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Revision 3619 - (show annotations)
Wed Oct 5 03:53:34 2011 UTC (7 years, 11 months ago) by gross
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some rescaling of permeability in the darcy solver added
1 # -*- coding: utf-8 -*-
2 ########################################################
3 #
4 # Copyright (c) 2003-2010 by University of Queensland
5 # Earth Systems Science Computational Center (ESSCC)
6 # http://www.uq.edu.au/esscc
7 #
8 # Primary Business: Queensland, Australia
9 # Licensed under the Open Software License version 3.0
10 # http://www.opensource.org/licenses/osl-3.0.php
11 #
12 ########################################################
13
14 __copyright__="""Copyright (c) 2003-2010 by University of Queensland
15 Earth Systems Science Computational Center (ESSCC)
16 http://www.uq.edu.au/esscc
17 Primary Business: Queensland, Australia"""
18 __license__="""Licensed under the Open Software License version 3.0
19 http://www.opensource.org/licenses/osl-3.0.php"""
20 __url__="https://launchpad.net/escript-finley"
21
22 """
23 Some models for flow
24
25 :var __author__: name of author
26 :var __copyright__: copyrights
27 :var __license__: licence agreement
28 :var __url__: url entry point on documentation
29 :var __version__: version
30 :var __date__: date of the version
31 """
32
33 __author__="Lutz Gross, l.gross@uq.edu.au"
34
35 import escript
36 import util
37 from linearPDEs import LinearPDE, LinearPDESystem, LinearSinglePDE, SolverOptions
38 from pdetools import HomogeneousSaddlePointProblem,Projector, ArithmeticTuple, PCG, NegativeNorm, GMRES
39
40 class DarcyFlow(object):
41 """
42 solves the problem
43
44 *u_i+k_{ij}*p_{,j} = g_i*
45 *u_{i,i} = f*
46
47 where *p* represents the pressure and *u* the Darcy flux. *k* represents the permeability,
48
49 :cvar EVAL: direct pressure gradient evaluation for flux
50 :cvar POST: global postprocessing of flux by solving the PDE *K_{ij} u_j + (w * K * l u_{k,k})_{,i}= - p_{,j} + K_{ij} g_j*
51 where *l* is the length scale, *K* is the inverse of the permeability tensor, and *w* is a positive weighting factor.
52 :cvar SMOOTH: global smoothing by solving the PDE *K_{ij} u_j= - p_{,j} + K_{ij} g_j*
53 """
54 EVAL="EVAL"
55 SIMPLE="EVAL"
56 POST="POST"
57 SMOOTH="SMOOTH"
58 def __init__(self, domain, useReduced=False, solver="EVAL", verbose=False, w=1.):
59 """
60 initializes the Darcy flux problem
61 :param domain: domain of the problem
62 :type domain: `Domain`
63 :param useReduced: uses reduced oreder on flux and pressure
64 :type useReduced: ``bool``
65 :param solver: solver method
66 :type solver: in [`DarcyFlow.EVAL`, `DarcyFlow.POST', `DarcyFlow.SMOOTH' ]
67 :param verbose: if ``True`` some information on the iteration progress are printed.
68 :type verbose: ``bool``
69 :param w: weighting factor for `DarcyFlow.POST` solver
70 :type w: ``float``
71
72 """
73 if not solver in [DarcyFlow.EVAL, DarcyFlow.POST, DarcyFlow.SMOOTH ] :
74 raise ValueError,"unknown solver %d."%solver
75
76 self.domain=domain
77 self.solver=solver
78 self.useReduced=useReduced
79 self.verbose=verbose
80 self.l=None
81 self.w=None
82
83 self.__pde_p=LinearSinglePDE(domain)
84 self.__pde_p.setSymmetryOn()
85 if self.useReduced: self.__pde_p.setReducedOrderOn()
86
87 if self.solver == self.EVAL:
88 self.__pde_v=None
89 if self.verbose: print "DarcyFlow: simple solver is used."
90
91 elif self.solver == self.POST:
92 if util.inf(w)<0.:
93 raise ValueError,"Weighting factor must be non-negative."
94 if self.verbose: print "DarcyFlow: global postprocessing of flux is used."
95 self.__pde_v=LinearPDESystem(domain)
96 self.__pde_v.setSymmetryOn()
97 if self.useReduced: self.__pde_v.setReducedOrderOn()
98 self.w=w
99 self.l=util.vol(self.domain)**(1./self.domain.getDim()) # length scale
100
101 elif self.solver == self.SMOOTH:
102 self.__pde_v=LinearPDESystem(domain)
103 self.__pde_v.setSymmetryOn()
104 if self.useReduced: self.__pde_v.setReducedOrderOn()
105 if self.verbose: print "DarcyFlow: flux smoothing is used."
106 self.w=0
107
108 self.__f=escript.Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("X"))
109 self.__g=escript.Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
110 self.location_of_fixed_pressure = escript.Scalar(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
111 self.location_of_fixed_flux = escript.Vector(0, self.__pde_p.getFunctionSpaceForCoefficient("q"))
112 self.perm_scale=1.
113
114
115 def setValue(self,f=None, g=None, location_of_fixed_pressure=None, location_of_fixed_flux=None, permeability=None):
116 """
117 assigns values to model parameters
118
119 :param f: volumetic sources/sinks
120 :type f: scalar value on the domain (e.g. `escript.Data`)
121 :param g: flux sources/sinks
122 :type g: vector values on the domain (e.g. `escript.Data`)
123 :param location_of_fixed_pressure: mask for locations where pressure is fixed
124 :type location_of_fixed_pressure: scalar value on the domain (e.g. `escript.Data`)
125 :param location_of_fixed_flux: mask for locations where flux is fixed.
126 :type location_of_fixed_flux: vector values on the domain (e.g. `escript.Data`)
127 :param permeability: permeability tensor. If scalar ``s`` is given the tensor with ``s`` on the main diagonal is used.
128 :type permeability: scalar or symmetric tensor values on the domain (e.g. `escript.Data`)
129
130 :note: the values of parameters which are not set by calling ``setValue`` are not altered.
131 :note: at any point on the boundary of the domain the pressure
132 (``location_of_fixed_pressure`` >0) or the normal component of the
133 flux (``location_of_fixed_flux[i]>0``) if direction of the normal
134 is along the *x_i* axis.
135
136 """
137 if location_of_fixed_pressure!=None:
138 self.location_of_fixed_pressure=util.wherePositive(location_of_fixed_pressure)
139 self.__pde_p.setValue(q=self.location_of_fixed_pressure)
140 if location_of_fixed_flux!=None:
141 self.location_of_fixed_flux=util.wherePositive(location_of_fixed_flux)
142 if not self.__pde_v == None: self.__pde_v.setValue(q=self.location_of_fixed_flux)
143
144 if permeability!=None:
145
146 perm=util.interpolate(permeability,self.__pde_p.getFunctionSpaceForCoefficient("A"))
147 self.perm_scale=util.Lsup(util.length(perm))
148 perm=perm*(1./self.perm_scale)
149
150 if perm.getRank()==0:
151
152 perm_inv=(1./perm)
153 perm_inv=perm_inv*util.kronecker(self.domain.getDim())
154 perm=perm*util.kronecker(self.domain.getDim())
155
156
157 elif perm.getRank()==2:
158 perm_inv=util.inverse(perm)
159 else:
160 raise ValueError,"illegal rank of permeability."
161
162 self.__permeability=perm
163 self.__permeability_inv=perm_inv
164
165 #====================
166 self.__pde_p.setValue(A=self.__permeability)
167 if self.solver == self.EVAL:
168 pass # no extra work required
169 elif self.solver == self.POST:
170 k=util.kronecker(self.domain.getDim())
171 self.omega = self.w*util.length(perm_inv)*self.l*self.domain.getSize()
172 self.__pde_v.setValue(D=self.__permeability_inv, A=self.omega*util.outer(k,k))
173 elif self.solver == self.SMOOTH:
174 self.__pde_v.setValue(D=self.__permeability_inv)
175
176 if g != None:
177 g=util.interpolate(g, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
178 if g.isEmpty():
179 g=Vector(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
180 else:
181 if not g.getShape()==(self.domain.getDim(),): raise ValueError,"illegal shape of g"
182 self.__g=g
183 if f !=None:
184 f=util.interpolate(f, self.__pde_p.getFunctionSpaceForCoefficient("Y"))
185 if f.isEmpty():
186 f=Scalar(0,self.__pde_p.getFunctionSpaceForCoefficient("Y"))
187 else:
188 if f.getRank()>0: raise ValueError,"illegal rank of f."
189 self.__f=f
190
191 def getSolverOptionsFlux(self):
192 """
193 Returns the solver options used to solve the flux problems
194 :return: `SolverOptions`
195 """
196 if self.__pde_v == None:
197 return None
198 else:
199 return self.__pde_v.getSolverOptions()
200
201 def setSolverOptionsFlux(self, options=None):
202 """
203 Sets the solver options used to solve the flux problems
204 If ``options`` is not present, the options are reset to default
205 :param options: `SolverOptions`
206 """
207 if not self.__pde_v == None:
208 self.__pde_v.setSolverOptions(options)
209
210 def getSolverOptionsPressure(self):
211 """
212 Returns the solver options used to solve the pressure problems
213 :return: `SolverOptions`
214 """
215 return self.__pde_p.getSolverOptions()
216
217 def setSolverOptionsPressure(self, options=None):
218 """
219 Sets the solver options used to solve the pressure problems
220 If ``options`` is not present, the options are reset to default
221
222 :param options: `SolverOptions`
223 :note: if the adaption of subtolerance is choosen, the tolerance set by ``options`` will be overwritten before the solver is called.
224 """
225 return self.__pde_p.setSolverOptions(options)
226
227 def solve(self, u0, p0):
228 """
229 solves the problem.
230
231 :param u0: initial guess for the flux. At locations in the domain marked by ``location_of_fixed_flux`` the value of ``u0`` is kept unchanged.
232 :type u0: vector value on the domain (e.g. `escript.Data`).
233 :param p0: initial guess for the pressure. At locations in the domain marked by ``location_of_fixed_pressure`` the value of ``p0`` is kept unchanged.
234 :type p0: scalar value on the domain (e.g. `escript.Data`).
235 :return: flux and pressure
236 :rtype: ``tuple`` of `escript.Data`.
237
238 """
239 self.__pde_p.setValue(X=self.__g * 1./self.perm_scale,
240 Y=self.__f,
241 y= - util.inner(self.domain.getNormal(),u0 * self.location_of_fixed_flux),
242 r=p0)
243 p=self.__pde_p.getSolution()
244 u = self.getFlux(p, u0)
245 return u,p
246
247 def getFlux(self,p, u0=None):
248 """
249 returns the flux for a given pressure ``p`` where the flux is equal to ``u0``
250 on locations where ``location_of_fixed_flux`` is positive (see `setValue`).
251 Notice that ``g`` is used, see `setValue`.
252
253 :param p: pressure.
254 :type p: scalar value on the domain (e.g. `escript.Data`).
255 :param u0: flux on the locations of the domain marked be ``location_of_fixed_flux``.
256 :type u0: vector values on the domain (e.g. `escript.Data`) or ``None``
257 :return: flux
258 :rtype: `escript.Data`
259 """
260 if self.solver == self.EVAL:
261 u = self.__g-self.perm_scale * util.tensor_mult(self.__permeability,util.grad(p))
262 elif self.solver == self.POST or self.solver == self.SMOOTH:
263 self.__pde_v.setValue(Y=util.tensor_mult(self.__permeability_inv,self.__g * 1./self.perm_scale)-util.grad(p))
264 if u0 == None:
265 self.__pde_v.setValue(r=escript.Data())
266 else:
267 self.__pde_v.setValue(r=u0)
268 u= self.__pde_v.getSolution() * self.perm_scale
269 return u
270
271 class StokesProblemCartesian(HomogeneousSaddlePointProblem):
272 """
273 solves
274
275 -(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
276 u_{i,i}=0
277
278 u=0 where fixed_u_mask>0
279 eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j
280
281 if surface_stress is not given 0 is assumed.
282
283 typical usage:
284
285 sp=StokesProblemCartesian(domain)
286 sp.setTolerance()
287 sp.initialize(...)
288 v,p=sp.solve(v0,p0)
289 sp.setStokesEquation(...) # new values for some parameters
290 v1,p1=sp.solve(v,p)
291 """
292 def __init__(self,domain,**kwargs):
293 """
294 initialize the Stokes Problem
295
296 The approximation spaces used for velocity (=Solution(domain)) and pressure (=ReducedSolution(domain)) must be
297 LBB complient, for instance using quadratic and linear approximation on the same element or using linear approximation
298 with macro elements for the pressure.
299
300 :param domain: domain of the problem.
301 :type domain: `Domain`
302 """
303 HomogeneousSaddlePointProblem.__init__(self,**kwargs)
304 self.domain=domain
305 self.__pde_v=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
306 self.__pde_v.setSymmetryOn()
307
308 self.__pde_prec=LinearPDE(domain)
309 self.__pde_prec.setReducedOrderOn()
310 self.__pde_prec.setSymmetryOn()
311
312 self.__pde_proj=LinearPDE(domain)
313 self.__pde_proj.setReducedOrderOn()
314 self.__pde_proj.setValue(D=1)
315 self.__pde_proj.setSymmetryOn()
316
317 def getSolverOptionsVelocity(self):
318 """
319 returns the solver options used solve the equation for velocity.
320
321 :rtype: `SolverOptions`
322 """
323 return self.__pde_v.getSolverOptions()
324 def setSolverOptionsVelocity(self, options=None):
325 """
326 set the solver options for solving the equation for velocity.
327
328 :param options: new solver options
329 :type options: `SolverOptions`
330 """
331 self.__pde_v.setSolverOptions(options)
332 def getSolverOptionsPressure(self):
333 """
334 returns the solver options used solve the equation for pressure.
335 :rtype: `SolverOptions`
336 """
337 return self.__pde_prec.getSolverOptions()
338 def setSolverOptionsPressure(self, options=None):
339 """
340 set the solver options for solving the equation for pressure.
341 :param options: new solver options
342 :type options: `SolverOptions`
343 """
344 self.__pde_prec.setSolverOptions(options)
345
346 def setSolverOptionsDiv(self, options=None):
347 """
348 set the solver options for solving the equation to project the divergence of
349 the velocity onto the function space of presure.
350
351 :param options: new solver options
352 :type options: `SolverOptions`
353 """
354 self.__pde_proj.setSolverOptions(options)
355 def getSolverOptionsDiv(self):
356 """
357 returns the solver options for solving the equation to project the divergence of
358 the velocity onto the function space of presure.
359
360 :rtype: `SolverOptions`
361 """
362 return self.__pde_proj.getSolverOptions()
363
364 def updateStokesEquation(self, v, p):
365 """
366 updates the Stokes equation to consider dependencies from ``v`` and ``p``
367 :note: This method can be overwritten by a subclass. Use `setStokesEquation` to set new values to model parameters.
368 """
369 pass
370 def setStokesEquation(self, f=None,fixed_u_mask=None,eta=None,surface_stress=None,stress=None, restoration_factor=None):
371 """
372 assigns new values to the model parameters.
373
374 :param f: external force
375 :type f: `Vector` object in `FunctionSpace` `Function` or similar
376 :param fixed_u_mask: mask of locations with fixed velocity.
377 :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
378 :param eta: viscosity
379 :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
380 :param surface_stress: normal surface stress
381 :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
382 :param stress: initial stress
383 :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
384 """
385 if eta !=None:
386 k=util.kronecker(self.domain.getDim())
387 kk=util.outer(k,k)
388 self.eta=util.interpolate(eta, escript.Function(self.domain))
389 self.__pde_prec.setValue(D=1/self.eta)
390 self.__pde_v.setValue(A=self.eta*(util.swap_axes(kk,0,3)+util.swap_axes(kk,1,3)))
391 if restoration_factor!=None:
392 n=self.domain.getNormal()
393 self.__pde_v.setValue(d=restoration_factor*util.outer(n,n))
394 if fixed_u_mask!=None:
395 self.__pde_v.setValue(q=fixed_u_mask)
396 if f!=None: self.__f=f
397 if surface_stress!=None: self.__surface_stress=surface_stress
398 if stress!=None: self.__stress=stress
399
400 def initialize(self,f=escript.Data(),fixed_u_mask=escript.Data(),eta=1,surface_stress=escript.Data(),stress=escript.Data(), restoration_factor=0):
401 """
402 assigns values to the model parameters
403
404 :param f: external force
405 :type f: `Vector` object in `FunctionSpace` `Function` or similar
406 :param fixed_u_mask: mask of locations with fixed velocity.
407 :type fixed_u_mask: `Vector` object on `FunctionSpace` `Solution` or similar
408 :param eta: viscosity
409 :type eta: `Scalar` object on `FunctionSpace` `Function` or similar
410 :param surface_stress: normal surface stress
411 :type surface_stress: `Vector` object on `FunctionSpace` `FunctionOnBoundary` or similar
412 :param stress: initial stress
413 :type stress: `Tensor` object on `FunctionSpace` `Function` or similar
414 """
415 self.setStokesEquation(f,fixed_u_mask, eta, surface_stress, stress, restoration_factor)
416
417 def Bv(self,v,tol):
418 """
419 returns inner product of element p and div(v)
420
421 :param v: a residual
422 :return: inner product of element p and div(v)
423 :rtype: ``float``
424 """
425 self.__pde_proj.setValue(Y=-util.div(v))
426 self.getSolverOptionsDiv().setTolerance(tol)
427 self.getSolverOptionsDiv().setAbsoluteTolerance(0.)
428 out=self.__pde_proj.getSolution()
429 return out
430
431 def inner_pBv(self,p,Bv):
432 """
433 returns inner product of element p and Bv=-div(v)
434
435 :param p: a pressure increment
436 :param Bv: a residual
437 :return: inner product of element p and Bv=-div(v)
438 :rtype: ``float``
439 """
440 return util.integrate(util.interpolate(p,escript.Function(self.domain))*util.interpolate(Bv, escript.Function(self.domain)))
441
442 def inner_p(self,p0,p1):
443 """
444 Returns inner product of p0 and p1
445
446 :param p0: a pressure
447 :param p1: a pressure
448 :return: inner product of p0 and p1
449 :rtype: ``float``
450 """
451 s0=util.interpolate(p0, escript.Function(self.domain))
452 s1=util.interpolate(p1, escript.Function(self.domain))
453 return util.integrate(s0*s1)
454
455 def norm_v(self,v):
456 """
457 returns the norm of v
458
459 :param v: a velovity
460 :return: norm of v
461 :rtype: non-negative ``float``
462 """
463 return util.sqrt(util.integrate(util.length(util.grad(v))**2))
464
465
466 def getDV(self, p, v, tol):
467 """
468 return the value for v for a given p
469
470 :param p: a pressure
471 :param v: a initial guess for the value v to return.
472 :return: dv given as *Adv=(f-Av-B^*p)*
473 """
474 self.updateStokesEquation(v,p)
475 self.__pde_v.setValue(Y=self.__f, y=self.__surface_stress)
476 self.getSolverOptionsVelocity().setTolerance(tol)
477 self.getSolverOptionsVelocity().setAbsoluteTolerance(0.)
478 if self.__stress.isEmpty():
479 self.__pde_v.setValue(X=p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
480 else:
481 self.__pde_v.setValue(X=self.__stress+p*util.kronecker(self.domain)-2*self.eta*util.symmetric(util.grad(v)))
482 out=self.__pde_v.getSolution()
483 return out
484
485 def norm_Bv(self,Bv):
486 """
487 Returns Bv (overwrite).
488
489 :rtype: equal to the type of p
490 :note: boundary conditions on p should be zero!
491 """
492 return util.sqrt(util.integrate(util.interpolate(Bv, escript.Function(self.domain))**2))
493
494 def solve_AinvBt(self,p, tol):
495 """
496 Solves *Av=B^*p* with accuracy `tol`
497
498 :param p: a pressure increment
499 :return: the solution of *Av=B^*p*
500 :note: boundary conditions on v should be zero!
501 """
502 self.__pde_v.setValue(Y=escript.Data(), y=escript.Data(), X=-p*util.kronecker(self.domain))
503 out=self.__pde_v.getSolution()
504 return out
505
506 def solve_prec(self,Bv, tol):
507 """
508 applies preconditioner for for *BA^{-1}B^** to *Bv*
509 with accuracy `self.getSubProblemTolerance()`
510
511 :param Bv: velocity increment
512 :return: *p=P(Bv)* where *P^{-1}* is an approximation of *BA^{-1}B^ * )*
513 :note: boundary conditions on p are zero.
514 """
515 self.__pde_prec.setValue(Y=Bv)
516 self.getSolverOptionsPressure().setTolerance(tol)
517 self.getSolverOptionsPressure().setAbsoluteTolerance(0.)
518 out=self.__pde_prec.getSolution()
519 return out

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