[7910] | 1 | """Class Quantity - Implements values at each 1d element |
---|
| 2 | |
---|
| 3 | To create: |
---|
| 4 | |
---|
| 5 | Quantity(domain, vertex_values) |
---|
| 6 | |
---|
| 7 | domain: Associated domain structure. Required. |
---|
| 8 | |
---|
| 9 | vertex_values: N x 2 array of values at each vertex for each element. |
---|
| 10 | Default None |
---|
| 11 | |
---|
| 12 | If vertex_values are None Create array of zeros compatible with domain. |
---|
| 13 | Otherwise check that it is compatible with dimenions of domain. |
---|
| 14 | Otherwise raise an exception |
---|
| 15 | """ |
---|
| 16 | |
---|
| 17 | |
---|
| 18 | |
---|
| 19 | class Quantity: |
---|
| 20 | |
---|
| 21 | |
---|
| 22 | def __init__(self, domain, vertex_values=None): |
---|
| 23 | #Initialise Quantity using optional vertex values. |
---|
| 24 | |
---|
| 25 | from domain import Domain |
---|
| 26 | from Numeric import Float |
---|
| 27 | from numpy import array, zeros |
---|
| 28 | |
---|
| 29 | msg = 'First argument in Quantity.__init__ ' |
---|
| 30 | msg += 'must be of class Domain (or a subclass thereof)' |
---|
| 31 | assert isinstance(domain, Domain), msg |
---|
| 32 | |
---|
| 33 | if vertex_values is None: |
---|
| 34 | N = domain.number_of_elements |
---|
| 35 | self.vertex_values = zeros((N, 2), Float) |
---|
| 36 | else: |
---|
| 37 | self.vertex_values = array(vertex_values, Float) |
---|
| 38 | |
---|
| 39 | N, V = self.vertex_values.shape |
---|
| 40 | assert V == 2,\ |
---|
| 41 | 'Two vertex values per element must be specified' |
---|
| 42 | |
---|
| 43 | |
---|
| 44 | msg = 'Number of vertex values (%d) must be consistent with'\ |
---|
| 45 | %N |
---|
| 46 | msg += 'number of elements in specified domain (%d).'\ |
---|
| 47 | %domain.number_of_elements |
---|
| 48 | |
---|
| 49 | assert N == domain.number_of_elements, msg |
---|
| 50 | |
---|
| 51 | self.domain = domain |
---|
| 52 | |
---|
| 53 | #Allocate space for other quantities |
---|
| 54 | self.centroid_values = zeros(N, Float) |
---|
| 55 | self.centroid_backup_values = zeros(N, Float) |
---|
| 56 | #self.edge_values = zeros((N, 2), Float) |
---|
| 57 | #edge values are values of the ends of each interval |
---|
| 58 | |
---|
| 59 | #Intialise centroid values |
---|
| 60 | self.interpolate() |
---|
| 61 | |
---|
| 62 | |
---|
| 63 | from Numeric import Float |
---|
| 64 | from numpy import zeros |
---|
| 65 | |
---|
| 66 | #Allocate space for boundary values |
---|
| 67 | #L = len(domain.boundary) |
---|
| 68 | self.boundary_values = zeros(2, Float) #assumes no parrellism |
---|
| 69 | |
---|
| 70 | #Allocate space for updates of conserved quantities by |
---|
| 71 | #flux calculations and forcing functions |
---|
| 72 | |
---|
| 73 | N = domain.number_of_elements |
---|
| 74 | self.explicit_update = zeros(N, Float ) |
---|
| 75 | self.semi_implicit_update = zeros(N, Float ) |
---|
| 76 | |
---|
| 77 | self.gradients = zeros(N, Float) |
---|
| 78 | self.qmax = zeros(self.centroid_values.shape, Float) |
---|
| 79 | self.qmin = zeros(self.centroid_values.shape, Float) |
---|
| 80 | |
---|
| 81 | self.beta = domain.beta |
---|
| 82 | |
---|
| 83 | |
---|
| 84 | def __len__(self): |
---|
| 85 | """ |
---|
| 86 | Returns number of intervals. |
---|
| 87 | """ |
---|
| 88 | return self.centroid_values.shape[0] |
---|
| 89 | |
---|
| 90 | def interpolate(self): |
---|
| 91 | """ |
---|
| 92 | Compute interpolated values at centroid |
---|
| 93 | Pre-condition: vertex_values have been set |
---|
| 94 | """ |
---|
| 95 | |
---|
| 96 | N = self.vertex_values.shape[0] |
---|
| 97 | for i in range(N): |
---|
| 98 | v0 = self.vertex_values[i, 0] |
---|
| 99 | v1 = self.vertex_values[i, 1] |
---|
| 100 | |
---|
| 101 | self.centroid_values[i] = (v0 + v1)/2.0 |
---|
| 102 | |
---|
| 103 | def set_values(self, X, location='vertices'): |
---|
| 104 | """Set values for quantity |
---|
| 105 | |
---|
| 106 | X: Compatible list, Numeric array (see below), constant or function |
---|
| 107 | location: Where values are to be stored. |
---|
| 108 | Permissible options are: vertices, centroid |
---|
| 109 | Default is "vertices" |
---|
| 110 | |
---|
| 111 | In case of location == 'centroid' the dimension values must |
---|
| 112 | be a list of a Numerical array of length N, N being the number |
---|
| 113 | of elements in the mesh. Otherwise it must be of dimension Nx2 |
---|
| 114 | |
---|
| 115 | The values will be stored in elements following their |
---|
| 116 | internal ordering. |
---|
| 117 | |
---|
| 118 | If values are described a function, it will be evaluated at specified points |
---|
| 119 | |
---|
| 120 | If selected location is vertices, values for centroid and edges |
---|
| 121 | will be assigned interpolated values. |
---|
| 122 | In any other case, only values for the specified locations |
---|
| 123 | will be assigned and the others will be left undefined. |
---|
| 124 | """ |
---|
| 125 | |
---|
| 126 | if location not in ['vertices', 'centroids']: |
---|
| 127 | msg = 'Invalid location: %s, (possible choices vertices, centroids)' %location |
---|
| 128 | raise msg |
---|
| 129 | |
---|
| 130 | if X is None: |
---|
| 131 | msg = 'Given values are None' |
---|
| 132 | raise msg |
---|
| 133 | |
---|
| 134 | import types |
---|
| 135 | |
---|
| 136 | if callable(X): |
---|
| 137 | #Use function specific method |
---|
| 138 | self.set_function_values(X, location) |
---|
| 139 | elif type(X) in [types.FloatType, types.IntType, types.LongType]: |
---|
| 140 | if location == 'centroids': |
---|
| 141 | self.centroid_values[:] = X |
---|
| 142 | else: |
---|
| 143 | self.vertex_values[:] = X |
---|
| 144 | |
---|
| 145 | else: |
---|
| 146 | #Use array specific method |
---|
| 147 | self.set_array_values(X, location) |
---|
| 148 | |
---|
| 149 | if location == 'vertices': |
---|
| 150 | #Intialise centroid and edge values |
---|
| 151 | self.interpolate() |
---|
| 152 | |
---|
| 153 | |
---|
| 154 | |
---|
| 155 | |
---|
| 156 | |
---|
| 157 | def set_function_values(self, f, location='vertices'): |
---|
| 158 | """Set values for quantity using specified function |
---|
| 159 | |
---|
| 160 | f: x -> z Function where x and z are arrays |
---|
| 161 | location: Where values are to be stored. |
---|
| 162 | Permissible options are: vertices, centroid |
---|
| 163 | Default is "vertices" |
---|
| 164 | """ |
---|
| 165 | |
---|
| 166 | if location == 'centroids': |
---|
| 167 | |
---|
| 168 | P = self.domain.centroids |
---|
| 169 | self.set_values(f(P), location) |
---|
| 170 | else: |
---|
| 171 | #Vertices |
---|
| 172 | P = self.domain.get_vertices() |
---|
| 173 | |
---|
| 174 | for i in range(2): |
---|
| 175 | self.vertex_values[:,i] = f(P[:,i]) |
---|
| 176 | |
---|
| 177 | def set_array_values(self, values, location='vertices'): |
---|
| 178 | """Set values for quantity |
---|
| 179 | |
---|
| 180 | values: Numeric array |
---|
| 181 | location: Where values are to be stored. |
---|
| 182 | Permissible options are: vertices, centroid, edges |
---|
| 183 | Default is "vertices" |
---|
| 184 | |
---|
| 185 | In case of location == 'centroid' the dimension values must |
---|
| 186 | be a list of a Numerical array of length N, N being the number |
---|
| 187 | of elements in the mesh. Otherwise it must be of dimension Nx2 |
---|
| 188 | |
---|
| 189 | The values will be stored in elements following their |
---|
| 190 | internal ordering. |
---|
| 191 | |
---|
| 192 | If selected location is vertices, values for centroid |
---|
| 193 | will be assigned interpolated values. |
---|
| 194 | In any other case, only values for the specified locations |
---|
| 195 | will be assigned and the others will be left undefined. |
---|
| 196 | """ |
---|
| 197 | |
---|
| 198 | from Numeric import Float |
---|
| 199 | from numpy import array |
---|
| 200 | |
---|
| 201 | values = array(values).astype(Float) |
---|
| 202 | |
---|
| 203 | N = self.centroid_values.shape[0] |
---|
| 204 | |
---|
| 205 | msg = 'Number of values must match number of elements' |
---|
| 206 | assert values.shape[0] == N, msg |
---|
| 207 | |
---|
| 208 | if location == 'centroids': |
---|
| 209 | assert len(values.shape) == 1, 'Values array must be 1d' |
---|
| 210 | self.centroid_values = values |
---|
| 211 | #elif location == 'edges': |
---|
| 212 | # assert len(values.shape) == 2, 'Values array must be 2d' |
---|
| 213 | # msg = 'Array must be N x 2' |
---|
| 214 | # self.edge_values = values |
---|
| 215 | else: |
---|
| 216 | assert len(values.shape) == 2, 'Values array must be 2d' |
---|
| 217 | msg = 'Array must be N x 2' |
---|
| 218 | assert values.shape[1] == 2, msg |
---|
| 219 | |
---|
| 220 | self.vertex_values = values |
---|
| 221 | |
---|
| 222 | |
---|
| 223 | def get_values(self, location='vertices', indices = None): |
---|
| 224 | """get values for quantity |
---|
| 225 | |
---|
| 226 | return X, Compatible list, Numeric array (see below) |
---|
| 227 | location: Where values are to be stored. |
---|
| 228 | Permissible options are: vertices, centroid |
---|
| 229 | and unique vertices. Default is 'vertices' |
---|
| 230 | |
---|
| 231 | In case of location == 'centroids' the dimension values must |
---|
| 232 | be a list of a Numerical array of length N, N being the number |
---|
| 233 | of elements. Otherwise it must be of dimension Nx3 |
---|
| 234 | |
---|
| 235 | The returned values with be a list the length of indices |
---|
| 236 | (N if indices = None). Each value will be a list of the three |
---|
| 237 | vertex values for this quantity. |
---|
| 238 | |
---|
| 239 | Indices is the set of element ids that the operation applies to. |
---|
| 240 | |
---|
| 241 | """ |
---|
| 242 | from Numeric import take |
---|
| 243 | |
---|
| 244 | if location not in ['vertices', 'centroids', 'unique vertices']: |
---|
| 245 | msg = 'Invalid location: %s' %location |
---|
| 246 | raise msg |
---|
| 247 | |
---|
| 248 | import types, Numeric |
---|
| 249 | assert type(indices) in [types.ListType, types.NoneType, |
---|
| 250 | Numeric.ArrayType],\ |
---|
| 251 | 'Indices must be a list or None' |
---|
| 252 | |
---|
| 253 | if location == 'centroids': |
---|
| 254 | if (indices == None): |
---|
| 255 | indices = range(len(self)) |
---|
| 256 | return take(self.centroid_values,indices) |
---|
| 257 | elif location == 'unique vertices': |
---|
| 258 | if (indices == None): |
---|
| 259 | indices=range(self.domain.coordinates.shape[0]) |
---|
| 260 | vert_values = [] |
---|
| 261 | #Go through list of unique vertices |
---|
| 262 | for unique_vert_id in indices: |
---|
| 263 | cells = self.domain.vertexlist[unique_vert_id] |
---|
| 264 | |
---|
| 265 | #In case there are unused points |
---|
| 266 | if cells is None: |
---|
| 267 | msg = 'Unique vertex not associated with cells' |
---|
| 268 | raise msg |
---|
| 269 | |
---|
| 270 | # Go through all cells, vertex pairs |
---|
| 271 | # Average the values |
---|
| 272 | sum = 0 |
---|
| 273 | for cell_id, vertex_id in cells: |
---|
| 274 | sum += self.vertex_values[cell_id, vertex_id] |
---|
| 275 | vert_values.append(sum/len(cells)) |
---|
| 276 | return Numeric.array(vert_values) |
---|
| 277 | else: |
---|
| 278 | if (indices == None): |
---|
| 279 | indices = range(len(self)) |
---|
| 280 | return take(self.vertex_values,indices) |
---|
| 281 | |
---|
| 282 | |
---|
| 283 | def get_vertex_values(self, |
---|
| 284 | x=True, |
---|
| 285 | smooth = None, |
---|
| 286 | precision = None, |
---|
| 287 | reduction = None): |
---|
| 288 | """Return vertex values like an OBJ format |
---|
| 289 | |
---|
| 290 | The vertex values are returned as one sequence in the 1D float array A. |
---|
| 291 | If requested the coordinates will be returned in 1D arrays X. |
---|
| 292 | |
---|
| 293 | The connectivity is represented as an integer array, V, of dimension |
---|
| 294 | M x 2, where M is the number of volumes. Each row has two indices |
---|
| 295 | into the X, A arrays defining the element. |
---|
| 296 | |
---|
| 297 | if smooth is True, vertex values corresponding to one common |
---|
| 298 | coordinate set will be smoothed according to the given |
---|
| 299 | reduction operator. In this case vertex coordinates will be |
---|
| 300 | de-duplicated. |
---|
| 301 | |
---|
| 302 | If no smoothings is required, vertex coordinates and values will |
---|
| 303 | be aggregated as a concatenation of values at |
---|
| 304 | vertices 0, vertices 1 |
---|
| 305 | |
---|
| 306 | |
---|
| 307 | Calling convention |
---|
| 308 | if x is True: |
---|
| 309 | X,A,V = get_vertex_values |
---|
| 310 | else: |
---|
| 311 | A,V = get_vertex_values |
---|
| 312 | |
---|
| 313 | """ |
---|
| 314 | |
---|
| 315 | from Numeric import Float, Int |
---|
| 316 | from numpy import concatenate, zeros, array, reshape |
---|
| 317 | |
---|
| 318 | |
---|
| 319 | if smooth is None: |
---|
| 320 | smooth = self.domain.smooth |
---|
| 321 | |
---|
| 322 | if precision is None: |
---|
| 323 | precision = Float |
---|
| 324 | |
---|
| 325 | if reduction is None: |
---|
| 326 | reduction = self.domain.reduction |
---|
| 327 | |
---|
| 328 | #Create connectivity |
---|
| 329 | |
---|
| 330 | if smooth == True: |
---|
| 331 | |
---|
| 332 | V = self.domain.get_vertices() |
---|
| 333 | N = len(self.domain.vertexlist) |
---|
| 334 | #N = len(self.domain.vertices) |
---|
| 335 | A = zeros(N, precision) |
---|
| 336 | |
---|
| 337 | #Smoothing loop |
---|
| 338 | for k in range(N): |
---|
| 339 | L = self.domain.vertexlist[k] |
---|
| 340 | #L = self.domain.vertices[k] |
---|
| 341 | |
---|
| 342 | #Go through all triangle, vertex pairs |
---|
| 343 | #contributing to vertex k and register vertex value |
---|
| 344 | |
---|
| 345 | if L is None: continue #In case there are unused points |
---|
| 346 | |
---|
| 347 | contributions = [] |
---|
| 348 | for volume_id, vertex_id in L: |
---|
| 349 | v = self.vertex_values[volume_id, vertex_id] |
---|
| 350 | contributions.append(v) |
---|
| 351 | |
---|
| 352 | A[k] = reduction(contributions) |
---|
| 353 | |
---|
| 354 | if x is True: |
---|
| 355 | #X = self.domain.coordinates[:,0].astype(precision) |
---|
| 356 | X = self.domain.coordinates[:].astype(precision) |
---|
| 357 | #Y = self.domain.coordinates[:,1].astype(precision) |
---|
| 358 | |
---|
| 359 | #return X, Y, A, V |
---|
| 360 | return X, A, V |
---|
| 361 | |
---|
| 362 | #else: |
---|
| 363 | return A, V |
---|
| 364 | else: |
---|
| 365 | #Don't smooth |
---|
| 366 | #obj machinery moved to general_mesh |
---|
| 367 | |
---|
| 368 | # Create a V like [[0 1 2], [3 4 5]....[3*m-2 3*m-1 3*m]] |
---|
| 369 | # These vert_id's will relate to the verts created below |
---|
| 370 | #m = len(self.domain) #Number of volumes |
---|
| 371 | #M = 3*m #Total number of unique vertices |
---|
| 372 | #V = reshape(array(range(M)).astype(Int), (m,3)) |
---|
| 373 | |
---|
| 374 | #V = self.domain.get_triangles(obj=True) |
---|
| 375 | V = self.domain.get_vertices |
---|
| 376 | #FIXME use get_vertices, when ready |
---|
| 377 | |
---|
| 378 | A = self.vertex_values.flat |
---|
| 379 | |
---|
| 380 | #Do vertex coordinates |
---|
| 381 | if x is True: |
---|
| 382 | X = self.domain.get_vertex_coordinates() |
---|
| 383 | |
---|
| 384 | #X = C[:,0:6:2].copy() |
---|
| 385 | #Y = C[:,1:6:2].copy() |
---|
| 386 | |
---|
| 387 | return X.flat, A, V |
---|
| 388 | else: |
---|
| 389 | return A, V |
---|
| 390 | |
---|
| 391 | def get_integral(self): |
---|
| 392 | """Compute the integral of quantity across entire domain |
---|
| 393 | """ |
---|
| 394 | integral = 0 |
---|
| 395 | for k in range(self.domain.number_of_elements): |
---|
| 396 | area = self.domain.areas[k] |
---|
| 397 | qc = self.centroid_values[k] |
---|
| 398 | integral += qc*area |
---|
| 399 | |
---|
| 400 | return integral |
---|
| 401 | |
---|
| 402 | |
---|
| 403 | def update(self, timestep): |
---|
| 404 | """Update centroid values based on values stored in |
---|
| 405 | explicit_update and semi_implicit_update as well as given timestep |
---|
| 406 | """ |
---|
| 407 | |
---|
| 408 | from Numeric import Float |
---|
| 409 | from numpy import sum, equal, ones |
---|
| 410 | |
---|
| 411 | N = self.centroid_values.shape[0] |
---|
| 412 | |
---|
| 413 | #Explicit updates |
---|
| 414 | self.centroid_values += timestep*self.explicit_update |
---|
| 415 | |
---|
| 416 | #Semi implicit updates |
---|
| 417 | denominator = ones(N, Float)-timestep*self.semi_implicit_update |
---|
| 418 | |
---|
| 419 | if sum(equal(denominator, 0.0)) > 0.0: |
---|
| 420 | msg = 'Zero division in semi implicit update. Call Stephen :-)' |
---|
| 421 | raise msg |
---|
| 422 | else: |
---|
| 423 | #Update conserved_quantities from semi implicit updates |
---|
| 424 | self.centroid_values /= denominator |
---|
| 425 | |
---|
| 426 | |
---|
| 427 | def compute_gradients(self): |
---|
| 428 | """Compute gradients of piecewise linear function defined by centroids of |
---|
| 429 | neighbouring volumes. |
---|
| 430 | """ |
---|
| 431 | |
---|
| 432 | #print 'compute_gradient' |
---|
| 433 | |
---|
| 434 | from Numeric import Float |
---|
| 435 | from numpy import array, zeros |
---|
| 436 | |
---|
| 437 | N = self.centroid_values.shape[0] |
---|
| 438 | |
---|
| 439 | |
---|
| 440 | G = self.gradients |
---|
| 441 | Q = self.centroid_values |
---|
| 442 | X = self.domain.centroids |
---|
| 443 | |
---|
| 444 | for k in range(N): |
---|
| 445 | |
---|
| 446 | # first and last elements have boundaries |
---|
| 447 | |
---|
| 448 | if k == 0: |
---|
| 449 | |
---|
| 450 | #Get data |
---|
| 451 | k0 = k |
---|
| 452 | k1 = k+1 |
---|
| 453 | k2 = k+2 |
---|
| 454 | |
---|
| 455 | q0 = Q[k0] |
---|
| 456 | q1 = Q[k1] |
---|
| 457 | q2 = Q[k2] |
---|
| 458 | |
---|
| 459 | x0 = X[k0] #V0 centroid |
---|
| 460 | x1 = X[k1] #V1 centroid |
---|
| 461 | x2 = X[k2] |
---|
| 462 | |
---|
| 463 | #Gradient |
---|
| 464 | #G[k] = (q1 - q0)/(x1 - x0) |
---|
| 465 | |
---|
| 466 | G[k] = (q1 - q0)*(x2 - x0)*(x2 - x0) - (q2 - q0)*(x1 - x0)*(x1 - x0) |
---|
| 467 | G[k] /= (x1 - x0)*(x2 - x0)*(x2 - x1) |
---|
| 468 | |
---|
| 469 | elif k == N-1: |
---|
| 470 | |
---|
| 471 | #Get data |
---|
| 472 | k0 = k |
---|
| 473 | k1 = k-1 |
---|
| 474 | k2 = k-2 |
---|
| 475 | |
---|
| 476 | q0 = Q[k0] |
---|
| 477 | q1 = Q[k1] |
---|
| 478 | q2 = Q[k2] |
---|
| 479 | |
---|
| 480 | x0 = X[k0] #V0 centroid |
---|
| 481 | x1 = X[k1] #V1 centroid |
---|
| 482 | x2 = X[k2] |
---|
| 483 | |
---|
| 484 | #Gradient |
---|
| 485 | #G[k] = (q1 - q0)/(x1 - x0) |
---|
| 486 | |
---|
| 487 | G[k] = (q1 - q0)*(x2 - x0)*(x2 - x0) - (q2 - q0)*(x1 - x0)*(x1 - x0) |
---|
| 488 | G[k] /= (x1 - x0)*(x2 - x0)*(x2 - x1) |
---|
| 489 | |
---|
| 490 | ## q0 = Q[k0] |
---|
| 491 | ## q1 = Q[k1] |
---|
| 492 | ## |
---|
| 493 | ## x0 = X[k0] #V0 centroid |
---|
| 494 | ## x1 = X[k1] #V1 centroid |
---|
| 495 | ## |
---|
| 496 | ## #Gradient |
---|
| 497 | ## G[k] = (q1 - q0)/(x1 - x0) |
---|
| 498 | |
---|
| 499 | else: |
---|
| 500 | #Interior Volume (2 neighbours) |
---|
| 501 | |
---|
| 502 | #Get data |
---|
| 503 | k0 = k-1 |
---|
| 504 | k2 = k+1 |
---|
| 505 | |
---|
| 506 | q0 = Q[k0] |
---|
| 507 | q1 = Q[k] |
---|
| 508 | q2 = Q[k2] |
---|
| 509 | |
---|
| 510 | x0 = X[k0] #V0 centroid |
---|
| 511 | x1 = X[k] #V1 centroid (Self) |
---|
| 512 | x2 = X[k2] #V2 centroid |
---|
| 513 | |
---|
| 514 | #Gradient |
---|
| 515 | #G[k] = (q2-q0)/(x2-x0) |
---|
| 516 | G[k] = ((q0-q1)/(x0-x1)*(x2-x1) - (q2-q1)/(x2-x1)*(x0-x1))/(x2-x0) |
---|
| 517 | |
---|
| 518 | |
---|
| 519 | def compute_minmod_gradients(self): |
---|
| 520 | """Compute gradients of piecewise linear function defined by centroids of |
---|
| 521 | neighbouring volumes. |
---|
| 522 | """ |
---|
| 523 | |
---|
| 524 | #print 'compute_minmod_gradients' |
---|
| 525 | |
---|
| 526 | from Numeric import Float,sign |
---|
| 527 | from numpy import array, zeros |
---|
| 528 | |
---|
| 529 | def xmin(a,b): |
---|
| 530 | return 0.5*(sign(a)+sign(b))*min(abs(a),abs(b)) |
---|
| 531 | |
---|
| 532 | def xmic(t,a,b): |
---|
| 533 | return xmin(t*xmin(a,b), 0.50*(a+b) ) |
---|
| 534 | |
---|
| 535 | |
---|
| 536 | |
---|
| 537 | N = self.centroid_values.shape[0] |
---|
| 538 | |
---|
| 539 | |
---|
| 540 | G = self.gradients |
---|
| 541 | Q = self.centroid_values |
---|
| 542 | X = self.domain.centroids |
---|
| 543 | |
---|
| 544 | for k in range(N): |
---|
| 545 | |
---|
| 546 | # first and last elements have boundaries |
---|
| 547 | |
---|
| 548 | if k == 0: |
---|
| 549 | |
---|
| 550 | #Get data |
---|
| 551 | k0 = k |
---|
| 552 | k1 = k+1 |
---|
| 553 | k2 = k+2 |
---|
| 554 | |
---|
| 555 | q0 = Q[k0] |
---|
| 556 | q1 = Q[k1] |
---|
| 557 | q2 = Q[k2] |
---|
| 558 | |
---|
| 559 | x0 = X[k0] #V0 centroid |
---|
| 560 | x1 = X[k1] #V1 centroid |
---|
| 561 | x2 = X[k2] |
---|
| 562 | |
---|
| 563 | #Gradient |
---|
| 564 | #G[k] = (q1 - q0)/(x1 - x0) |
---|
| 565 | |
---|
| 566 | G[k] = (q1 - q0)*(x2 - x0)*(x2 - x0) - (q2 - q0)*(x1 - x0)*(x1 - x0) |
---|
| 567 | G[k] /= (x1 - x0)*(x2 - x0)*(x2 - x1) |
---|
| 568 | |
---|
| 569 | elif k == N-1: |
---|
| 570 | |
---|
| 571 | #Get data |
---|
| 572 | k0 = k |
---|
| 573 | k1 = k-1 |
---|
| 574 | k2 = k-2 |
---|
| 575 | |
---|
| 576 | q0 = Q[k0] |
---|
| 577 | q1 = Q[k1] |
---|
| 578 | q2 = Q[k2] |
---|
| 579 | |
---|
| 580 | x0 = X[k0] #V0 centroid |
---|
| 581 | x1 = X[k1] #V1 centroid |
---|
| 582 | x2 = X[k2] |
---|
| 583 | |
---|
| 584 | #Gradient |
---|
| 585 | #G[k] = (q1 - q0)/(x1 - x0) |
---|
| 586 | |
---|
| 587 | G[k] = (q1 - q0)*(x2 - x0)*(x2 - x0) - (q2 - q0)*(x1 - x0)*(x1 - x0) |
---|
| 588 | G[k] /= (x1 - x0)*(x2 - x0)*(x2 - x1) |
---|
| 589 | |
---|
| 590 | ## #Get data |
---|
| 591 | ## k0 = k |
---|
| 592 | ## k1 = k-1 |
---|
| 593 | ## |
---|
| 594 | ## q0 = Q[k0] |
---|
| 595 | ## q1 = Q[k1] |
---|
| 596 | ## |
---|
| 597 | ## x0 = X[k0] #V0 centroid |
---|
| 598 | ## x1 = X[k1] #V1 centroid |
---|
| 599 | ## |
---|
| 600 | ## #Gradient |
---|
| 601 | ## G[k] = (q1 - q0)/(x1 - x0) |
---|
| 602 | |
---|
| 603 | elif (self.domain.wet_nodes[k,0] == 2) & (self.domain.wet_nodes[k,1] == 2): |
---|
| 604 | G[k] = 0.0 |
---|
| 605 | |
---|
| 606 | else: |
---|
| 607 | #Interior Volume (2 neighbours) |
---|
| 608 | |
---|
| 609 | #Get data |
---|
| 610 | k0 = k-1 |
---|
| 611 | k2 = k+1 |
---|
| 612 | |
---|
| 613 | q0 = Q[k0] |
---|
| 614 | q1 = Q[k] |
---|
| 615 | q2 = Q[k2] |
---|
| 616 | |
---|
| 617 | x0 = X[k0] #V0 centroid |
---|
| 618 | x1 = X[k] #V1 centroid (Self) |
---|
| 619 | x2 = X[k2] #V2 centroid |
---|
| 620 | |
---|
| 621 | # assuming uniform grid |
---|
| 622 | d1 = (q1 - q0)/(x1-x0) |
---|
| 623 | d2 = (q2 - q1)/(x2-x1) |
---|
| 624 | |
---|
| 625 | #Gradient |
---|
| 626 | #G[k] = (d1+d2)*0.5 |
---|
| 627 | #G[k] = (d1*(x2-x1) - d2*(x0-x1))/(x2-x0) |
---|
| 628 | G[k] = xmic( self.domain.beta, d1, d2 ) |
---|
| 629 | |
---|
| 630 | |
---|
| 631 | def extrapolate_first_order(self): |
---|
| 632 | """Extrapolate conserved quantities from centroid to |
---|
| 633 | vertices for each volume using |
---|
| 634 | first order scheme. |
---|
| 635 | """ |
---|
| 636 | |
---|
| 637 | qc = self.centroid_values |
---|
| 638 | qv = self.vertex_values |
---|
| 639 | |
---|
| 640 | for i in range(2): |
---|
| 641 | qv[:,i] = qc |
---|
| 642 | |
---|
| 643 | |
---|
| 644 | def extrapolate_second_order(self): |
---|
| 645 | """Extrapolate conserved quantities from centroid to |
---|
| 646 | vertices for each volume using |
---|
| 647 | second order scheme. |
---|
| 648 | """ |
---|
| 649 | if self.domain.limiter == "pyvolution": |
---|
| 650 | #Z = self.gradients |
---|
| 651 | #print "gradients 1",Z |
---|
| 652 | self.compute_gradients() |
---|
| 653 | #print "gradients 2",Z |
---|
| 654 | |
---|
| 655 | #Z = self.gradients |
---|
| 656 | #print "gradients 1",Z |
---|
| 657 | #self.compute_minmod_gradients() |
---|
| 658 | #print "gradients 2", Z |
---|
| 659 | |
---|
| 660 | G = self.gradients |
---|
| 661 | V = self.domain.vertices |
---|
| 662 | qc = self.centroid_values |
---|
| 663 | qv = self.vertex_values |
---|
| 664 | |
---|
| 665 | #Check each triangle |
---|
| 666 | for k in range(self.domain.number_of_elements): |
---|
| 667 | #Centroid coordinates |
---|
| 668 | x = self.domain.centroids[k] |
---|
| 669 | |
---|
| 670 | #vertex coordinates |
---|
| 671 | x0, x1 = V[k,:] |
---|
| 672 | |
---|
| 673 | #Extrapolate |
---|
| 674 | qv[k,0] = qc[k] + G[k]*(x0-x) |
---|
| 675 | qv[k,1] = qc[k] + G[k]*(x1-x) |
---|
| 676 | self.limit_pyvolution() |
---|
| 677 | elif self.domain.limiter == "minmod_steve": |
---|
| 678 | self.limit_minmod() |
---|
| 679 | else: |
---|
| 680 | self.limit_range() |
---|
| 681 | |
---|
| 682 | |
---|
| 683 | |
---|
| 684 | def limit_minmod(self): |
---|
| 685 | #Z = self.gradients |
---|
| 686 | #print "gradients 1",Z |
---|
| 687 | self.compute_minmod_gradients() |
---|
| 688 | #print "gradients 2", Z |
---|
| 689 | |
---|
| 690 | G = self.gradients |
---|
| 691 | V = self.domain.vertices |
---|
| 692 | qc = self.centroid_values |
---|
| 693 | qv = self.vertex_values |
---|
| 694 | |
---|
| 695 | #Check each triangle |
---|
| 696 | for k in range(self.domain.number_of_elements): |
---|
| 697 | #Centroid coordinates |
---|
| 698 | x = self.domain.centroids[k] |
---|
| 699 | |
---|
| 700 | #vertex coordinates |
---|
| 701 | x0, x1 = V[k,:] |
---|
| 702 | |
---|
| 703 | #Extrapolate |
---|
| 704 | qv[k,0] = qc[k] + G[k]*(x0-x) |
---|
| 705 | qv[k,1] = qc[k] + G[k]*(x1-x) |
---|
| 706 | |
---|
| 707 | |
---|
| 708 | def limit_pyvolution(self): |
---|
| 709 | """ |
---|
| 710 | Limit slopes for each volume to eliminate artificial variance |
---|
| 711 | introduced by e.g. second order extrapolator |
---|
| 712 | |
---|
| 713 | This is an unsophisticated limiter as it does not take into |
---|
| 714 | account dependencies among quantities. |
---|
| 715 | |
---|
| 716 | precondition: |
---|
| 717 | vertex values are estimated from gradient |
---|
| 718 | postcondition: |
---|
| 719 | vertex values are updated |
---|
| 720 | """ |
---|
| 721 | from Numeric import Float |
---|
| 722 | from numpy import zeros |
---|
| 723 | |
---|
| 724 | N = self.domain.number_of_elements |
---|
| 725 | beta = self.domain.beta |
---|
| 726 | #beta = 0.8 |
---|
| 727 | |
---|
| 728 | qc = self.centroid_values |
---|
| 729 | qv = self.vertex_values |
---|
| 730 | |
---|
| 731 | #Find min and max of this and neighbour's centroid values |
---|
| 732 | qmax = self.qmax |
---|
| 733 | qmin = self.qmin |
---|
| 734 | |
---|
| 735 | for k in range(N): |
---|
| 736 | qmax[k] = qmin[k] = qc[k] |
---|
| 737 | for i in range(2): |
---|
| 738 | n = self.domain.neighbours[k,i] |
---|
| 739 | if n >= 0: |
---|
| 740 | qn = qc[n] #Neighbour's centroid value |
---|
| 741 | |
---|
| 742 | qmin[k] = min(qmin[k], qn) |
---|
| 743 | qmax[k] = max(qmax[k], qn) |
---|
| 744 | |
---|
| 745 | |
---|
| 746 | #Diffences between centroids and maxima/minima |
---|
| 747 | dqmax = qmax - qc |
---|
| 748 | dqmin = qmin - qc |
---|
| 749 | |
---|
| 750 | #Deltas between vertex and centroid values |
---|
| 751 | dq = zeros(qv.shape, Float) |
---|
| 752 | for i in range(2): |
---|
| 753 | dq[:,i] = qv[:,i] - qc |
---|
| 754 | |
---|
| 755 | #Phi limiter |
---|
| 756 | for k in range(N): |
---|
| 757 | |
---|
| 758 | #Find the gradient limiter (phi) across vertices |
---|
| 759 | phi = 1.0 |
---|
| 760 | for i in range(2): |
---|
| 761 | r = 1.0 |
---|
| 762 | if (dq[k,i] > 0): r = dqmax[k]/dq[k,i] |
---|
| 763 | if (dq[k,i] < 0): r = dqmin[k]/dq[k,i] |
---|
| 764 | |
---|
| 765 | phi = min( min(r*beta, 1), phi ) |
---|
| 766 | |
---|
| 767 | #Then update using phi limiter |
---|
| 768 | for i in range(2): |
---|
| 769 | qv[k,i] = qc[k] + phi*dq[k,i] |
---|
| 770 | |
---|
| 771 | def limit_range(self): |
---|
| 772 | import sys |
---|
| 773 | from Numeric import Float |
---|
| 774 | from numpy import zeros |
---|
| 775 | from util import minmod, minmod_kurganov, maxmod, vanleer, vanalbada |
---|
| 776 | limiter = self.domain.limiter |
---|
| 777 | #print limiter |
---|
| 778 | |
---|
| 779 | #print 'limit_range' |
---|
| 780 | N = self.domain.number_of_elements |
---|
| 781 | qc = self.centroid_values |
---|
| 782 | qv = self.vertex_values |
---|
| 783 | C = self.domain.centroids |
---|
| 784 | X = self.domain.vertices |
---|
| 785 | beta_p = zeros(N,Float) |
---|
| 786 | beta_m = zeros(N,Float) |
---|
| 787 | beta_x = zeros(N,Float) |
---|
| 788 | |
---|
| 789 | for k in range(N): |
---|
| 790 | |
---|
| 791 | n0 = self.domain.neighbours[k,0] |
---|
| 792 | n1 = self.domain.neighbours[k,1] |
---|
| 793 | |
---|
| 794 | if ( n0 >= 0) & (n1 >= 0): |
---|
| 795 | #SLOPE DERIVATIVE LIMIT |
---|
| 796 | beta_p[k] = (qc[k]-qc[k-1])/(C[k]-C[k-1]) |
---|
| 797 | beta_m[k] = (qc[k+1]-qc[k])/(C[k+1]-C[k]) |
---|
| 798 | beta_x[k] = (qc[k+1]-qc[k-1])/(C[k+1]-C[k-1]) |
---|
| 799 | |
---|
| 800 | dq = zeros(qv.shape, Float) |
---|
| 801 | for i in range(2): |
---|
| 802 | dq[:,i] =self.domain.vertices[:,i]-self.domain.centroids |
---|
| 803 | |
---|
| 804 | #Phi limiter |
---|
| 805 | for k in range(N): |
---|
| 806 | n0 = self.domain.neighbours[k,0] |
---|
| 807 | n1 = self.domain.neighbours[k,1] |
---|
| 808 | if n0 < 0: |
---|
| 809 | #phi = (qc[k+1] - qc[k])/(C[k+1] - C[k]) #This is the original |
---|
| 810 | phi = (qc[k+1] - qc[k])/(C[k+1] - C[k]) |
---|
| 811 | elif n1 < 0: |
---|
| 812 | #phi = (qc[k] - qc[k-1])/(C[k] - C[k-1]) #This is the original |
---|
| 813 | phi = (qc[k] - qc[k-1])/(C[k] - C[k-1]) |
---|
| 814 | else: |
---|
| 815 | if limiter == "minmod": |
---|
| 816 | phi = minmod(beta_p[k],beta_m[k]) #(beta_p[k]+1.0e-15,beta_m[k]) |
---|
| 817 | elif limiter == "minmod_kurganov":#Change this |
---|
| 818 | # Also known as monotonized central difference limiter if theta = 2.0 |
---|
| 819 | theta = 2.0 |
---|
| 820 | phi = minmod_kurganov(theta*beta_p[k],theta*beta_m[k],beta_x[k]) |
---|
| 821 | elif limiter == "superbee": |
---|
| 822 | slope1 = minmod(beta_m[k],2.0*beta_p[k]) |
---|
| 823 | slope2 = minmod(2.0*beta_m[k],beta_p[k]) |
---|
| 824 | phi = maxmod(slope1,slope2) |
---|
| 825 | elif limiter == "vanleer": |
---|
| 826 | phi = vanleer(beta_p[k],beta_m[k]) |
---|
| 827 | elif limiter == "vanalbada": |
---|
| 828 | phi = vanalbada(beta_m[k],beta_p[k]) |
---|
| 829 | |
---|
| 830 | for i in range(2): |
---|
| 831 | qv[k,i] = qc[k] + phi*dq[k,i] |
---|
| 832 | |
---|
| 833 | def limit_steve_slope(self): |
---|
| 834 | |
---|
| 835 | import sys |
---|
| 836 | from Numeric import Float |
---|
| 837 | from numpy import zeros |
---|
| 838 | from util import minmod, minmod_kurganov, maxmod, vanleer |
---|
| 839 | |
---|
| 840 | N = self.domain.number_of_elements |
---|
| 841 | limiter = self.domain.limiter |
---|
| 842 | limiter_type = self.domain.limiter_type |
---|
| 843 | |
---|
| 844 | qc = self.centroid_values |
---|
| 845 | qv = self.vertex_values |
---|
| 846 | |
---|
| 847 | #Find min and max of this and neighbour's centroid values |
---|
| 848 | beta_p = zeros(N,Float) |
---|
| 849 | beta_m = zeros(N,Float) |
---|
| 850 | beta_x = zeros(N,Float) |
---|
| 851 | C = self.domain.centroids |
---|
| 852 | X = self.domain.vertices |
---|
| 853 | |
---|
| 854 | for k in range(N): |
---|
| 855 | |
---|
| 856 | n0 = self.domain.neighbours[k,0] |
---|
| 857 | n1 = self.domain.neighbours[k,1] |
---|
| 858 | |
---|
| 859 | if (n0 >= 0) & (n1 >= 0): |
---|
| 860 | # Check denominator not zero |
---|
| 861 | if (qc[k+1]-qc[k]) == 0.0: |
---|
| 862 | beta_p[k] = float(sys.maxint) |
---|
| 863 | beta_m[k] = float(sys.maxint) |
---|
| 864 | else: |
---|
| 865 | #STEVE LIMIT |
---|
| 866 | beta_p[k] = (qc[k]-qc[k-1])/(qc[k+1]-qc[k]) |
---|
| 867 | beta_m[k] = (qc[k+2]-qc[k+1])/(qc[k+1]-qc[k]) |
---|
| 868 | |
---|
| 869 | #Deltas between vertex and centroid values |
---|
| 870 | dq = zeros(qv.shape, Float) |
---|
| 871 | for i in range(2): |
---|
| 872 | dq[:,i] =self.domain.vertices[:,i]-self.domain.centroids |
---|
| 873 | |
---|
| 874 | #Phi limiter |
---|
| 875 | for k in range(N): |
---|
| 876 | |
---|
| 877 | phi = 0.0 |
---|
| 878 | if limiter == "flux_minmod": |
---|
| 879 | #FLUX MINMOD |
---|
| 880 | phi = minmod_kurganov(1.0,beta_m[k],beta_p[k]) |
---|
| 881 | elif limiter == "flux_superbee": |
---|
| 882 | #FLUX SUPERBEE |
---|
| 883 | phi = max(0.0,min(1.0,2.0*beta_m[k]),min(2.0,beta_m[k]))+max(0.0,min(1.0,2.0*beta_p[k]),min(2.0,beta_p[k]))-1.0 |
---|
| 884 | elif limiter == "flux_muscl": |
---|
| 885 | #FLUX MUSCL |
---|
| 886 | phi = max(0.0,min(2.0,2.0*beta_m[k],2.0*beta_p[k],0.5*(beta_m[k]+beta_p[k]))) |
---|
| 887 | elif limiter == "flux_vanleer": |
---|
| 888 | #FLUX VAN LEER |
---|
| 889 | phi = (beta_m[k]+abs(beta_m[k]))/(1.0+abs(beta_m[k]))+(beta_p[k]+abs(beta_p[k]))/(1.0+abs(beta_p[k]))-1.0 |
---|
| 890 | |
---|
| 891 | #Then update using phi limiter |
---|
| 892 | n = self.domain.neighbours[k,1] |
---|
| 893 | if n>=0: |
---|
| 894 | #qv[k,0] = qc[k] - 0.5*phi*(qc[k+1]-qc[k]) |
---|
| 895 | #qv[k,1] = qc[k] + 0.5*phi*(qc[k+1]-qc[k]) |
---|
| 896 | qv[k,0] = qc[k] + 0.5*phi*(qv[k,0]-qc[k]) |
---|
| 897 | qv[k,1] = qc[k] + 0.5*phi*(qv[k,1]-qc[k]) |
---|
| 898 | else: |
---|
| 899 | qv[k,i] = qc[k] |
---|
| 900 | |
---|
| 901 | def backup_centroid_values(self): |
---|
| 902 | # Call correct module function |
---|
| 903 | # (either from this module or C-extension) |
---|
| 904 | #backup_centroid_values(self) |
---|
| 905 | |
---|
| 906 | self.centroid_backup_values[:] = (self.centroid_values).astype('f') |
---|
| 907 | |
---|
| 908 | def saxpy_centroid_values(self,a,b): |
---|
| 909 | # Call correct module function |
---|
| 910 | # (either from this module or C-extension) |
---|
| 911 | self.centroid_values[:] = (a*self.centroid_values + b*self.centroid_backup_values).astype('f') |
---|
| 912 | |
---|
| 913 | class Conserved_quantity(Quantity): |
---|
| 914 | """Class conserved quantity adds to Quantity: |
---|
| 915 | |
---|
| 916 | storage and method for updating, and |
---|
| 917 | methods for extrapolation from centropid to vertices inluding |
---|
| 918 | gradients and limiters |
---|
| 919 | """ |
---|
| 920 | |
---|
| 921 | def __init__(self, domain, vertex_values=None): |
---|
| 922 | Quantity.__init__(self, domain, vertex_values) |
---|
| 923 | |
---|
| 924 | print "Use Quantity instead of Conserved_quantity" |
---|
| 925 | |
---|
| 926 | """ |
---|
| 927 | ## closePlots crashes with non-interactive matplotlib. (Sudi, 23 July 2010) |
---|
| 928 | ##def newLinePlot(title='Simple Plot'): |
---|
| 929 | ## import Gnuplot |
---|
| 930 | ## g = Gnuplot.Gnuplot() |
---|
| 931 | ## g.title(title) |
---|
| 932 | ## g('set data style linespoints') |
---|
| 933 | ## g.xlabel('x') |
---|
| 934 | ## g.ylabel('y') |
---|
| 935 | ## return g |
---|
| 936 | ## |
---|
| 937 | ##def linePlot(g,x,y): |
---|
| 938 | ## import Gnuplot |
---|
| 939 | ## g.plot(Gnuplot.PlotItems.Data(x.flat,y.flat)) |
---|
| 940 | |
---|
| 941 | def newLinePlot(title='Simple Plot'): |
---|
| 942 | import pylab as g |
---|
| 943 | g.ion() |
---|
| 944 | g.hold(False) |
---|
| 945 | g.title(title) |
---|
| 946 | g.xlabel('x') |
---|
| 947 | g.ylabel('y') |
---|
| 948 | |
---|
| 949 | |
---|
| 950 | def linePlot(x,y): |
---|
| 951 | import pylab as g |
---|
| 952 | g.plot(x.flat,y.flat) |
---|
| 953 | |
---|
| 954 | |
---|
| 955 | def closePlots(): |
---|
| 956 | import pylab as g |
---|
| 957 | g.close('all') |
---|
| 958 | |
---|
| 959 | if __name__ == "__main__": |
---|
| 960 | #from domain import Domain |
---|
| 961 | from shallow_water_domain import Domain |
---|
| 962 | from numpy import arange |
---|
| 963 | |
---|
| 964 | points1 = [0.0, 1.0, 2.0, 3.0] |
---|
| 965 | vertex_values = [[1.0,2.0],[4.0,5.0],[-1.0,2.0]] |
---|
| 966 | |
---|
| 967 | D1 = Domain(points1) |
---|
| 968 | |
---|
| 969 | Q1 = Quantity(D1, vertex_values) |
---|
| 970 | |
---|
| 971 | print Q1.vertex_values |
---|
| 972 | print Q1.centroid_values |
---|
| 973 | |
---|
| 974 | new_vertex_values = [[2.0,1.0],[3.0,4.0],[-2.0,4.0]] |
---|
| 975 | |
---|
| 976 | Q1.set_values(new_vertex_values) |
---|
| 977 | |
---|
| 978 | print Q1.vertex_values |
---|
| 979 | print Q1.centroid_values |
---|
| 980 | |
---|
| 981 | new_centroid_values = [20,30,40] |
---|
| 982 | Q1.set_values(new_centroid_values,'centroids') |
---|
| 983 | |
---|
| 984 | print Q1.vertex_values |
---|
| 985 | print Q1.centroid_values |
---|
| 986 | |
---|
| 987 | class FunClass: |
---|
| 988 | def __init__(self,value): |
---|
| 989 | self.value = value |
---|
| 990 | |
---|
| 991 | def __call__(self,x): |
---|
| 992 | return self.value*(x**2) |
---|
| 993 | |
---|
| 994 | |
---|
| 995 | fun = FunClass(1.0) |
---|
| 996 | Q1.set_values(fun,'vertices') |
---|
| 997 | |
---|
| 998 | print Q1.vertex_values |
---|
| 999 | print Q1.centroid_values |
---|
| 1000 | |
---|
| 1001 | Xc = Q1.domain.vertices |
---|
| 1002 | Qc = Q1.vertex_values |
---|
| 1003 | print Xc |
---|
| 1004 | print Qc |
---|
| 1005 | |
---|
| 1006 | Qc[1,0] = 3 |
---|
| 1007 | |
---|
| 1008 | Q1.extrapolate_second_order() |
---|
| 1009 | #Q1.limit_minmod() |
---|
| 1010 | |
---|
| 1011 | newLinePlot('plots') |
---|
| 1012 | linePlot(Xc,Qc) |
---|
| 1013 | raw_input('press return') |
---|
| 1014 | |
---|
| 1015 | points2 = arange(10) |
---|
| 1016 | D2 = Domain(points2) |
---|
| 1017 | |
---|
| 1018 | Q2 = Quantity(D2) |
---|
| 1019 | Q2.set_values(fun,'vertices') |
---|
| 1020 | Xc = Q2.domain.vertices |
---|
| 1021 | Qc = Q2.vertex_values |
---|
| 1022 | linePlot(Xc,Qc) |
---|
| 1023 | raw_input('press return') |
---|
| 1024 | |
---|
| 1025 | |
---|
| 1026 | Q2.extrapolate_second_order() |
---|
| 1027 | #Q2.limit_minmod() |
---|
| 1028 | Xc = Q2.domain.vertices |
---|
| 1029 | Qc = Q2.vertex_values |
---|
| 1030 | print Q2.centroid_values |
---|
| 1031 | print Qc |
---|
| 1032 | linePlot(Xc,Qc) |
---|
| 1033 | raw_input('press return') |
---|
| 1034 | |
---|
| 1035 | |
---|
| 1036 | for i in range(10): |
---|
| 1037 | import pylab as g |
---|
| 1038 | g.hold(True) |
---|
| 1039 | fun = FunClass(i/10.0) |
---|
| 1040 | Q2.set_values(fun,'centroids') |
---|
| 1041 | Q2.extrapolate_second_order() |
---|
| 1042 | #Q2.limit_minmod() |
---|
| 1043 | Qc = Q2.vertex_values |
---|
| 1044 | linePlot(Xc,Qc) |
---|
| 1045 | raw_input('press return') |
---|
| 1046 | |
---|
| 1047 | raw_input('press return to quit') |
---|
| 1048 | closePlots() |
---|
| 1049 | """ |
---|