocalVector(dm, &Qloc); CHKERRQ(ierr);
954   ierr = VecGetSize(Qloc, &lnodes); CHKERRQ(ierr);
955   lnodes /= ncompq;
956 
957   {
958     // Print grid information
959     CeedInt gdofs, odofs;
960     int comm_size;
961     char box_faces_str[PETSC_MAX_PATH_LEN] = "NONE";
962     ierr = VecGetSize(Q, &gdofs); CHKERRQ(ierr);
963     ierr = VecGetLocalSize(Q, &odofs); CHKERRQ(ierr);
964     ierr = MPI_Comm_size(comm, &comm_size); CHKERRQ(ierr);
965     ierr = PetscOptionsGetString(NULL, NULL, "-dm_plex_box_faces", box_faces_str,
966                                  sizeof(box_faces_str), NULL); CHKERRQ(ierr);
967     if (!test) {
968       ierr = PetscPrintf(comm, "Global FEM dofs: %D (%D owned) on %d rank(s)\n",
969                          gdofs, odofs, comm_size); CHKERRQ(ierr);
970       ierr = PetscPrintf(comm, "Local FEM nodes: %D\n", lnodes); CHKERRQ(ierr);
971       ierr = PetscPrintf(comm, "dm_plex_box_faces: %s\n", box_faces_str);
972       CHKERRQ(ierr);
973     }
974 
975   }
976 
977   // Set up global mass vector
978   ierr = VecDuplicate(Q, &user->M); CHKERRQ(ierr);
979 
980   // Set up CEED
981   // CEED Bases
982   CeedInit(ceedresource, &ceed);
983   numP = degree + 1;
984   numQ = numP + qextra;
985   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompq, numP, numQ, CEED_GAUSS,
986                                   &basisq);
987   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompx, 2, numQ, CEED_GAUSS,
988                                   &basisx);
989   CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompx, 2, numP,
990                                   CEED_GAUSS_LOBATTO, &basisxc);
991 
992   ierr = DMGetCoordinateDM(dm, &dmcoord); CHKERRQ(ierr);
993   ierr = DMPlexSetClosurePermutationTensor(dmcoord, PETSC_DETERMINE, NULL);
994   CHKERRQ(ierr);
995 
996   // CEED Restrictions
997   ierr = CreateRestrictionFromPlex(ceed, dm, degree+1, &restrictq);
998   CHKERRQ(ierr);
999   ierr = CreateRestrictionFromPlex(ceed, dmcoord, 2, &restrictx); CHKERRQ(ierr);
1000   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd); CHKERRQ(ierr);
1001   localNelem = cEnd - cStart;
1002   CeedInt numQdim = CeedIntPow(numQ, dim);
1003   CeedElemRestrictionCreateStrided(ceed, localNelem, numQdim,
1004                                    localNelem*numQdim, qdatasize,
1005                                    CEED_STRIDES_BACKEND, &restrictqdi);
1006   CeedElemRestrictionCreateStrided(ceed, localNelem, PetscPowInt(numP, dim),
1007                                    localNelem*PetscPowInt(numP, dim), ncompx,
1008                                    CEED_STRIDES_BACKEND, &restrictxcoord);
1009 
1010   ierr = DMGetCoordinatesLocal(dm, &Xloc); CHKERRQ(ierr);
1011   ierr = CreateVectorFromPetscVec(ceed, Xloc, &xcorners); CHKERRQ(ierr);
1012 
1013   // Create the CEED vectors that will be needed in setup
1014   CeedInt Nqpts;
1015   CeedBasisGetNumQuadraturePoints(basisq, &Nqpts);
1016   CeedVectorCreate(ceed, qdatasize*localNelem*Nqpts, &qdata);
1017   CeedElemRestrictionCreateVector(restrictq, &q0ceed, NULL);
1018 
1019   // Create the Q-function that builds the quadrature data for the NS operator
1020   CeedQFunctionCreateInterior(ceed, 1, problem->setup, problem->setup_loc,
1021                               &qf_setup);
1022   CeedQFunctionAddInput(qf_setup, "dx", ncompx*dim, CEED_EVAL_GRAD);
1023   CeedQFunctionAddInput(qf_setup, "weight", 1, CEED_EVAL_WEIGHT);
1024   CeedQFunctionAddOutput(qf_setup, "qdata", qdatasize, CEED_EVAL_NONE);
1025 
1026   // Create the Q-function that sets the ICs of the operator
1027   CeedQFunctionCreateInterior(ceed, 1, problem->ics, problem->ics_loc, &qf_ics);
1028   CeedQFunctionAddInput(qf_ics, "x", ncompx, CEED_EVAL_INTERP);
1029   CeedQFunctionAddOutput(qf_ics, "q0", ncompq, CEED_EVAL_NONE);
1030 
1031   qf_rhs = NULL;
1032   if (problem->apply_rhs) { // Create the Q-function that defines the action of the RHS operator
1033     CeedQFunctionCreateInterior(ceed, 1, problem->apply_rhs,
1034                                 problem->apply_rhs_loc, &qf_rhs);
1035     CeedQFunctionAddInput(qf_rhs, "q", ncompq, CEED_EVAL_INTERP);
1036     CeedQFunctionAddInput(qf_rhs, "dq", ncompq*dim, CEED_EVAL_GRAD);
1037     CeedQFunctionAddInput(qf_rhs, "qdata", qdatasize, CEED_EVAL_NONE);
1038     CeedQFunctionAddInput(qf_rhs, "x", ncompx, CEED_EVAL_INTERP);
1039     CeedQFunctionAddOutput(qf_rhs, "v", ncompq, CEED_EVAL_INTERP);
1040     CeedQFunctionAddOutput(qf_rhs, "dv", ncompq*dim, CEED_EVAL_GRAD);
1041   }
1042 
1043   qf_ifunction = NULL;
1044   if (problem->apply_ifunction) { // Create the Q-function that defines the action of the IFunction
1045     CeedQFunctionCreateInterior(ceed, 1, problem->apply_ifunction,
1046                                 problem->apply_ifunction_loc, &qf_ifunction);
1047     CeedQFunctionAddInput(qf_ifunction, "q", ncompq, CEED_EVAL_INTERP);
1048     CeedQFunctionAddInput(qf_ifunction, "dq", ncompq*dim, CEED_EVAL_GRAD);
1049     CeedQFunctionAddInput(qf_ifunction, "qdot", ncompq, CEED_EVAL_INTERP);
1050     CeedQFunctionAddInput(qf_ifunction, "qdata", qdatasize, CEED_EVAL_NONE);
1051     CeedQFunctionAddInput(qf_ifunction, "x", ncompx, CEED_EVAL_INTERP);
1052     CeedQFunctionAddOutput(qf_ifunction, "v", ncompq, CEED_EVAL_INTERP);
1053     CeedQFunctionAddOutput(qf_ifunction, "dv", ncompq*dim, CEED_EVAL_GRAD);
1054   }
1055 
1056   // Create the operator that builds the quadrature data for the NS operator
1057   CeedOperatorCreate(ceed, qf_setup, NULL, NULL, &op_setup);
1058   CeedOperatorSetField(op_setup, "dx", restrictx, basisx, CEED_VECTOR_ACTIVE);
1059   CeedOperatorSetField(op_setup, "weight", CEED_ELEMRESTRICTION_NONE,
1060                        basisx, CEED_VECTOR_NONE);
1061   CeedOperatorSetField(op_setup, "qdata", restrictqdi,
1062                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
1063 
1064   // Create the operator that sets the ICs
1065   CeedOperatorCreate(ceed, qf_ics, NULL, NULL, &op_ics);
1066   CeedOperatorSetField(op_ics, "x", restrictx, basisxc, CEED_VECTOR_ACTIVE);
1067   CeedOperatorSetField(op_ics, "q0", restrictq,
1068                        CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
1069 
1070   CeedElemRestrictionCreateVector(restrictq, &user->qceed, NULL);
1071   CeedElemRestrictionCreateVector(restrictq, &user->qdotceed, NULL);
1072   CeedElemRestrictionCreateVector(restrictq, &user->gceed, NULL);
1073 
1074   if (qf_rhs) { // Create the RHS physics operator
1075     CeedOperator op;
1076     CeedOperatorCreate(ceed, qf_rhs, NULL, NULL, &op);
1077     CeedOperatorSetField(op, "q", restrictq, basisq, CEED_VECTOR_ACTIVE);
1078     CeedOperatorSetField(op, "dq", restrictq, basisq, CEED_VECTOR_ACTIVE);
1079     CeedOperatorSetField(op, "qdata", restrictqdi,
1080                          CEED_BASIS_COLLOCATED, qdata);
1081     CeedOperatorSetField(op, "x", restrictx, basisx, xcorners);
1082     CeedOperatorSetField(op, "v", restrictq, basisq, CEED_VECTOR_ACTIVE);
1083     CeedOperatorSetField(op, "dv", restrictq, basisq, CEED_VECTOR_ACTIVE);
1084     user->op_rhs = op;
1085   }
1086 
1087   if (qf_ifunction) { // Create the IFunction operator
1088     CeedOperator op;
1089     CeedOperatorCreate(ceed, qf_ifunction, NULL, NULL, &op);
1090     CeedOperatorSetField(op, "q", restrictq, basisq, CEED_VECTOR_ACTIVE);
1091     CeedOperatorSetField(op, "dq", restrictq, basisq, CEED_VECTOR_ACTIVE);
1092     CeedOperatorSetField(op, "qdot", restrictq, basisq, user->qdotceed);
1093     CeedOperatorSetField(op, "qdata", restrictqdi,
1094                          CEED_BASIS_COLLOCATED, qdata);
1095     CeedOperatorSetField(op, "x", restrictx, basisx, xcorners);
1096     CeedOperatorSetField(op, "v", restrictq, basisq, CEED_VECTOR_ACTIVE);
1097     CeedOperatorSetField(op, "dv", restrictq, basisq, CEED_VECTOR_ACTIVE);
1098     user->op_ifunction = op;
1099   }
1100 
1101   CeedQFunctionSetContext(qf_ics, &ctxSetup, sizeof ctxSetup);
1102   CeedScalar ctxNS[8] = {lambda, mu, k, cv, cp, g, Rd};
1103   struct Advection2dContext_ ctxAdvection2d = {
1104     .CtauS = CtauS,
1105     .strong_form = strong_form,
1106     .stabilization = stab,
1107   };
1108   switch (problemChoice) {
1109   case NS_DENSITY_CURRENT:
1110     if (qf_rhs) CeedQFunctionSetContext(qf_rhs, &ctxNS, sizeof ctxNS);
1111     if (qf_ifunction) CeedQFunctionSetContext(qf_ifunction, &ctxNS,
1112           sizeof ctxNS);
1113     break;
1114   case NS_ADVECTION:
1115   case NS_ADVECTION2D:
1116     if (qf_rhs) CeedQFunctionSetContext(qf_rhs, &ctxAdvection2d,
1117                                           sizeof ctxAdvection2d);
1118     if (qf_ifunction) CeedQFunctionSetContext(qf_ifunction, &ctxAdvection2d,
1119           sizeof ctxAdvection2d);
1120   }
1121 
1122   // Set up PETSc context
1123   // Set up units structure
1124   units->meter = meter;
1125   units->kilogram = kilogram;
1126   units->second = second;
1127   units->Kelvin = Kelvin;
1128   units->Pascal = Pascal;
1129   units->JperkgK = JperkgK;
1130   units->mpersquareds = mpersquareds;
1131   units->WpermK = WpermK;
1132   units->kgpercubicm = kgpercubicm;
1133   units->kgpersquaredms = kgpersquaredms;
1134   units->Joulepercubicm = Joulepercubicm;
1135 
1136   // Set up user structure
1137   user->comm = comm;
1138   user->outputfreq = outputfreq;
1139   user->contsteps = contsteps;
1140   user->units = units;
1141   user->dm = dm;
1142   user->dmviz = dmviz;
1143   user->interpviz = interpviz;
1144   user->ceed = ceed;
1145 
1146   // Calculate qdata and ICs
1147   // Set up state global and local vectors
1148   ierr = VecZeroEntries(Q); CHKERRQ(ierr);
1149 
1150   ierr = VectorPlacePetscVec(q0ceed, Qloc); CHKERRQ(ierr);
1151 
1152   // Apply Setup Ceed Operators
1153   ierr = VectorPlacePetscVec(xcorners, Xloc); CHKERRQ(ierr);
1154   CeedOperatorApply(op_setup, xcorners, qdata, CEED_REQUEST_IMMEDIATE);
1155   ierr = ComputeLumpedMassMatrix(ceed, dm, restrictq, basisq, restrictqdi, qdata,
1156                                  user->M); CHKERRQ(ierr);
1157 
1158   ierr = ICs_FixMultiplicity(op_ics, xcorners, q0ceed, dm, Qloc, Q, restrictq,
1159                              &ctxSetup, 0.0);
1160   if (1) { // Record boundary values from initial condition and override DMPlexInsertBoundaryValues()
1161     // We use this for the main simulation DM because the reference DMPlexInsertBoundaryValues() is very slow.  If we
1162     // disable this, we should still get the same results due to the problem->bc function, but with potentially much
1163     // slower execution.
1164     Vec Qbc;
1165     ierr = DMGetNamedLocalVector(dm, "Qbc", &Qbc); CHKERRQ(ierr);
1166     ierr = VecCopy(Qloc, Qbc); CHKERRQ(ierr);
1167     ierr = VecZeroEntries(Qloc); CHKERRQ(ierr);
1168     ierr = DMGlobalToLocal(dm, Q, INSERT_VALUES, Qloc); CHKERRQ(ierr);
1169     ierr = VecAXPY(Qbc, -1., Qloc); CHKERRQ(ierr);
1170     ierr = DMRestoreNamedLocalVector(dm, "Qbc", &Qbc); CHKERRQ(ierr);
1171     ierr = PetscObjectComposeFunction((PetscObject)dm,
1172                                       "DMPlexInsertBoundaryValues_C", DMPlexInsertBoundaryValues_NS);
1173     CHKERRQ(ierr);
1174   }
1175 
1176   MPI_Comm_rank(comm, &rank);
1177   if (!rank) {ierr = PetscMkdir(user->outputfolder); CHKERRQ(ierr);}
1178   // Gather initial Q values
1179   // In case of continuation of simulation, set up initial values from binary file
1180   if (contsteps) { // continue from existent solution
1181     PetscViewer viewer;
1182     char filepath[PETSC_MAX_PATH_LEN];
1183     // Read input
1184     ierr = PetscSNPrintf(filepath, sizeof filepath, "%s/ns-solution.bin",
1185                          user->outputfolder);
1186     CHKERRQ(ierr);
1187     ierr = PetscViewerBinaryOpen(comm, filepath, FILE_MODE_READ, &viewer);
1188     CHKERRQ(ierr);
1189     ierr = VecLoad(Q, viewer); CHKERRQ(ierr);
1190     ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
1191   }
1192   ierr = DMRestoreLocalVector(dm, &Qloc); CHKERRQ(ierr);
1193 
1194   // Create and setup TS
1195   ierr = TSCreate(comm, &ts); CHKERRQ(ierr);
1196   ierr = TSSetDM(ts, dm); CHKERRQ(ierr);
1197   if (implicit) {
1198     ierr = TSSetType(ts, TSBDF); CHKERRQ(ierr);
1199     if (user->op_ifunction) {
1200       ierr = TSSetIFunction(ts, NULL, IFunction_NS, &user); CHKERRQ(ierr);
1201     } else {                    // Implicit integrators can fall back to using an RHSFunction
1202       ierr = TSSetRHSFunction(ts, NULL, RHS_NS, &user); CHKERRQ(ierr);
1203     }
1204   } else {
1205     if (!user->op_rhs) SETERRQ(comm,PETSC_ERR_ARG_NULL,
1206                                  "Problem does not provide RHSFunction");
1207     ierr = TSSetType(ts, TSRK); CHKERRQ(ierr);
1208     ierr = TSRKSetType(ts, TSRK5F); CHKERRQ(ierr);
1209     ierr = TSSetRHSFunction(ts, NULL, RHS_NS, &user); CHKERRQ(ierr);
1210   }
1211   ierr = TSSetMaxTime(ts, 500. * units->second); CHKERRQ(ierr);
1212   ierr = TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER); CHKERRQ(ierr);
1213   ierr = TSSetTimeStep(ts, 1.e-2 * units->second); CHKERRQ(ierr);
1214   if (test) {ierr = TSSetMaxSteps(ts, 1); CHKERRQ(ierr);}
1215   ierr = TSGetAdapt(ts, &adapt); CHKERRQ(ierr);
1216   ierr = TSAdaptSetStepLimits(adapt,
1217                               1.e-12 * units->second,
1218                               1.e2 * units->second); CHKERRQ(ierr);
1219   ierr = TSSetFromOptions(ts); CHKERRQ(ierr);
1220   if (!contsteps) { // print initial condition
1221     if (!test) {
1222       ierr = TSMonitor_NS(ts, 0, 0., Q, user); CHKERRQ(ierr);
1223     }
1224   } else { // continue from time of last output
1225     PetscReal time;
1226     PetscInt count;
1227     PetscViewer viewer;
1228     char filepath[PETSC_MAX_PATH_LEN];
1229     ierr = PetscSNPrintf(filepath, sizeof filepath, "%s/ns-time.bin",
1230                          user->outputfolder); CHKERRQ(ierr);
1231     ierr = PetscViewerBinaryOpen(comm, filepath, FILE_MODE_READ, &viewer);
1232     CHKERRQ(ierr);
1233     ierr = PetscViewerBinaryRead(viewer, &time, 1, &count, PETSC_REAL);
1234     CHKERRQ(ierr);
1235     ierr = PetscViewerDestroy(&viewer); CHKERRQ(ierr);
1236     ierr = TSSetTime(ts, time * user->units->second); CHKERRQ(ierr);
1237   }
1238   if (!test) {
1239     ierr = TSMonitorSet(ts, TSMonitor_NS, user, NULL); CHKERRQ(ierr);
1240   }
1241 
1242   // Solve
1243   start = MPI_Wtime();
1244   ierr = PetscBarrier((PetscObject)ts); CHKERRQ(ierr);
1245   ierr = TSSolve(ts, Q); CHKERRQ(ierr);
1246   cpu_time_used = MPI_Wtime() - start;
1247   ierr = TSGetSolveTime(ts, &ftime); CHKERRQ(ierr);
1248   ierr = MPI_Allreduce(MPI_IN_PLACE, &cpu_time_used, 1, MPI_DOUBLE, MPI_MIN,
1249                        comm); CHKERRQ(ierr);
1250   if (!test) {
1251     ierr = PetscPrintf(PETSC_COMM_WORLD,
1252                        "Time taken for solution (sec): %g\n",
1253                        (double)cpu_time_used); CHKERRQ(ierr);
1254   }
1255 
1256   // Get error
1257   if (problem->non_zero_time && !test) {
1258     Vec Qexact, Qexactloc;
1259     PetscReal norm;
1260     ierr = DMCreateGlobalVector(dm, &Qexact); CHKERRQ(ierr);
1261     ierr = DMGetLocalVector(dm, &Qexactloc); CHKERRQ(ierr);
1262     ierr = VecGetSize(Qexactloc, &lnodes); CHKERRQ(ierr);
1263 
1264     ierr = ICs_FixMultiplicity(op_ics, xcorners, q0ceed, dm, Qexactloc, Qexact,
1265                                restrictq, &ctxSetup, ftime); CHKERRQ(ierr);
1266 
1267     ierr = VecAXPY(Q, -1.0, Qexact);  CHKERRQ(ierr);
1268     ierr = VecNorm(Q, NORM_MAX, &norm); CHKERRQ(ierr);
1269     CeedVectorDestroy(&q0ceed);
1270     ierr = PetscPrintf(PETSC_COMM_WORLD,
1271                        "Max Error: %g\n",
1272                        (double)norm); CHKERRQ(ierr);
1273     // Clean up vectors
1274     ierr = DMRestoreLocalVector(dm, &Qexactloc); CHKERRQ(ierr);
1275     ierr = VecDestroy(&Qexact); CHKERRQ(ierr);
1276   }
1277 
1278   // Output Statistics
1279   ierr = TSGetStepNumber(ts,&steps); CHKERRQ(ierr);
1280   if (!test) {
1281     ierr = PetscPrintf(PETSC_COMM_WORLD,
1282                        "Time integrator took %D time steps to reach final time %g\n",
1283                        steps, (double)ftime); CHKERRQ(ierr);
1284   }
1285 
1286   // Clean up libCEED
1287   CeedVectorDestroy(&qdata);
1288   CeedVectorDestroy(&user->qceed);
1289   CeedVectorDestroy(&user->qdotceed);
1290   CeedVectorDestroy(&user->gceed);
1291   CeedVectorDestroy(&xcorners);
1292   CeedBasisDestroy(&basisq);
1293   CeedBasisDestroy(&basisx);
1294   CeedBasisDestroy(&basisxc);
1295   CeedElemRestrictionDestroy(&restrictq);
1296   CeedElemRestrictionDestroy(&restrictx);
1297   CeedElemRestrictionDestroy(&restrictqdi);
1298   CeedElemRestrictionDestroy(&restrictxcoord);
1299   CeedQFunctionDestroy(&qf_setup);
1300   CeedQFunctionDestroy(&qf_ics);
1301   CeedQFunctionDestroy(&qf_rhs);
1302   CeedQFunctionDestroy(&qf_ifunction);
1303   CeedOperatorDestroy(&op_setup);
1304   CeedOperatorDestroy(&op_ics);
1305   CeedOperatorDestroy(&user->op_rhs);
1306   CeedOperatorDestroy(&user->op_ifunction);
1307   CeedDestroy(&ceed);
1308 
1309   // Clean up PETSc
1310   ierr = VecDestroy(&Q); CHKERRQ(ierr);
1311   ierr = VecDestroy(&user->M); CHKERRQ(ierr);
1312   ierr = MatDestroy(&interpviz); CHKERRQ(ierr);
1313   ierr = DMDestroy(&dmviz); CHKERRQ(ierr);
1314   ierr = TSDestroy(&ts); CHKERRQ(ierr);
1315   ierr = DMDestroy(&dm); CHKERRQ(ierr);
1316   ierr = PetscFree(units); CHKERRQ(ierr);
1317   ierr = PetscFree(user); CHKERRQ(ierr);
1318   return PetscFinalize();
1319 }
1320 
1321