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# $Id$ |
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|
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""" |
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solvers for the stokes problem |
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|
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@var __author__: name of author |
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@var __copyright__: copyrights |
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@var __license__: licence agreement |
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@var __url__: url entry point on documentation |
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@var __version__: version |
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@var __date__: date of the version |
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""" |
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|
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__author__="Lutz Gross, l.gross@uq.edu.au" |
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__copyright__=""" Copyright (c) 2006 by ACcESS MNRF |
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http://www.access.edu.au |
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Primary Business: Queensland, Australia""" |
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__license__="""Licensed under the Open Software License version 3.0 |
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http://www.opensource.org/licenses/osl-3.0.php""" |
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__url__="http://www.iservo.edu.au/esys" |
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__version__="$Revision$" |
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__date__="$Date$" |
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|
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from esys.escript import * |
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from esys.escript.pdetools import SaddlePointProblem |
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from esys.escript.linearPDEs import LinearPDE |
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from esys.finley import Rectangle |
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|
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class SimpleStokesProblem(SaddlePointProblem): |
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""" |
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simple example of saddle point problem |
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""" |
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def __init__(self,domain): |
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super(SimpleStokesProblem, self).__init__(self) |
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|
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self.__pde_u=LinearPDE(domain) |
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self.__pde_u.setSymmetryOn() |
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self.__pde_u.setValue(A=identityTensor4(dom)) |
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|
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self.__pde_p=LinearPDE(domain) |
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self.__pde_p.setReducedOrderOn() |
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self.__pde_p.setSymmetryOn() |
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self.__pde_p.setValue(D=1.) |
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|
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def initialize(self,f=Data(),fixed_u_mask=Data()): |
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self.__pde_u.setValue(q=fixed_u_mask,Y=f) |
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def inner(self,p0,p1): |
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return integrate(p0*p1,Function(self.__pde_p.getDomain())) |
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|
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def solve_f(self,u,p,tol=1.e-8): |
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self.__pde_u.setTolerance(tol) |
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self.__pde_u.setValue(X=grad(u)+p*kronecker(self.__pde_u.getDomain())) |
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return self.__pde_u.getSolution() |
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def solve_g(self,u,tol=1.e-8): |
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self.__pde_p.setTolerance(tol) |
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self.__pde_p.setValue(X=-u) |
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dp=self.__pde_p.getSolution() |
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return dp |
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|
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class StokesProblem(SaddlePointProblem): |
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""" |
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simple example of saddle point problem |
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""" |
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def __init__(self,domain): |
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super(StokesProblem, self).__init__(self) |
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self.domain=domain |
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self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim()) |
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self.__pde_u.setSymmetryOn() |
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|
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self.__pde_p=LinearPDE(domain) |
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self.__pde_p.setReducedOrderOn() |
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self.__pde_p.setSymmetryOn() |
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|
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def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1): |
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self.eta=eta |
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A =self.__pde_u.createCoefficientOfGeneralPDE("A") |
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for i in range(self.domain.getDim()): |
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for j in range(self.domain.getDim()): |
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A[i,j,j,i] += self.eta |
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A[i,j,i,j] += self.eta |
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self.__pde_p.setValue(D=1./self.eta) |
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self.__pde_u.setValue(A=A,q=fixed_u_mask,Y=f) |
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|
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def inner(self,p0,p1): |
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return integrate(p0*p1,Function(self.__pde_p.getDomain())) |
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|
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def solve_f(self,u,p,tol=1.e-8): |
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self.__pde_u.setTolerance(tol) |
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g=grad(u) |
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self.__pde_u.setValue(X=self.eta*symmetric(g)+p*kronecker(self.__pde_u.getDomain())) |
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return self.__pde_u.getSolution() |
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|
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def solve_g(self,u,tol=1.e-8): |
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self.__pde_p.setTolerance(tol) |
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self.__pde_p.setValue(X=-u) |
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dp=self.__pde_p.getSolution() |
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return dp |
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|
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NE=50 |
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dom=Rectangle(NE,NE,order=2) |
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# prop=SimpleStokesProblem(dom) |
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prop=StokesProblem(dom) |
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x=dom.getX() |
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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) |
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u0=Vector(0.,Solution(dom)) |
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u0[0]=x[1]*whereZero(x[1]-1.) |
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p0=Scalar(0,ReducedSolution(dom)) |
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# prop.initialize(fixed_u_mask=mask) |
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prop.initialize(fixed_u_mask=mask,eta=10.) |
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u,p=prop.solve(u0,p0,tolerance=0.01) |
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# saveVTK("stokes.xml",u=u,p=p,m=mask,u0=u0) |
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|
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eta=whereNegative(x[1]-0.5)*1.e6+whereNonNegative(x[1]-0.5) |
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prop.initialize(fixed_u_mask=mask,eta=eta) |
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u,p=prop.solve(u0,p0,tolerance=0.01,tolerance_u=0.1,accepted_reduction=0.8) |
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saveVTK("stokes.xml",u=u,p=p,m=mask,u0=u0) |
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|
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# vim: expandtab shiftwidth=4: |
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