| 1 |
# |
| 2 |
# $Id$ |
| 3 |
# |
| 4 |
####################################################### |
| 5 |
# |
| 6 |
# Copyright 2003-2007 by ACceSS MNRF |
| 7 |
# Copyright 2007 by University of Queensland |
| 8 |
# |
| 9 |
# http://esscc.uq.edu.au |
| 10 |
# Primary Business: Queensland, Australia |
| 11 |
# Licensed under the Open Software License version 3.0 |
| 12 |
# http://www.opensource.org/licenses/osl-3.0.php |
| 13 |
# |
| 14 |
####################################################### |
| 15 |
# |
| 16 |
|
| 17 |
""" |
| 18 |
solvers for the stokes problem |
| 19 |
|
| 20 |
@var __author__: name of author |
| 21 |
@var __copyright__: copyrights |
| 22 |
@var __license__: licence agreement |
| 23 |
@var __url__: url entry point on documentation |
| 24 |
@var __version__: version |
| 25 |
@var __date__: date of the version |
| 26 |
""" |
| 27 |
|
| 28 |
__author__="Lutz Gross, l.gross@uq.edu.au" |
| 29 |
__copyright__=""" Copyright (c) 2006 by ACcESS MNRF |
| 30 |
http://www.access.edu.au |
| 31 |
Primary Business: Queensland, Australia""" |
| 32 |
__license__="""Licensed under the Open Software License version 3.0 |
| 33 |
http://www.opensource.org/licenses/osl-3.0.php""" |
| 34 |
__url__="http://www.iservo.edu.au/esys" |
| 35 |
__version__="$Revision$" |
| 36 |
__date__="$Date$" |
| 37 |
|
| 38 |
from esys.escript import * |
| 39 |
from esys.escript.pdetools import SaddlePointProblem |
| 40 |
from esys.escript.linearPDEs import LinearPDE |
| 41 |
from esys.finley import Rectangle |
| 42 |
|
| 43 |
class SimpleStokesProblem(SaddlePointProblem): |
| 44 |
""" |
| 45 |
simple example of saddle point problem |
| 46 |
""" |
| 47 |
def __init__(self,domain): |
| 48 |
super(SimpleStokesProblem, self).__init__(self) |
| 49 |
|
| 50 |
self.__pde_u=LinearPDE(domain) |
| 51 |
self.__pde_u.setSymmetryOn() |
| 52 |
self.__pde_u.setValue(A=identityTensor4(dom)) |
| 53 |
|
| 54 |
self.__pde_p=LinearPDE(domain) |
| 55 |
self.__pde_p.setReducedOrderOn() |
| 56 |
self.__pde_p.setSymmetryOn() |
| 57 |
self.__pde_p.setValue(D=1.) |
| 58 |
|
| 59 |
def initialize(self,f=Data(),fixed_u_mask=Data()): |
| 60 |
self.__pde_u.setValue(q=fixed_u_mask,Y=f) |
| 61 |
def inner(self,p0,p1): |
| 62 |
return integrate(p0*p1,Function(self.__pde_p.getDomain())) |
| 63 |
|
| 64 |
def solve_f(self,u,p,tol=1.e-8): |
| 65 |
self.__pde_u.setTolerance(tol) |
| 66 |
self.__pde_u.setValue(X=grad(u)+p*kronecker(self.__pde_u.getDomain())) |
| 67 |
return self.__pde_u.getSolution() |
| 68 |
def solve_g(self,u,tol=1.e-8): |
| 69 |
self.__pde_p.setTolerance(tol) |
| 70 |
self.__pde_p.setValue(X=-u) |
| 71 |
dp=self.__pde_p.getSolution() |
| 72 |
return dp |
| 73 |
|
| 74 |
class StokesProblem(SaddlePointProblem): |
| 75 |
""" |
| 76 |
simple example of saddle point problem |
| 77 |
""" |
| 78 |
def __init__(self,domain): |
| 79 |
super(StokesProblem, self).__init__(self) |
| 80 |
self.domain=domain |
| 81 |
self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim()) |
| 82 |
self.__pde_u.setSymmetryOn() |
| 83 |
|
| 84 |
self.__pde_p=LinearPDE(domain) |
| 85 |
self.__pde_p.setReducedOrderOn() |
| 86 |
self.__pde_p.setSymmetryOn() |
| 87 |
|
| 88 |
def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1): |
| 89 |
self.eta=eta |
| 90 |
A =self.__pde_u.createCoefficientOfGeneralPDE("A") |
| 91 |
for i in range(self.domain.getDim()): |
| 92 |
for j in range(self.domain.getDim()): |
| 93 |
A[i,j,j,i] += self.eta |
| 94 |
A[i,j,i,j] += self.eta |
| 95 |
self.__pde_p.setValue(D=1./self.eta) |
| 96 |
self.__pde_u.setValue(A=A,q=fixed_u_mask,Y=f) |
| 97 |
|
| 98 |
def inner(self,p0,p1): |
| 99 |
return integrate(p0*p1,Function(self.__pde_p.getDomain())) |
| 100 |
|
| 101 |
def solve_f(self,u,p,tol=1.e-8): |
| 102 |
self.__pde_u.setTolerance(tol) |
| 103 |
g=grad(u) |
| 104 |
self.__pde_u.setValue(X=self.eta*symmetric(g)+p*kronecker(self.__pde_u.getDomain())) |
| 105 |
return self.__pde_u.getSolution() |
| 106 |
|
| 107 |
def solve_g(self,u,tol=1.e-8): |
| 108 |
self.__pde_p.setTolerance(tol) |
| 109 |
self.__pde_p.setValue(X=-u) |
| 110 |
dp=self.__pde_p.getSolution() |
| 111 |
return dp |
| 112 |
|
| 113 |
NE=50 |
| 114 |
dom=Rectangle(NE,NE,order=2) |
| 115 |
# prop=SimpleStokesProblem(dom) |
| 116 |
prop=StokesProblem(dom) |
| 117 |
x=dom.getX() |
| 118 |
mask=(whereZero(x[0])+whereZero(x[0]-1.)+whereZero(x[1]-1.))*unitVector(0,dom)+(whereZero(x[1]-1.)+whereZero(x[1]))*unitVector(1,dom) |
| 119 |
u0=Vector(0.,Solution(dom)) |
| 120 |
u0[0]=x[1]*whereZero(x[1]-1.) |
| 121 |
p0=Scalar(0,ReducedSolution(dom)) |
| 122 |
# prop.initialize(fixed_u_mask=mask) |
| 123 |
prop.initialize(fixed_u_mask=mask,eta=10.) |
| 124 |
u,p=prop.solve(u0,p0,tolerance=0.01) |
| 125 |
# saveVTK("stokes.xml",u=u,p=p,m=mask,u0=u0) |
| 126 |
|
| 127 |
eta=whereNegative(x[1]-0.5)*1.e6+whereNonNegative(x[1]-0.5) |
| 128 |
prop.initialize(fixed_u_mask=mask,eta=eta) |
| 129 |
u,p=prop.solve(u0,p0,tolerance=0.01,tolerance_u=0.1,accepted_reduction=0.8) |
| 130 |
saveVTK("stokes.xml",u=u,p=p,m=mask,u0=u0) |
| 131 |
|
| 132 |
# vim: expandtab shiftwidth=4: |
Parent Directory
| 
Revision Log