1 | """Class Domain - 1D domains for finite-volume computations of |
---|
2 | the shallow water wave equation |
---|
3 | |
---|
4 | |
---|
5 | Copyright 2004 |
---|
6 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
---|
7 | Geoscience Australia |
---|
8 | """ |
---|
9 | |
---|
10 | from generic_boundary_conditions import * |
---|
11 | |
---|
12 | |
---|
13 | class Domain: |
---|
14 | |
---|
15 | def __init__(self, |
---|
16 | coordinates, |
---|
17 | boundary = None, |
---|
18 | conserved_quantities = None, |
---|
19 | evolved_quantities = None, |
---|
20 | other_quantities = None, |
---|
21 | tagged_elements = None): |
---|
22 | """ |
---|
23 | Build 1D elements from x coordinates |
---|
24 | """ |
---|
25 | |
---|
26 | from Numeric import array, zeros, Float, Int |
---|
27 | |
---|
28 | from config import timestepping_method |
---|
29 | from config import CFL |
---|
30 | |
---|
31 | #Store Points |
---|
32 | self.coordinates = array(coordinates) |
---|
33 | |
---|
34 | |
---|
35 | #Register number of Elements |
---|
36 | self.number_of_elements = N = len(self.coordinates)-1 |
---|
37 | |
---|
38 | self.beta = 1.0 |
---|
39 | self.set_limiter("minmod_kurganov") |
---|
40 | self.set_CFL(CFL) |
---|
41 | self.set_timestepping_method(timestepping_method) |
---|
42 | |
---|
43 | self.wet_nodes = zeros((N,2), Int) # should this be here |
---|
44 | |
---|
45 | #Allocate space for neighbour and boundary structures |
---|
46 | self.neighbours = zeros((N, 2), Int) |
---|
47 | #self.neighbour_edges = zeros((N, 2), Int) |
---|
48 | self.neighbour_vertices = zeros((N, 2), Int) |
---|
49 | self.number_of_boundaries = zeros(N, Int) |
---|
50 | self.surrogate_neighbours = zeros((N, 2), Int) |
---|
51 | |
---|
52 | #Allocate space for geometric quantities |
---|
53 | self.vertices = zeros((N, 2), Float) |
---|
54 | self.centroids = zeros(N, Float) |
---|
55 | self.areas = zeros(N, Float) |
---|
56 | |
---|
57 | self.max_speed_array = zeros(N, Float) |
---|
58 | |
---|
59 | |
---|
60 | self.normals = zeros((N, 2), Float) |
---|
61 | |
---|
62 | for i in range(N): |
---|
63 | xl = self.coordinates[i] |
---|
64 | xr = self.coordinates[i+1] |
---|
65 | self.vertices[i,0] = xl |
---|
66 | self.vertices[i,1] = xr |
---|
67 | |
---|
68 | centroid = (xl+xr)/2.0 |
---|
69 | self.centroids[i] = centroid |
---|
70 | |
---|
71 | msg = 'Coordinates should be ordered, smallest to largest' |
---|
72 | assert xr>xl, msg |
---|
73 | |
---|
74 | #The normal vectors |
---|
75 | # - point outward from each edge |
---|
76 | # - are orthogonal to the edge |
---|
77 | # - have unit length |
---|
78 | # - Are enumerated by left vertex then right vertex normals |
---|
79 | |
---|
80 | nl = -1.0 |
---|
81 | nr = 1.0 |
---|
82 | self.normals[i,:] = [nl, nr] |
---|
83 | |
---|
84 | self.areas[i] = (xr-xl) |
---|
85 | |
---|
86 | # # print 'N', N |
---|
87 | # # print 'Centroid', self.centroids |
---|
88 | # # print 'Areas', self.areas |
---|
89 | # # print 'Vertex_Coordinates', self.vertices |
---|
90 | |
---|
91 | #Initialise Neighbours (-1 means that it is a boundary neighbour) |
---|
92 | self.neighbours[i, :] = [-1, -1] |
---|
93 | #Initialise edge ids of neighbours |
---|
94 | #Initialise vertex ids of neighbours |
---|
95 | #In case of boundaries this slot is not used |
---|
96 | #self.neighbour_edges[i, :] = [-1, -1] |
---|
97 | self.neighbour_vertices[i, :] = [-1, -1] |
---|
98 | |
---|
99 | self.build_vertexlist() |
---|
100 | |
---|
101 | #Build neighbour structure |
---|
102 | self.build_neighbour_structure() |
---|
103 | |
---|
104 | #Build surrogate neighbour structure |
---|
105 | self.build_surrogate_neighbour_structure() |
---|
106 | |
---|
107 | #Build boundary dictionary mapping (id, edge) to symbolic tags |
---|
108 | #Build boundary dictionary mapping (id, vertex) to symbolic tags |
---|
109 | self.build_boundary_dictionary(boundary) |
---|
110 | |
---|
111 | #Build tagged element dictionary mapping (tag) to array of elements |
---|
112 | self.build_tagged_elements_dictionary(tagged_elements) |
---|
113 | |
---|
114 | from quantity import Quantity, Conserved_quantity |
---|
115 | #from quantity_domain import Quantity, Conserved_quantity |
---|
116 | |
---|
117 | #List of quantity names entering |
---|
118 | #the conservation equations |
---|
119 | #(Must be a subset of quantities) |
---|
120 | if conserved_quantities is None: |
---|
121 | self.conserved_quantities = [] |
---|
122 | else: |
---|
123 | self.conserved_quantities = conserved_quantities |
---|
124 | |
---|
125 | if evolved_quantities is None: |
---|
126 | self.evolved_quantities = self.conserved_quantities |
---|
127 | else: |
---|
128 | self.evolved_quantities = evolved_quantities |
---|
129 | |
---|
130 | if other_quantities is None: |
---|
131 | self.other_quantities = [] |
---|
132 | else: |
---|
133 | self.other_quantities = other_quantities |
---|
134 | |
---|
135 | |
---|
136 | #Build dictionary of Quantity instances keyed by quantity names |
---|
137 | self.quantities = {} |
---|
138 | |
---|
139 | #print self.conserved_quantities |
---|
140 | #print self.evolved_quantities |
---|
141 | |
---|
142 | |
---|
143 | #FIXME: remove later - maybe OK, though.... |
---|
144 | for name in self.evolved_quantities: |
---|
145 | self.quantities[name] = Quantity(self) |
---|
146 | for name in self.other_quantities: |
---|
147 | self.quantities[name] = Quantity(self) |
---|
148 | |
---|
149 | #Create an empty list for explicit forcing terms |
---|
150 | self.forcing_terms = [] |
---|
151 | |
---|
152 | #Defaults |
---|
153 | from config import max_smallsteps, beta_w, beta_h, epsilon, CFL |
---|
154 | self.beta_w = beta_w |
---|
155 | self.beta_h = beta_h |
---|
156 | self.epsilon = epsilon |
---|
157 | |
---|
158 | #FIXME: Maybe have separate orders for h-limiter and w-limiter? |
---|
159 | #Or maybe get rid of order altogether and use beta_w and beta_h |
---|
160 | self.default_order = 1 |
---|
161 | self.order = self.default_order |
---|
162 | |
---|
163 | self.default_time_order = 1 |
---|
164 | self.time_order = self.default_time_order |
---|
165 | |
---|
166 | self.smallsteps = 0 |
---|
167 | self.max_smallsteps = max_smallsteps |
---|
168 | self.number_of_steps = 0 |
---|
169 | self.number_of_first_order_steps = 0 |
---|
170 | |
---|
171 | #Model time |
---|
172 | self.time = 0.0 |
---|
173 | self.finaltime = None |
---|
174 | self.min_timestep = self.max_timestep = 0.0 |
---|
175 | self.starttime = 0 #Physical starttime if any (0 is 1 Jan 1970 00:00:00) |
---|
176 | #Checkpointing and storage |
---|
177 | from config import default_datadir |
---|
178 | self.set_datadir(default_datadir) |
---|
179 | self.filename = 'domain' |
---|
180 | self.checkpoint = False |
---|
181 | |
---|
182 | def __len__(self): |
---|
183 | return self.number_of_elements |
---|
184 | |
---|
185 | def build_vertexlist(self): |
---|
186 | """Build vertexlist index by vertex ids and for each entry (point id) |
---|
187 | build a list of (triangles, vertex_id) pairs that use the point |
---|
188 | as vertex. |
---|
189 | |
---|
190 | Preconditions: |
---|
191 | self.coordinates and self.triangles are defined |
---|
192 | |
---|
193 | Postcondition: |
---|
194 | self.vertexlist is built |
---|
195 | """ |
---|
196 | from Numeric import array |
---|
197 | |
---|
198 | vertexlist = [None]*len(self.coordinates) |
---|
199 | for i in range(self.number_of_elements): |
---|
200 | |
---|
201 | #a = self.triangles[i, 0] |
---|
202 | #b = self.triangles[i, 1] |
---|
203 | #c = self.triangles[i, 2] |
---|
204 | a = i |
---|
205 | b = i + 1 |
---|
206 | |
---|
207 | #Register the vertices v as lists of |
---|
208 | #(triangle_id, vertex_id) tuples associated with them |
---|
209 | #This is used for smoothing |
---|
210 | #for vertex_id, v in enumerate([a,b,c]): |
---|
211 | for vertex_id, v in enumerate([a,b]): |
---|
212 | if vertexlist[v] is None: |
---|
213 | vertexlist[v] = [] |
---|
214 | |
---|
215 | vertexlist[v].append( (i, vertex_id) ) |
---|
216 | |
---|
217 | self.vertexlist = vertexlist |
---|
218 | |
---|
219 | |
---|
220 | def build_neighbour_structure(self): |
---|
221 | """Update all registered triangles to point to their neighbours. |
---|
222 | |
---|
223 | Also, keep a tally of the number of boundaries for each triangle |
---|
224 | |
---|
225 | Postconditions: |
---|
226 | neighbours and neighbour_edges is populated |
---|
227 | neighbours and neighbour_vertices is populated |
---|
228 | number_of_boundaries integer array is defined. |
---|
229 | """ |
---|
230 | |
---|
231 | #Step 1: |
---|
232 | #Build dictionary mapping from segments (2-tuple of points) |
---|
233 | #to left hand side edge (facing neighbouring triangle) |
---|
234 | |
---|
235 | N = self.number_of_elements |
---|
236 | neighbourdict = {} |
---|
237 | #l_edge = 0 |
---|
238 | #r_edge = 1 |
---|
239 | l_vertex = 0 |
---|
240 | r_vertex = 1 |
---|
241 | for i in range(N): |
---|
242 | |
---|
243 | #Register all segments as keys mapping to current triangle |
---|
244 | #and segment id |
---|
245 | #a = self.triangles[i, 0] |
---|
246 | #b = self.triangles[i, 1] |
---|
247 | #c = self.triangles[i, 2] |
---|
248 | a = self.vertices[i,0] |
---|
249 | b = self.vertices[i,1] |
---|
250 | |
---|
251 | """ |
---|
252 | if neighbourdict.has_key((a,b)): |
---|
253 | msg = "Edge 2 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[a,b][1],neighbourdict[a,b][0]) |
---|
254 | raise msg |
---|
255 | if neighbourdict.has_key((b,c)): |
---|
256 | msg = "Edge 0 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[b,c][1],neighbourdict[b,c][0]) |
---|
257 | raise msg |
---|
258 | if neighbourdict.has_key((c,a)): |
---|
259 | msg = "Edge 1 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[c,a][1],neighbourdict[c,a][0]) |
---|
260 | raise msg |
---|
261 | """ |
---|
262 | #neighbourdict[a,b] = (i, 2) #(id, edge) |
---|
263 | #neighbourdict[b,c] = (i, 0) #(id, edge) |
---|
264 | #neighbourdict[c,a] = (i, 1) #(id, edge) |
---|
265 | #neighbourdict[a,b] = (i, 1) #(id, edge) |
---|
266 | #neighbourdict[b,a] = (i, 0) #(id, edge) |
---|
267 | #neighbourdict[a,l_edge] = (i, 0) #(id, edge) |
---|
268 | #neighbourdict[b,r_edge] = (i, 1) #(id, edge) |
---|
269 | neighbourdict[a,l_vertex] = (i, 0) #(id, vertex) |
---|
270 | neighbourdict[b,r_vertex] = (i, 1) #(id, vertex) |
---|
271 | |
---|
272 | |
---|
273 | #Step 2: |
---|
274 | #Go through triangles again, but this time |
---|
275 | #reverse direction of segments and lookup neighbours. |
---|
276 | for i in range(N): |
---|
277 | #a = self.triangles[i, 0] |
---|
278 | #b = self.triangles[i, 1] |
---|
279 | #c = self.triangles[i, 2] |
---|
280 | |
---|
281 | a = self.vertices[i,0] |
---|
282 | b = self.vertices[i,1] |
---|
283 | |
---|
284 | #self.number_of_boundaries[i] = 3 |
---|
285 | self.number_of_boundaries[i] = 2 |
---|
286 | #if neighbourdict.has_key((b,l_edge)): |
---|
287 | if neighbourdict.has_key((b,l_vertex)): |
---|
288 | #self.neighbours[i, 1] = neighbourdict[b,l_edge][0] |
---|
289 | #self.neighbour_edges[i, 1] = neighbourdict[b,l_edge][1] |
---|
290 | self.neighbours[i, 1] = neighbourdict[b,l_vertex][0] |
---|
291 | self.neighbour_vertices[i, 1] = neighbourdict[b,l_vertex][1] |
---|
292 | self.number_of_boundaries[i] -= 1 |
---|
293 | |
---|
294 | #if neighbourdict.has_key((a,r_edge)): |
---|
295 | if neighbourdict.has_key((a,r_vertex)): |
---|
296 | #self.neighbours[i, 0] = neighbourdict[a,r_edge][0] |
---|
297 | #self.neighbour_edges[i, 0] = neighbourdict[a,r_edge][1] |
---|
298 | self.neighbours[i, 0] = neighbourdict[a,r_vertex][0] |
---|
299 | self.neighbour_vertices[i, 0] = neighbourdict[a,r_vertex][1] |
---|
300 | self.number_of_boundaries[i] -= 1 |
---|
301 | |
---|
302 | #if neighbourdict.has_key((b,a)): |
---|
303 | # self.neighbours[i, 1] = neighbourdict[b,a][0] |
---|
304 | # self.neighbour_edges[i, 1] = neighbourdict[b,a][1] |
---|
305 | # self.number_of_boundaries[i] -= 1 |
---|
306 | |
---|
307 | #if neighbourdict.has_key((c,b)): |
---|
308 | # self.neighbours[i, 0] = neighbourdict[c,b][0] |
---|
309 | # self.neighbour_edges[i, 0] = neighbourdict[c,b][1] |
---|
310 | # self.number_of_boundaries[i] -= 1 |
---|
311 | |
---|
312 | #if neighbourdict.has_key((a,b)): |
---|
313 | # self.neighbours[i, 0] = neighbourdict[a,b][0] |
---|
314 | # self.neighbour_edges[i, 0] = neighbourdict[a,b][1] |
---|
315 | # self.number_of_boundaries[i] -= 1 |
---|
316 | |
---|
317 | def build_surrogate_neighbour_structure(self): |
---|
318 | """Build structure where each triangle edge points to its neighbours |
---|
319 | if they exist. Otherwise point to the triangle itself. |
---|
320 | |
---|
321 | The surrogate neighbour structure is useful for computing gradients |
---|
322 | based on centroid values of neighbours. |
---|
323 | |
---|
324 | Precondition: Neighbour structure is defined |
---|
325 | Postcondition: |
---|
326 | Surrogate neighbour structure is defined: |
---|
327 | surrogate_neighbours: i0, i1, i2 where all i_k >= 0 point to |
---|
328 | triangles. |
---|
329 | |
---|
330 | """ |
---|
331 | |
---|
332 | N = self.number_of_elements |
---|
333 | for i in range(N): |
---|
334 | #Find all neighbouring volumes that are not boundaries |
---|
335 | #for k in range(3): |
---|
336 | for k in range(2): |
---|
337 | if self.neighbours[i, k] < 0: |
---|
338 | self.surrogate_neighbours[i, k] = i #Point this triangle |
---|
339 | else: |
---|
340 | self.surrogate_neighbours[i, k] = self.neighbours[i, k] |
---|
341 | |
---|
342 | def build_boundary_dictionary(self, boundary = None): |
---|
343 | """Build or check the dictionary of boundary tags. |
---|
344 | self.boundary is a dictionary of tags, |
---|
345 | keyed by volume id and edge: |
---|
346 | { (id, edge): tag, ... } |
---|
347 | |
---|
348 | Postconditions: |
---|
349 | self.boundary is defined. |
---|
350 | """ |
---|
351 | |
---|
352 | from config import default_boundary_tag |
---|
353 | |
---|
354 | if boundary is None: |
---|
355 | boundary = {} |
---|
356 | for vol_id in range(self.number_of_elements): |
---|
357 | #for edge_id in range(0, 3): |
---|
358 | #for edge_id in range(0, 2): |
---|
359 | for vertex_id in range(0, 2): |
---|
360 | #if self.neighbours[vol_id, edge_id] < 0: |
---|
361 | if self.neighbours[vol_id, vertex_id] < 0: |
---|
362 | #boundary[(vol_id, edge_id)] = default_boundary_tag |
---|
363 | boundary[(vol_id, vertex_id)] = default_boundary_tag |
---|
364 | else: |
---|
365 | #Check that all keys in given boundary exist |
---|
366 | #for vol_id, edge_id in boundary.keys(): |
---|
367 | for vol_id, vertex_id in boundary.keys(): |
---|
368 | #msg = 'Segment (%d, %d) does not exist' %(vol_id, edge_id) |
---|
369 | msg = 'Segment (%d, %d) does not exist' %(vol_id, vertex_id) |
---|
370 | a, b = self.neighbours.shape |
---|
371 | #assert vol_id < a and edge_id < b, msg |
---|
372 | assert vol_id < a and vertex_id < b, msg |
---|
373 | |
---|
374 | #FIXME: This assert violates internal boundaries (delete it) |
---|
375 | #msg = 'Segment (%d, %d) is not a boundary' %(vol_id, edge_id) |
---|
376 | #assert self.neighbours[vol_id, edge_id] < 0, msg |
---|
377 | |
---|
378 | #Check that all boundary segments are assigned a tag |
---|
379 | for vol_id in range(self.number_of_elements): |
---|
380 | #for edge_id in range(0, 3): |
---|
381 | #for edge_id in range(0, 2): |
---|
382 | for vertex_id in range(0, 2): |
---|
383 | #if self.neighbours[vol_id, edge_id] < 0: |
---|
384 | if self.neighbours[vol_id, vertex_id] < 0: |
---|
385 | #if not boundary.has_key( (vol_id, edge_id) ): |
---|
386 | if not boundary.has_key( (vol_id, vertex_id) ): |
---|
387 | msg = 'WARNING: Given boundary does not contain ' |
---|
388 | #msg += 'tags for edge (%d, %d). '\ |
---|
389 | # %(vol_id, edge_id) |
---|
390 | msg += 'tags for vertex (%d, %d). '\ |
---|
391 | %(vol_id, vertex_id) |
---|
392 | msg += 'Assigning default tag (%s).'\ |
---|
393 | %default_boundary_tag |
---|
394 | |
---|
395 | #FIXME: Print only as per verbosity |
---|
396 | #print msg |
---|
397 | |
---|
398 | #FIXME: Make this situation an error in the future |
---|
399 | #and make another function which will |
---|
400 | #enable default boundary-tags where |
---|
401 | #tags a not specified |
---|
402 | #boundary[ (vol_id, edge_id) ] =\ |
---|
403 | boundary[ (vol_id, vertex_id) ] =\ |
---|
404 | default_boundary_tag |
---|
405 | |
---|
406 | |
---|
407 | |
---|
408 | self.boundary = boundary |
---|
409 | |
---|
410 | def build_tagged_elements_dictionary(self, tagged_elements = None): |
---|
411 | """Build the dictionary of element tags. |
---|
412 | self.tagged_elements is a dictionary of element arrays, |
---|
413 | keyed by tag: |
---|
414 | { (tag): [e1, e2, e3..] } |
---|
415 | |
---|
416 | Postconditions: |
---|
417 | self.element_tag is defined |
---|
418 | """ |
---|
419 | from Numeric import array, Int |
---|
420 | |
---|
421 | if tagged_elements is None: |
---|
422 | tagged_elements = {} |
---|
423 | else: |
---|
424 | #Check that all keys in given boundary exist |
---|
425 | for tag in tagged_elements.keys(): |
---|
426 | tagged_elements[tag] = array(tagged_elements[tag]).astype(Int) |
---|
427 | |
---|
428 | msg = 'Not all elements exist. ' |
---|
429 | assert max(tagged_elements[tag]) < self.number_of_elements, msg |
---|
430 | #print "tagged_elements", tagged_elements |
---|
431 | self.tagged_elements = tagged_elements |
---|
432 | |
---|
433 | |
---|
434 | def set_quantities_to_be_stored(self, q): |
---|
435 | """Specify which quantities will be stored in the sww file. |
---|
436 | |
---|
437 | q must be either: |
---|
438 | - the name of a quantity |
---|
439 | - a list of quantity names |
---|
440 | - None |
---|
441 | |
---|
442 | In the two first cases, the named quantities will be stored at each |
---|
443 | yieldstep |
---|
444 | (This is in addition to the quantities elevation and friction) |
---|
445 | If q is None, storage will be switched off altogether. |
---|
446 | """ |
---|
447 | |
---|
448 | |
---|
449 | if q is None: |
---|
450 | self.quantities_to_be_stored = [] |
---|
451 | self.store = False |
---|
452 | return |
---|
453 | |
---|
454 | if isinstance(q, basestring): |
---|
455 | q = [q] # Turn argument into a list |
---|
456 | |
---|
457 | #Check correcness |
---|
458 | for quantity_name in q: |
---|
459 | msg = 'Quantity %s is not a valid conserved quantity' %quantity_name |
---|
460 | assert quantity_name in self.conserved_quantities, msg |
---|
461 | |
---|
462 | self.quantities_to_be_stored = q |
---|
463 | |
---|
464 | |
---|
465 | |
---|
466 | |
---|
467 | |
---|
468 | def get_boundary_tags(self): |
---|
469 | """Return list of available boundary tags |
---|
470 | """ |
---|
471 | |
---|
472 | tags = {} |
---|
473 | for v in self.boundary.values(): |
---|
474 | tags[v] = 1 |
---|
475 | |
---|
476 | return tags.keys() |
---|
477 | |
---|
478 | def get_vertex_coordinates(self, obj = False): |
---|
479 | """Return all vertex coordinates. |
---|
480 | Return all vertex coordinates for all triangles as an Nx6 array |
---|
481 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
---|
482 | |
---|
483 | if obj is True, the x/y pairs are returned in a 3*N x 2 array. |
---|
484 | FIXME, we might make that the default. |
---|
485 | FIXME Maybe use keyword: continuous = False for this condition? |
---|
486 | |
---|
487 | |
---|
488 | """ |
---|
489 | |
---|
490 | if obj is True: |
---|
491 | from Numeric import concatenate, reshape |
---|
492 | #V = self.vertex_coordinates |
---|
493 | V = self.vertices |
---|
494 | #return concatenate( (V[:,0:2], V[:,2:4], V[:,4:6]), axis=0) |
---|
495 | |
---|
496 | N = V.shape[0] |
---|
497 | #return reshape(V, (3*N, 2)) |
---|
498 | return reshape(V, (N, 2)) |
---|
499 | else: |
---|
500 | #return self.vertex_coordinates |
---|
501 | return self.vertices |
---|
502 | |
---|
503 | def get_conserved_quantities(self, vol_id, vertex=None):#, edge=None): |
---|
504 | """Get conserved quantities at volume vol_id |
---|
505 | |
---|
506 | If vertex is specified use it as index for vertex values |
---|
507 | If edge is specified use it as index for edge values |
---|
508 | If neither are specified use centroid values |
---|
509 | If both are specified an exeception is raised |
---|
510 | |
---|
511 | Return value: Vector of length == number_of_conserved quantities |
---|
512 | |
---|
513 | """ |
---|
514 | |
---|
515 | from Numeric import zeros, Float |
---|
516 | |
---|
517 | #if not (vertex is None):# or edge is None): |
---|
518 | # msg = 'Values for both vertex and edge was specified.' |
---|
519 | # msg += 'Only one (or none) is allowed.' |
---|
520 | # raise msg |
---|
521 | |
---|
522 | q = zeros( len(self.conserved_quantities), Float) |
---|
523 | |
---|
524 | for i, name in enumerate(self.conserved_quantities): |
---|
525 | Q = self.quantities[name] |
---|
526 | if vertex is not None: |
---|
527 | q[i] = Q.vertex_values[vol_id, vertex] |
---|
528 | #elif edge is not None: |
---|
529 | # q[i] = Q.edge_values[vol_id, edge] |
---|
530 | else: |
---|
531 | q[i] = Q.centroid_values[vol_id] |
---|
532 | |
---|
533 | return q |
---|
534 | |
---|
535 | |
---|
536 | def get_evolved_quantities(self, vol_id, vertex=None):#, edge=None): |
---|
537 | """Get evolved quantities at volume vol_id |
---|
538 | |
---|
539 | If vertex is specified use it as index for vertex values |
---|
540 | If edge is specified use it as index for edge values |
---|
541 | If neither are specified use centroid values |
---|
542 | If both are specified an exeception is raised |
---|
543 | |
---|
544 | Return value: Vector of length == number_of_evolved quantities |
---|
545 | |
---|
546 | """ |
---|
547 | |
---|
548 | from Numeric import zeros, Float |
---|
549 | |
---|
550 | #if not (vertex is None):# or edge is None): |
---|
551 | # msg = 'Values for both vertex and edge was specified.' |
---|
552 | # msg += 'Only one (or none) is allowed.' |
---|
553 | # raise msg |
---|
554 | |
---|
555 | q = zeros( len(self.evolved_quantities), Float) |
---|
556 | |
---|
557 | for i, name in enumerate(self.evolved_quantities): |
---|
558 | Q = self.quantities[name] |
---|
559 | if vertex is not None: |
---|
560 | q[i] = Q.vertex_values[vol_id, vertex] |
---|
561 | #elif edge is not None: |
---|
562 | # q[i] = Q.edge_values[vol_id, edge] |
---|
563 | else: |
---|
564 | q[i] = Q.centroid_values[vol_id] |
---|
565 | |
---|
566 | return q |
---|
567 | |
---|
568 | |
---|
569 | def get_centroids(self): |
---|
570 | """Return all coordinates of centroids |
---|
571 | Return x coordinate of centroid for each element as a N array |
---|
572 | """ |
---|
573 | |
---|
574 | return self.centroids |
---|
575 | |
---|
576 | def get_vertices(self): |
---|
577 | """Return all coordinates of centroids |
---|
578 | Return x coordinate of centroid for each element as a N array |
---|
579 | """ |
---|
580 | |
---|
581 | return self.vertices |
---|
582 | |
---|
583 | def get_coordinate(self, elem_id, vertex=None): |
---|
584 | """Return coordinate of centroid, |
---|
585 | or left or right vertex. |
---|
586 | Left vertex (vertex=0). Right vertex (vertex=1) |
---|
587 | """ |
---|
588 | |
---|
589 | if vertex is None: |
---|
590 | return self.centroids[elem_id] |
---|
591 | else: |
---|
592 | return self.vertices[elem_id,vertex] |
---|
593 | |
---|
594 | def get_area(self, elem_id): |
---|
595 | """Return area of element id |
---|
596 | """ |
---|
597 | |
---|
598 | return self.areas[elem_id] |
---|
599 | |
---|
600 | def get_quantity(self, name, location='vertices', indices = None): |
---|
601 | """Get values for named quantity |
---|
602 | |
---|
603 | name: Name of quantity |
---|
604 | |
---|
605 | In case of location == 'centroids' the dimension values must |
---|
606 | be a list of a Numerical array of length N, N being the number |
---|
607 | of elements. Otherwise it must be of dimension Nx3. |
---|
608 | |
---|
609 | Indices is the set of element ids that the operation applies to. |
---|
610 | |
---|
611 | The values will be stored in elements following their |
---|
612 | internal ordering. |
---|
613 | """ |
---|
614 | |
---|
615 | return self.quantities[name].get_values( location, indices = indices) |
---|
616 | |
---|
617 | def get_centroid_coordinates(self): |
---|
618 | """Return all centroid coordinates. |
---|
619 | Return all centroid coordinates for all triangles as an Nx2 array |
---|
620 | (ordered as x0, y0 for each triangle) |
---|
621 | """ |
---|
622 | return self.centroids |
---|
623 | |
---|
624 | |
---|
625 | def get_timestepping_method(self): |
---|
626 | return self.timestepping_method |
---|
627 | |
---|
628 | def set_timestepping_method(self,timestepping_method): |
---|
629 | |
---|
630 | if timestepping_method in ['euler', 'rk2', 'rk3']: |
---|
631 | self.timestepping_method = timestepping_method |
---|
632 | return |
---|
633 | |
---|
634 | msg = '%s is an incorrect timestepping type'% timestepping_method |
---|
635 | raise Exception, msg |
---|
636 | |
---|
637 | |
---|
638 | def set_quantity(self, name, *args, **kwargs): |
---|
639 | """Set values for named quantity |
---|
640 | |
---|
641 | |
---|
642 | One keyword argument is documented here: |
---|
643 | expression = None, # Arbitrary expression |
---|
644 | |
---|
645 | expression: |
---|
646 | Arbitrary expression involving quantity names |
---|
647 | |
---|
648 | See Quantity.set_values for further documentation. |
---|
649 | """ |
---|
650 | |
---|
651 | #FIXME (Ole): Allow new quantities here |
---|
652 | #from quantity import Quantity, Conserved_quantity |
---|
653 | #Create appropriate quantity object |
---|
654 | # #if name in self.conserved_quantities: |
---|
655 | # # self.quantities[name] = Conserved_quantity(self) |
---|
656 | # #else: |
---|
657 | # # self.quantities[name] = Quantity(self) |
---|
658 | |
---|
659 | |
---|
660 | #Do the expression stuff |
---|
661 | if kwargs.has_key('expression'): |
---|
662 | expression = kwargs['expression'] |
---|
663 | del kwargs['expression'] |
---|
664 | |
---|
665 | Q = self.create_quantity_from_expression(expression) |
---|
666 | kwargs['quantity'] = Q |
---|
667 | |
---|
668 | #Assign values |
---|
669 | self.quantities[name].set_values(*args, **kwargs) |
---|
670 | |
---|
671 | def set_boundary(self, boundary_map): |
---|
672 | """Associate boundary objects with tagged boundary segments. |
---|
673 | |
---|
674 | Input boundary_map is a dictionary of boundary objects keyed |
---|
675 | by symbolic tags to matched against tags in the internal dictionary |
---|
676 | self.boundary. |
---|
677 | |
---|
678 | As result one pointer to a boundary object is stored for each vertex |
---|
679 | in the list self.boundary_objects. |
---|
680 | More entries may point to the same boundary object |
---|
681 | |
---|
682 | Schematically the mapping is from two dictionaries to one list |
---|
683 | where the index is used as pointer to the boundary_values arrays |
---|
684 | within each quantity. |
---|
685 | |
---|
686 | self.boundary: (vol_id, edge_id): tag |
---|
687 | boundary_map (input): tag: boundary_object |
---|
688 | ---------------------------------------------- |
---|
689 | self.boundary_objects: ((vol_id, edge_id), boundary_object) |
---|
690 | |
---|
691 | |
---|
692 | Pre-condition: |
---|
693 | self.boundary has been built. |
---|
694 | |
---|
695 | Post-condition: |
---|
696 | self.boundary_objects is built |
---|
697 | |
---|
698 | If a tag from the domain doesn't appear in the input dictionary an |
---|
699 | exception is raised. |
---|
700 | However, if a tag is not used to the domain, no error is thrown. |
---|
701 | FIXME: This would lead to implementation of a |
---|
702 | default boundary condition |
---|
703 | |
---|
704 | Note: If a segment is listed in the boundary dictionary and if it is |
---|
705 | not None, it *will* become a boundary - |
---|
706 | even if there is a neighbouring triangle. |
---|
707 | This would be the case for internal boundaries |
---|
708 | |
---|
709 | Boundary objects that are None will be skipped. |
---|
710 | |
---|
711 | FIXME: If set_boundary is called multiple times and if Boundary |
---|
712 | object is changed into None, the neighbour structure will not be |
---|
713 | restored!!! |
---|
714 | """ |
---|
715 | |
---|
716 | self.boundary_objects = [] |
---|
717 | self.boundary_map = boundary_map #Store for use with eg. boundary_stats. |
---|
718 | |
---|
719 | #FIXME: Try to remove the sorting and fix test_mesh.py |
---|
720 | x = self.boundary.keys() |
---|
721 | x.sort() |
---|
722 | |
---|
723 | #Loop through edges that lie on the boundary and associate them with |
---|
724 | #callable boundary objects depending on their tags |
---|
725 | #for k, (vol_id, edge_id) in enumerate(x): |
---|
726 | for k, (vol_id, vertex_id) in enumerate(x): |
---|
727 | #tag = self.boundary[ (vol_id, edge_id) ] |
---|
728 | tag = self.boundary[ (vol_id, vertex_id) ] |
---|
729 | |
---|
730 | if boundary_map.has_key(tag): |
---|
731 | B = boundary_map[tag] #Get callable boundary object |
---|
732 | |
---|
733 | if B is not None: |
---|
734 | #self.boundary_objects.append( ((vol_id, edge_id), B) ) |
---|
735 | #self.neighbours[vol_id, edge_id] = -len(self.boundary_objects) |
---|
736 | self.boundary_objects.append( ((vol_id, vertex_id), B) ) |
---|
737 | self.neighbours[vol_id, vertex_id] = -len(self.boundary_objects) |
---|
738 | else: |
---|
739 | pass |
---|
740 | #FIXME: Check and perhaps fix neighbour structure |
---|
741 | |
---|
742 | else: |
---|
743 | msg = 'ERROR (domain.py): Tag "%s" has not been ' %tag |
---|
744 | msg += 'bound to a boundary object.\n' |
---|
745 | msg += 'All boundary tags defined in domain must appear ' |
---|
746 | msg += 'in the supplied dictionary.\n' |
---|
747 | msg += 'The tags are: %s' %self.get_boundary_tags() |
---|
748 | raise msg |
---|
749 | |
---|
750 | |
---|
751 | |
---|
752 | def check_integrity(self): |
---|
753 | #Mesh.check_integrity(self) |
---|
754 | |
---|
755 | #print self.quantities |
---|
756 | #print self.conserved_quantities |
---|
757 | |
---|
758 | for quantity in self.conserved_quantities: |
---|
759 | msg = 'Conserved quantities must be a subset of all quantities' |
---|
760 | assert quantity in self.quantities, msg |
---|
761 | |
---|
762 | for quantity in self.evolved_quantities: |
---|
763 | msg = 'Evolved quantities must be a subset of all quantities' |
---|
764 | assert quantity in self.quantities, msg |
---|
765 | |
---|
766 | # #assert hasattr(self, 'boundary_objects') |
---|
767 | |
---|
768 | def write_time(self): |
---|
769 | print self.timestepping_statistics() |
---|
770 | |
---|
771 | def timestepping_statistics(self): |
---|
772 | """Return string with time stepping statistics for printing or logging |
---|
773 | """ |
---|
774 | |
---|
775 | msg = '' |
---|
776 | if self.min_timestep == self.max_timestep: |
---|
777 | msg += 'Time = %.4f, delta t = %.8f, steps=%d (%d)'\ |
---|
778 | %(self.time, self.min_timestep, self.number_of_steps, |
---|
779 | self.number_of_first_order_steps) |
---|
780 | elif self.min_timestep > self.max_timestep: |
---|
781 | msg += 'Time = %.4f, steps=%d (%d)'\ |
---|
782 | %(self.time, self.number_of_steps, |
---|
783 | self.number_of_first_order_steps) |
---|
784 | else: |
---|
785 | msg += 'Time = %.4f, delta t in [%.8f, %.8f], steps=%d (%d)'\ |
---|
786 | %(self.time, self.min_timestep, |
---|
787 | self.max_timestep, self.number_of_steps, |
---|
788 | self.number_of_first_order_steps) |
---|
789 | |
---|
790 | return msg |
---|
791 | |
---|
792 | def get_name(self): |
---|
793 | return self.filename |
---|
794 | |
---|
795 | def set_name(self, name): |
---|
796 | self.filename = name |
---|
797 | |
---|
798 | def get_datadir(self): |
---|
799 | return self.datadir |
---|
800 | |
---|
801 | def set_datadir(self, name): |
---|
802 | self.datadir = name |
---|
803 | |
---|
804 | def set_CFL(self, cfl): |
---|
805 | if cfl > 1.0: |
---|
806 | print 'WARNING: Setting CFL condition to %f which is greater than 1' % cfl |
---|
807 | self.CFL = cfl |
---|
808 | |
---|
809 | def get_CFL(self): |
---|
810 | return self.CFL |
---|
811 | |
---|
812 | def set_filename(self, name): |
---|
813 | self.filename = name |
---|
814 | |
---|
815 | def get_filename(self): |
---|
816 | return self.filename |
---|
817 | |
---|
818 | def get_limiter(self): |
---|
819 | return self.limiter |
---|
820 | |
---|
821 | def set_limiter(self,limiter): |
---|
822 | |
---|
823 | possible_limiters = \ |
---|
824 | ['pyvolution', 'minmod_steve', 'minmod', 'minmod_kurganov', 'superbee', 'vanleer', 'vanalbada'] |
---|
825 | |
---|
826 | if limiter in possible_limiters: |
---|
827 | self.limiter = limiter |
---|
828 | return |
---|
829 | |
---|
830 | msg = '%s is an incorrect limiter type.\n'% limiter |
---|
831 | msg += 'Possible types are: '+ ", ".join(["%s" % el for el in possible_limiters]) |
---|
832 | raise Exception, msg |
---|
833 | |
---|
834 | |
---|
835 | #-------------------------- |
---|
836 | # Main components of evolve |
---|
837 | #-------------------------- |
---|
838 | |
---|
839 | def evolve(self, yieldstep = None, |
---|
840 | finaltime = None, |
---|
841 | duration = None, |
---|
842 | skip_initial_step = False): |
---|
843 | """Evolve model through time starting from self.starttime. |
---|
844 | |
---|
845 | |
---|
846 | yieldstep: Interval between yields where results are stored, |
---|
847 | statistics written and domain inspected or |
---|
848 | possibly modified. If omitted the internal predefined |
---|
849 | max timestep is used. |
---|
850 | Internally, smaller timesteps may be taken. |
---|
851 | |
---|
852 | duration: Duration of simulation |
---|
853 | |
---|
854 | finaltime: Time where simulation should end. This is currently |
---|
855 | relative time. So it's the same as duration. |
---|
856 | |
---|
857 | If both duration and finaltime are given an exception is thrown. |
---|
858 | |
---|
859 | |
---|
860 | skip_initial_step: Boolean flag that decides whether the first |
---|
861 | yield step is skipped or not. This is useful for example to avoid |
---|
862 | duplicate steps when multiple evolve processes are dove tailed. |
---|
863 | |
---|
864 | |
---|
865 | Evolve is implemented as a generator and is to be called as such, e.g. |
---|
866 | |
---|
867 | for t in domain.evolve(yieldstep, finaltime): |
---|
868 | <Do something with domain and t> |
---|
869 | |
---|
870 | |
---|
871 | All times are given in seconds |
---|
872 | |
---|
873 | """ |
---|
874 | |
---|
875 | from config import min_timestep, max_timestep, epsilon |
---|
876 | |
---|
877 | # FIXME: Maybe lump into a larger check prior to evolving |
---|
878 | msg = 'Boundary tags must be bound to boundary objects before ' |
---|
879 | msg += 'evolving system, ' |
---|
880 | msg += 'e.g. using the method set_boundary.\n' |
---|
881 | msg += 'This system has the boundary tags %s '\ |
---|
882 | %self.get_boundary_tags() |
---|
883 | assert hasattr(self, 'boundary_objects'), msg |
---|
884 | |
---|
885 | |
---|
886 | if yieldstep is None: |
---|
887 | yieldstep = max_timestep |
---|
888 | else: |
---|
889 | yieldstep = float(yieldstep) |
---|
890 | |
---|
891 | self._order_ = self.default_order |
---|
892 | |
---|
893 | |
---|
894 | if finaltime is not None and duration is not None: |
---|
895 | # print 'F', finaltime, duration |
---|
896 | msg = 'Only one of finaltime and duration may be specified' |
---|
897 | raise msg |
---|
898 | else: |
---|
899 | if finaltime is not None: |
---|
900 | self.finaltime = float(finaltime) |
---|
901 | if duration is not None: |
---|
902 | self.finaltime = self.starttime + float(duration) |
---|
903 | |
---|
904 | |
---|
905 | |
---|
906 | N = len(self) # Number of triangles |
---|
907 | self.yieldtime = 0.0 # Track time between 'yields' |
---|
908 | |
---|
909 | # Initialise interval of timestep sizes (for reporting only) |
---|
910 | self.min_timestep = max_timestep |
---|
911 | self.max_timestep = min_timestep |
---|
912 | self.number_of_steps = 0 |
---|
913 | self.number_of_first_order_steps = 0 |
---|
914 | |
---|
915 | |
---|
916 | # Update ghosts |
---|
917 | self.update_ghosts() |
---|
918 | |
---|
919 | # Initial update of vertex and edge values |
---|
920 | self.distribute_to_vertices_and_edges() |
---|
921 | |
---|
922 | # Update extrema if necessary (for reporting) |
---|
923 | self.update_extrema() |
---|
924 | |
---|
925 | # Initial update boundary values |
---|
926 | self.update_boundary() |
---|
927 | |
---|
928 | # Or maybe restore from latest checkpoint |
---|
929 | if self.checkpoint is True: |
---|
930 | self.goto_latest_checkpoint() |
---|
931 | |
---|
932 | if skip_initial_step is False: |
---|
933 | yield(self.time) # Yield initial values |
---|
934 | |
---|
935 | while True: |
---|
936 | |
---|
937 | # Evolve One Step, using appropriate timestepping method |
---|
938 | if self.get_timestepping_method() == 'euler': |
---|
939 | self.evolve_one_euler_step(yieldstep,finaltime) |
---|
940 | |
---|
941 | elif self.get_timestepping_method() == 'rk2': |
---|
942 | self.evolve_one_rk2_step(yieldstep,finaltime) |
---|
943 | |
---|
944 | elif self.get_timestepping_method() == 'rk3': |
---|
945 | self.evolve_one_rk3_step(yieldstep,finaltime) |
---|
946 | |
---|
947 | |
---|
948 | # Update extrema if necessary (for reporting) |
---|
949 | self.update_extrema() |
---|
950 | |
---|
951 | |
---|
952 | |
---|
953 | self.yieldtime += self.timestep |
---|
954 | self.number_of_steps += 1 |
---|
955 | if self._order_ == 1: |
---|
956 | self.number_of_first_order_steps += 1 |
---|
957 | |
---|
958 | |
---|
959 | # Yield results |
---|
960 | if finaltime is not None and self.time >= finaltime-epsilon: |
---|
961 | |
---|
962 | if self.time > finaltime: |
---|
963 | # FIXME (Ole, 30 April 2006): Do we need this check? |
---|
964 | # Probably not (Ole, 18 September 2008). Now changed to |
---|
965 | # Exception |
---|
966 | msg = 'WARNING (domain.py): time overshot finaltime. ' |
---|
967 | msg += 'Contact Ole.Nielsen@ga.gov.au' |
---|
968 | raise Exception, msg |
---|
969 | |
---|
970 | |
---|
971 | # Yield final time and stop |
---|
972 | self.time = finaltime |
---|
973 | yield(self.time) |
---|
974 | break |
---|
975 | |
---|
976 | if self.yieldtime >= yieldstep: |
---|
977 | # Yield (intermediate) time and allow inspection of domain |
---|
978 | |
---|
979 | if self.checkpoint is True: |
---|
980 | self.store_checkpoint() |
---|
981 | self.delete_old_checkpoints() |
---|
982 | |
---|
983 | # Pass control on to outer loop for more specific actions |
---|
984 | |
---|
985 | yield(self.time) |
---|
986 | |
---|
987 | # Reinitialise |
---|
988 | self.yieldtime = 0.0 |
---|
989 | self.min_timestep = max_timestep |
---|
990 | self.max_timestep = min_timestep |
---|
991 | self.number_of_steps = 0 |
---|
992 | self.number_of_first_order_steps = 0 |
---|
993 | #self.max_speed_array = 0.0 |
---|
994 | |
---|
995 | |
---|
996 | def evolve_one_euler_step(self, yieldstep, finaltime): |
---|
997 | """ |
---|
998 | One Euler Time Step |
---|
999 | Q^{n+1} = E(h) Q^n |
---|
1000 | """ |
---|
1001 | |
---|
1002 | |
---|
1003 | # Compute fluxes across each element edge |
---|
1004 | self.compute_fluxes() |
---|
1005 | |
---|
1006 | # Update timestep to fit yieldstep and finaltime |
---|
1007 | self.update_timestep(yieldstep, finaltime) |
---|
1008 | |
---|
1009 | # Update conserved quantities |
---|
1010 | self.update_conserved_quantities() |
---|
1011 | |
---|
1012 | # Update ghosts |
---|
1013 | self.update_ghosts() |
---|
1014 | |
---|
1015 | # Update vertex and edge values |
---|
1016 | self.distribute_to_vertices_and_edges() |
---|
1017 | |
---|
1018 | # Update boundary values |
---|
1019 | self.update_boundary() |
---|
1020 | |
---|
1021 | # Update time |
---|
1022 | self.time += self.timestep |
---|
1023 | |
---|
1024 | |
---|
1025 | |
---|
1026 | |
---|
1027 | def evolve_one_rk2_step(self, yieldstep, finaltime): |
---|
1028 | """ |
---|
1029 | One 2nd order RK timestep |
---|
1030 | Q^{n+1} = 0.5 Q^n + 0.5 E(h)^2 Q^n |
---|
1031 | """ |
---|
1032 | |
---|
1033 | # Save initial conserved quantities values |
---|
1034 | self.backup_conserved_quantities() |
---|
1035 | |
---|
1036 | #-------------------------------------- |
---|
1037 | # First euler step |
---|
1038 | #-------------------------------------- |
---|
1039 | |
---|
1040 | # Compute fluxes across each element edge |
---|
1041 | self.compute_fluxes() |
---|
1042 | |
---|
1043 | # Update timestep to fit yieldstep and finaltime |
---|
1044 | self.update_timestep(yieldstep, finaltime) |
---|
1045 | |
---|
1046 | # Update conserved quantities |
---|
1047 | self.update_conserved_quantities() |
---|
1048 | |
---|
1049 | # Update ghosts |
---|
1050 | self.update_ghosts() |
---|
1051 | |
---|
1052 | # Update vertex and edge values |
---|
1053 | self.distribute_to_vertices_and_edges() |
---|
1054 | |
---|
1055 | # Update boundary values |
---|
1056 | self.update_boundary() |
---|
1057 | |
---|
1058 | # Update time |
---|
1059 | self.time += self.timestep |
---|
1060 | |
---|
1061 | #------------------------------------ |
---|
1062 | # Second Euler step |
---|
1063 | #------------------------------------ |
---|
1064 | |
---|
1065 | # Compute fluxes across each element edge |
---|
1066 | self.compute_fluxes() |
---|
1067 | |
---|
1068 | # Update conserved quantities |
---|
1069 | self.update_conserved_quantities() |
---|
1070 | |
---|
1071 | #------------------------------------ |
---|
1072 | # Combine initial and final values |
---|
1073 | # of conserved quantities and cleanup |
---|
1074 | #------------------------------------ |
---|
1075 | |
---|
1076 | # Combine steps |
---|
1077 | self.saxpy_conserved_quantities(0.5, 0.5) |
---|
1078 | |
---|
1079 | #----------------------------------- |
---|
1080 | # clean up vertex values |
---|
1081 | #----------------------------------- |
---|
1082 | |
---|
1083 | # Update ghosts |
---|
1084 | self.update_ghosts() |
---|
1085 | |
---|
1086 | # Update vertex and edge values |
---|
1087 | self.distribute_to_vertices_and_edges() |
---|
1088 | |
---|
1089 | # Update boundary values |
---|
1090 | self.update_boundary() |
---|
1091 | |
---|
1092 | |
---|
1093 | |
---|
1094 | def evolve_one_rk3_step(self, yieldstep, finaltime): |
---|
1095 | """ |
---|
1096 | One 3rd order RK timestep |
---|
1097 | Q^(1) = 3/4 Q^n + 1/4 E(h)^2 Q^n (at time t^n + h/2) |
---|
1098 | Q^{n+1} = 1/3 Q^n + 2/3 E(h) Q^(1) (at time t^{n+1}) |
---|
1099 | """ |
---|
1100 | |
---|
1101 | # Save initial initial conserved quantities values |
---|
1102 | self.backup_conserved_quantities() |
---|
1103 | |
---|
1104 | initial_time = self.time |
---|
1105 | |
---|
1106 | #-------------------------------------- |
---|
1107 | # First euler step |
---|
1108 | #-------------------------------------- |
---|
1109 | |
---|
1110 | # Compute fluxes across each element edge |
---|
1111 | self.compute_fluxes() |
---|
1112 | |
---|
1113 | # Update timestep to fit yieldstep and finaltime |
---|
1114 | self.update_timestep(yieldstep, finaltime) |
---|
1115 | |
---|
1116 | # Update conserved quantities |
---|
1117 | self.update_conserved_quantities() |
---|
1118 | |
---|
1119 | # Update ghosts |
---|
1120 | self.update_ghosts() |
---|
1121 | |
---|
1122 | # Update vertex and edge values |
---|
1123 | self.distribute_to_vertices_and_edges() |
---|
1124 | |
---|
1125 | # Update boundary values |
---|
1126 | self.update_boundary() |
---|
1127 | |
---|
1128 | # Update time |
---|
1129 | self.time += self.timestep |
---|
1130 | |
---|
1131 | #------------------------------------ |
---|
1132 | # Second Euler step |
---|
1133 | #------------------------------------ |
---|
1134 | |
---|
1135 | # Compute fluxes across each element edge |
---|
1136 | self.compute_fluxes() |
---|
1137 | |
---|
1138 | # Update conserved quantities |
---|
1139 | self.update_conserved_quantities() |
---|
1140 | |
---|
1141 | #------------------------------------ |
---|
1142 | #Combine steps to obtain intermediate |
---|
1143 | #solution at time t^n + 0.5 h |
---|
1144 | #------------------------------------ |
---|
1145 | |
---|
1146 | # Combine steps |
---|
1147 | self.saxpy_conserved_quantities(0.25, 0.75) |
---|
1148 | |
---|
1149 | # Update ghosts |
---|
1150 | self.update_ghosts() |
---|
1151 | |
---|
1152 | # Update vertex and edge values |
---|
1153 | self.distribute_to_vertices_and_edges() |
---|
1154 | |
---|
1155 | # Update boundary values |
---|
1156 | self.update_boundary() |
---|
1157 | |
---|
1158 | # Set substep time |
---|
1159 | self.time = initial_time + self.timestep*0.5 |
---|
1160 | |
---|
1161 | #------------------------------------ |
---|
1162 | # Third Euler step |
---|
1163 | #------------------------------------ |
---|
1164 | |
---|
1165 | # Compute fluxes across each element edge |
---|
1166 | self.compute_fluxes() |
---|
1167 | |
---|
1168 | # Update conserved quantities |
---|
1169 | self.update_conserved_quantities() |
---|
1170 | |
---|
1171 | #------------------------------------ |
---|
1172 | # Combine final and initial values |
---|
1173 | # and cleanup |
---|
1174 | #------------------------------------ |
---|
1175 | |
---|
1176 | # Combine steps |
---|
1177 | self.saxpy_conserved_quantities(2.0/3.0, 1.0/3.0) |
---|
1178 | |
---|
1179 | # Update ghosts |
---|
1180 | self.update_ghosts() |
---|
1181 | |
---|
1182 | # Update vertex and edge values |
---|
1183 | self.distribute_to_vertices_and_edges() |
---|
1184 | |
---|
1185 | # Update boundary values |
---|
1186 | self.update_boundary() |
---|
1187 | |
---|
1188 | # Set new time |
---|
1189 | self.time = initial_time + self.timestep |
---|
1190 | |
---|
1191 | |
---|
1192 | def backup_conserved_quantities(self): |
---|
1193 | N = len(self) # Number_of_triangles |
---|
1194 | |
---|
1195 | # Backup conserved_quantities centroid values |
---|
1196 | for name in self.conserved_quantities: |
---|
1197 | Q = self.quantities[name] |
---|
1198 | Q.backup_centroid_values() |
---|
1199 | |
---|
1200 | def saxpy_conserved_quantities(self,a,b): |
---|
1201 | N = len(self) #number_of_triangles |
---|
1202 | |
---|
1203 | # Backup conserved_quantities centroid values |
---|
1204 | for name in self.conserved_quantities: |
---|
1205 | Q = self.quantities[name] |
---|
1206 | Q.saxpy_centroid_values(a,b) |
---|
1207 | |
---|
1208 | |
---|
1209 | #============================== |
---|
1210 | # John Jakeman's old evolve code |
---|
1211 | #============================= |
---|
1212 | |
---|
1213 | def evolve_john(self, yieldstep = None, finaltime = None, |
---|
1214 | skip_initial_step = False): |
---|
1215 | """Evolve model from time=0.0 to finaltime yielding results |
---|
1216 | every yieldstep. |
---|
1217 | |
---|
1218 | Internally, smaller timesteps may be taken. |
---|
1219 | |
---|
1220 | Evolve is implemented as a generator and is to be called as such, e.g. |
---|
1221 | |
---|
1222 | for t in domain.evolve(timestep, yieldstep, finaltime): |
---|
1223 | <Do something with domain and t> |
---|
1224 | |
---|
1225 | """ |
---|
1226 | |
---|
1227 | from config import min_timestep, max_timestep, epsilon |
---|
1228 | |
---|
1229 | #FIXME: Maybe lump into a larger check prior to evolving |
---|
1230 | msg = 'Boundary tags must be bound to boundary objects before evolving system, ' |
---|
1231 | msg += 'e.g. using the method set_boundary.\n' |
---|
1232 | msg += 'This system has the boundary tags %s ' %self.get_boundary_tags() |
---|
1233 | assert hasattr(self, 'boundary_objects'), msg |
---|
1234 | |
---|
1235 | # #self.set_defaults() |
---|
1236 | |
---|
1237 | if yieldstep is None: |
---|
1238 | yieldstep = max_timestep |
---|
1239 | else: |
---|
1240 | yieldstep = float(yieldstep) |
---|
1241 | |
---|
1242 | self.order = self.default_order |
---|
1243 | |
---|
1244 | self.time_order = self.default_time_order |
---|
1245 | |
---|
1246 | self.yieldtime = 0.0 #Time between 'yields' |
---|
1247 | |
---|
1248 | #Initialise interval of timestep sizes (for reporting only) |
---|
1249 | # SEEMS WIERD |
---|
1250 | self.min_timestep = max_timestep |
---|
1251 | self.max_timestep = min_timestep |
---|
1252 | self.finaltime = finaltime |
---|
1253 | self.number_of_steps = 0 |
---|
1254 | self.number_of_first_order_steps = 0 |
---|
1255 | |
---|
1256 | #update ghosts |
---|
1257 | self.update_ghosts() |
---|
1258 | |
---|
1259 | #Initial update of vertex and edge values |
---|
1260 | self.distribute_to_vertices_and_edges() |
---|
1261 | |
---|
1262 | #Initial update boundary values |
---|
1263 | self.update_boundary() |
---|
1264 | |
---|
1265 | #Or maybe restore from latest checkpoint |
---|
1266 | if self.checkpoint is True: |
---|
1267 | self.goto_latest_checkpoint() |
---|
1268 | |
---|
1269 | if skip_initial_step is False: |
---|
1270 | yield(self.time) #Yield initial values |
---|
1271 | |
---|
1272 | while True: |
---|
1273 | if self.time_order == 1: |
---|
1274 | #Compute fluxes across each element edge |
---|
1275 | self.compute_fluxes() |
---|
1276 | #Update timestep to fit yieldstep and finaltime |
---|
1277 | self.update_timestep(yieldstep, finaltime) |
---|
1278 | #Compute forcing terms |
---|
1279 | self.compute_forcing_terms() |
---|
1280 | #Update conserved quantities |
---|
1281 | self.update_conserved_quantities(self.timestep) |
---|
1282 | #update ghosts |
---|
1283 | #self.update_ghosts() |
---|
1284 | #Update vertex and edge values |
---|
1285 | self.distribute_to_vertices_and_edges() |
---|
1286 | #Update boundary values |
---|
1287 | self.update_boundary() |
---|
1288 | |
---|
1289 | elif self.time_order == 2: |
---|
1290 | |
---|
1291 | self.compute_timestep() #self.compute_fluxes() !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
---|
1292 | |
---|
1293 | #Solve inhomogeneous operator for half a timestep |
---|
1294 | self.solve_inhomogenous_second_order(yieldstep, finaltime) |
---|
1295 | |
---|
1296 | #Solve homogeneous operator for full timestep using |
---|
1297 | #Harten second order timestepping |
---|
1298 | self.solve_homogenous_second_order(yieldstep,finaltime) |
---|
1299 | |
---|
1300 | #Solve inhomogeneous operator for half a timestep |
---|
1301 | self.solve_inhomogenous_second_order(yieldstep, finaltime) |
---|
1302 | |
---|
1303 | #Update time |
---|
1304 | self.time += self.timestep |
---|
1305 | self.yieldtime += self.timestep |
---|
1306 | self.number_of_steps += 1 |
---|
1307 | if self.order == 1: |
---|
1308 | self.number_of_first_order_steps += 1 |
---|
1309 | |
---|
1310 | #Yield results |
---|
1311 | if finaltime is not None and abs(self.time - finaltime) < epsilon: |
---|
1312 | |
---|
1313 | #FIXME: There is a rare situation where the |
---|
1314 | #final time step is stored twice. Can we make a test? |
---|
1315 | |
---|
1316 | # Yield final time and stop |
---|
1317 | yield(self.time) |
---|
1318 | break |
---|
1319 | |
---|
1320 | |
---|
1321 | if abs(self.yieldtime - yieldstep) < epsilon: |
---|
1322 | # Yield (intermediate) time and allow inspection of domain |
---|
1323 | |
---|
1324 | if self.checkpoint is True: |
---|
1325 | self.store_checkpoint() |
---|
1326 | self.delete_old_checkpoints() |
---|
1327 | |
---|
1328 | #Pass control on to outer loop for more specific actions |
---|
1329 | yield(self.time) |
---|
1330 | |
---|
1331 | # Reinitialise |
---|
1332 | self.yieldtime = 0.0 |
---|
1333 | self.min_timestep = max_timestep |
---|
1334 | self.max_timestep = min_timestep |
---|
1335 | self.number_of_steps = 0 |
---|
1336 | self.number_of_first_order_steps = 0 |
---|
1337 | |
---|
1338 | def solve_inhomogenous_second_order(self,yieldstep, finaltime): |
---|
1339 | |
---|
1340 | #Update timestep to fit yieldstep and finaltime |
---|
1341 | self.update_timestep(yieldstep, finaltime) |
---|
1342 | #Compute forcing terms |
---|
1343 | self.compute_forcing_terms() |
---|
1344 | #Update conserved quantities |
---|
1345 | self.update_conserved_quantities(0.5*self.timestep) |
---|
1346 | #Update vertex and edge values |
---|
1347 | self.distribute_to_vertices_and_edges() |
---|
1348 | #Update boundary values |
---|
1349 | self.update_boundary() |
---|
1350 | |
---|
1351 | def solve_homogenous_second_order(self,yieldstep,finaltime): |
---|
1352 | """Use Shu Second order timestepping to update |
---|
1353 | conserved quantities |
---|
1354 | |
---|
1355 | q^{n+1/2} = q^{n}+0.5*dt*F^{n} |
---|
1356 | q^{n+1} = q^{n}+dt*F^{n+1/2} |
---|
1357 | """ |
---|
1358 | import copy |
---|
1359 | from Numeric import zeros,Float |
---|
1360 | |
---|
1361 | N = self.number_of_elements |
---|
1362 | |
---|
1363 | self.compute_fluxes() |
---|
1364 | #Update timestep to fit yieldstep and finaltime |
---|
1365 | self.update_timestep(yieldstep, finaltime) |
---|
1366 | #Compute forcing terms |
---|
1367 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
---|
1368 | #ADDING THIS WILL NEED TO REMOVE ZEROING IN COMPUTE_FORCING |
---|
1369 | #self.compute_forcing_terms() |
---|
1370 | |
---|
1371 | QC = zeros((N,len(self.conserved_quantities)),Float) |
---|
1372 | QF = zeros((N,len(self.conserved_quantities)),Float) |
---|
1373 | |
---|
1374 | i = 0 |
---|
1375 | for name in self.conserved_quantities: |
---|
1376 | Q = self.quantities[name] |
---|
1377 | #Store the centroid values at time t^n |
---|
1378 | QC[:,i] = copy.copy(Q.centroid_values) |
---|
1379 | QF[:,i] = copy.copy(Q.explicit_update) |
---|
1380 | #Update conserved quantities |
---|
1381 | Q.update(self.timestep) |
---|
1382 | i+=1 |
---|
1383 | |
---|
1384 | #Update vertex and edge values |
---|
1385 | self.distribute_to_vertices_and_edges() |
---|
1386 | #Update boundary values |
---|
1387 | self.update_boundary() |
---|
1388 | |
---|
1389 | self.compute_fluxes() |
---|
1390 | self.update_timestep(yieldstep, finaltime) |
---|
1391 | #Compute forcing terms |
---|
1392 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
---|
1393 | #self.compute_forcing_terms() |
---|
1394 | |
---|
1395 | i = 0 |
---|
1396 | for name in self.conserved_quantities: |
---|
1397 | Q = self.quantities[name] |
---|
1398 | Q.centroid_values = QC[:,i] |
---|
1399 | Q.explicit_update = 0.5*(Q.explicit_update+QF[:,i]) |
---|
1400 | #Update conserved quantities |
---|
1401 | Q.update(self.timestep) |
---|
1402 | i+=1 |
---|
1403 | |
---|
1404 | #Update vertex and edge values |
---|
1405 | self.distribute_to_vertices_and_edges() |
---|
1406 | #Update boundary values |
---|
1407 | self.update_boundary() |
---|
1408 | |
---|
1409 | def solve_homogenous_second_order_harten(self,yieldstep,finaltime): |
---|
1410 | """Use Harten Second order timestepping to update |
---|
1411 | conserved quantities |
---|
1412 | |
---|
1413 | q^{n+1/2} = q^{n}+0.5*dt*F^{n} |
---|
1414 | q^{n+1} = q^{n}+dt*F^{n+1/2} |
---|
1415 | """ |
---|
1416 | import copy |
---|
1417 | from Numeric import zeros,Float |
---|
1418 | |
---|
1419 | N = self.number_of_elements |
---|
1420 | |
---|
1421 | self.compute_fluxes() |
---|
1422 | #Update timestep to fit yieldstep and finaltime |
---|
1423 | self.update_timestep(yieldstep, finaltime) |
---|
1424 | #Compute forcing terms |
---|
1425 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
---|
1426 | #ADDING THIS WILL NEED TO REMOVE ZEROING IN COMPUTE_FORCING |
---|
1427 | #self.compute_forcing_terms() |
---|
1428 | |
---|
1429 | QC = zeros((N,len(self.conserved_quantities)),Float) |
---|
1430 | |
---|
1431 | i = 0 |
---|
1432 | for name in self.conserved_quantities: |
---|
1433 | Q = self.quantities[name] |
---|
1434 | #Store the centroid values at time t^n |
---|
1435 | QC[:,i] = copy.copy(Q.centroid_values) |
---|
1436 | #Update conserved quantities |
---|
1437 | Q.update(0.5*self.timestep) |
---|
1438 | i+=1 |
---|
1439 | |
---|
1440 | #Update vertex and edge values |
---|
1441 | self.distribute_to_vertices_and_edges() |
---|
1442 | #Update boundary values |
---|
1443 | self.update_boundary() |
---|
1444 | |
---|
1445 | self.compute_fluxes() |
---|
1446 | self.update_timestep(yieldstep, finaltime) |
---|
1447 | #Compute forcing terms |
---|
1448 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
---|
1449 | #self.compute_forcing_terms() |
---|
1450 | |
---|
1451 | i = 0 |
---|
1452 | for name in self.conserved_quantities: |
---|
1453 | Q = self.quantities[name] |
---|
1454 | Q.centroid_values = QC[:,i] |
---|
1455 | #Update conserved quantities |
---|
1456 | Q.update(self.timestep) |
---|
1457 | i+=1 |
---|
1458 | |
---|
1459 | #Update vertex and edge values |
---|
1460 | self.distribute_to_vertices_and_edges() |
---|
1461 | #Update boundary values |
---|
1462 | self.update_boundary() |
---|
1463 | |
---|
1464 | def distribute_to_vertices_and_edges(self): |
---|
1465 | """Extrapolate conserved quantities from centroid to |
---|
1466 | vertices and edge-midpoints for each volume |
---|
1467 | |
---|
1468 | Default implementation is straight first order, |
---|
1469 | i.e. constant values throughout each element and |
---|
1470 | no reference to non-conserved quantities. |
---|
1471 | """ |
---|
1472 | |
---|
1473 | for name in self.conserved_quantities: |
---|
1474 | Q = self.quantities[name] |
---|
1475 | if self.order == 1: |
---|
1476 | Q.extrapolate_first_order() |
---|
1477 | elif self.order == 2: |
---|
1478 | Q.extrapolate_second_order() |
---|
1479 | #Q.limit() |
---|
1480 | else: |
---|
1481 | raise 'Unknown order' |
---|
1482 | #Q.interpolate_from_vertices_to_edges() |
---|
1483 | |
---|
1484 | |
---|
1485 | def update_ghosts(self): |
---|
1486 | pass |
---|
1487 | |
---|
1488 | def update_boundary(self): |
---|
1489 | """Go through list of boundary objects and update boundary values |
---|
1490 | for all conserved quantities on boundary. |
---|
1491 | """ |
---|
1492 | |
---|
1493 | #FIXME: Update only those that change (if that can be worked out) |
---|
1494 | #FIXME: Boundary objects should not include ghost nodes. |
---|
1495 | #for i, ((vol_id, edge_id), B) in enumerate(self.boundary_objects): |
---|
1496 | # q = B.evaluate(vol_id, edge_id) |
---|
1497 | for i, ((vol_id, vertex_id), B) in enumerate(self.boundary_objects): |
---|
1498 | q = B.evaluate(vol_id, vertex_id) |
---|
1499 | #print 'q ',q |
---|
1500 | for j, name in enumerate(self.evolved_quantities): |
---|
1501 | #print 'name %s j = %f \n'%(name,j) |
---|
1502 | Q = self.quantities[name] |
---|
1503 | Q.boundary_values[i] = q[j] |
---|
1504 | |
---|
1505 | def update_timestep(self, yieldstep, finaltime): |
---|
1506 | |
---|
1507 | from config import min_timestep, max_timestep |
---|
1508 | |
---|
1509 | # self.timestep is calculated from speed of characteristics |
---|
1510 | # Apply CFL condition here |
---|
1511 | timestep = min(self.CFL*self.flux_timestep, max_timestep) |
---|
1512 | |
---|
1513 | #Record maximal and minimal values of timestep for reporting |
---|
1514 | self.max_timestep = max(timestep, self.max_timestep) |
---|
1515 | self.min_timestep = min(timestep, self.min_timestep) |
---|
1516 | |
---|
1517 | #Protect against degenerate time steps |
---|
1518 | if timestep < min_timestep: |
---|
1519 | |
---|
1520 | #Number of consecutive small steps taken b4 taking action |
---|
1521 | self.smallsteps += 1 |
---|
1522 | |
---|
1523 | if self.smallsteps > self.max_smallsteps: |
---|
1524 | self.smallsteps = 0 #Reset |
---|
1525 | |
---|
1526 | if self.order == 1: |
---|
1527 | msg = 'WARNING: Too small timestep %.16f reached '\ |
---|
1528 | %timestep |
---|
1529 | msg += 'even after %d steps of 1 order scheme'\ |
---|
1530 | %self.max_smallsteps |
---|
1531 | print msg |
---|
1532 | timestep = min_timestep #Try enforcing min_step |
---|
1533 | |
---|
1534 | #raise msg |
---|
1535 | else: |
---|
1536 | #Try to overcome situation by switching to 1 order |
---|
1537 | print "changing Order 1" |
---|
1538 | self.order = 1 |
---|
1539 | |
---|
1540 | else: |
---|
1541 | self.smallsteps = 0 |
---|
1542 | if self.order == 1 and self.default_order == 2: |
---|
1543 | self.order = 2 |
---|
1544 | |
---|
1545 | |
---|
1546 | #Ensure that final time is not exceeded |
---|
1547 | if finaltime is not None and self.time + timestep > finaltime: |
---|
1548 | timestep = finaltime-self.time |
---|
1549 | |
---|
1550 | #Ensure that model time is aligned with yieldsteps |
---|
1551 | if self.yieldtime + timestep > yieldstep: |
---|
1552 | timestep = yieldstep-self.yieldtime |
---|
1553 | |
---|
1554 | self.timestep = timestep |
---|
1555 | |
---|
1556 | def update_extrema(self): |
---|
1557 | pass |
---|
1558 | |
---|
1559 | def compute_forcing_terms(self): |
---|
1560 | """If there are any forcing functions driving the system |
---|
1561 | they should be defined in Domain subclass and appended to |
---|
1562 | the list self.forcing_terms |
---|
1563 | """ |
---|
1564 | #Clears explicit_update needed for second order method |
---|
1565 | if self.time_order == 2: |
---|
1566 | for name in self.conserved_quantities: |
---|
1567 | Q = self.quantities[name] |
---|
1568 | Q.explicit_update[:] = 0.0 |
---|
1569 | |
---|
1570 | for f in self.forcing_terms: |
---|
1571 | f(self) |
---|
1572 | |
---|
1573 | |
---|
1574 | def update_derived_quantites(self): |
---|
1575 | pass |
---|
1576 | |
---|
1577 | #def update_conserved_quantities(self): |
---|
1578 | def update_conserved_quantities(self): |
---|
1579 | """Update vectors of conserved quantities using previously |
---|
1580 | computed fluxes specified forcing functions. |
---|
1581 | """ |
---|
1582 | |
---|
1583 | from Numeric import ones, sum, equal, Float |
---|
1584 | |
---|
1585 | N = self.number_of_elements |
---|
1586 | d = len(self.conserved_quantities) |
---|
1587 | |
---|
1588 | timestep = self.timestep |
---|
1589 | |
---|
1590 | #Compute forcing terms |
---|
1591 | self.compute_forcing_terms() |
---|
1592 | |
---|
1593 | #Update conserved_quantities |
---|
1594 | for name in self.conserved_quantities: |
---|
1595 | Q = self.quantities[name] |
---|
1596 | Q.update(timestep) |
---|
1597 | |
---|
1598 | |
---|
1599 | |
---|
1600 | if __name__ == "__main__": |
---|
1601 | |
---|
1602 | points1 = [0.0, 1.0, 2.0, 3.0] |
---|
1603 | D1 = Domain(points1) |
---|
1604 | |
---|
1605 | print D1.get_coordinate(0) |
---|
1606 | print D1.get_coordinate(0,1) |
---|
1607 | print 'Number of Elements = ',D1.number_of_elements |
---|
1608 | |
---|
1609 | try: |
---|
1610 | print D1.get_coordinate(3) |
---|
1611 | except: |
---|
1612 | pass |
---|
1613 | else: |
---|
1614 | msg = 'Should have raised an out of bounds exception' |
---|
1615 | raise msg |
---|
1616 | |
---|
1617 | #points2 = [0.0, 1.0, 2.0, 3.0, 2.5] |
---|
1618 | #D2 = Domain(points2) |
---|