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# $Id:$ |
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# |
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####################################################### |
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# |
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# Copyright 2008 by University of Queensland |
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# |
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# http://esscc.uq.edu.au |
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# Primary Business: Queensland, Australia |
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# 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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# |
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####################################################### |
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# |
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|
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""" |
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Some models for flow |
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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) 2008 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 escript import * |
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import util |
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from linearPDEs import LinearPDE |
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from pdetools import HomogeneousSaddlePointProblem |
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|
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class StokesProblemCartesian(HomogeneousSaddlePointProblem): |
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""" |
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solves |
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|
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-(eta*(u_{i,j}+u_{j,i}))_j - p_i = f_i |
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u_{i,i}=0 |
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|
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u=0 where fixed_u_mask>0 |
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eta*(u_{i,j}+u_{j,i})*n_j=surface_stress |
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|
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if surface_stress is not give 0 is assumed. |
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|
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typical usage: |
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|
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sp=StokesProblemCartesian(domain) |
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sp.setTolerance() |
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sp.initialize(...) |
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v,p=sp.solve(v0,p0) |
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""" |
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def __init__(self,domain,**kwargs): |
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HomogeneousSaddlePointProblem.__init__(self,**kwargs) |
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self.domain=domain |
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self.vol=util.integrate(1.,Function(self.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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self.__pde_u.setSolverMethod(preconditioner=LinearPDE.ILU0) |
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|
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self.__pde_prec=LinearPDE(domain) |
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self.__pde_prec.setReducedOrderOn() |
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self.__pde_prec.setSymmetryOn() |
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|
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self.__pde_proj=LinearPDE(domain) |
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self.__pde_proj.setReducedOrderOn() |
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self.__pde_proj.setSymmetryOn() |
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self.__pde_proj.setValue(D=1.) |
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|
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def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1,surface_stress=Data()): |
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self.eta=eta |
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A =self.__pde_u.createCoefficientOfGeneralPDE("A") |
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self.__pde_u.setValue(A=Data()) |
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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] += 1. |
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A[i,j,i,j] += 1. |
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self.__pde_prec.setValue(D=1./self.eta) |
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self.__pde_u.setValue(A=A*self.eta,q=fixed_u_mask,Y=f,y=surface_stress) |
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|
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def B(self,arg): |
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d=util.div(arg) |
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self.__pde_proj.setValue(Y=d) |
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self.__pde_proj.setTolerance(self.getSubProblemTolerance()) |
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return self.__pde_proj.getSolution(verbose=self.show_details) |
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|
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def inner(self,p0,p1): |
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s0=util.interpolate(p0,Function(self.domain)) |
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s1=util.interpolate(p1,Function(self.domain)) |
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return util.integrate(s0*s1) |
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|
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def getStress(self,u): |
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mg=util.grad(u) |
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return 2.*self.eta*util.symmetric(mg) |
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|
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def solve_A(self,u,p): |
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""" |
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solves Av=f-Au-B^*p (v=0 on fixed_u_mask) |
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""" |
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self.__pde_u.setTolerance(self.getSubProblemTolerance()) |
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self.__pde_u.setValue(X=-self.getStress(u)-p*util.kronecker(self.domain)) |
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return self.__pde_u.getSolution(verbose=self.show_details) |
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|
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def solve_prec(self,p): |
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self.__pde_prec.setTolerance(self.getSubProblemTolerance()) |
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self.__pde_prec.setValue(Y=p) |
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q=self.__pde_prec.getSolution(verbose=self.show_details) |
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return q |
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def stoppingcriterium(self,Bv,v,p): |
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n_r=util.sqrt(self.inner(Bv,Bv)) |
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n_v=util.Lsup(v) |
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if self.verbose: print "PCG step %s: L2(div(v)) = %s, Lsup(v)=%s"%(self.iter,n_r,n_v) |
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self.iter+=1 |
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if n_r <= self.vol**(1./2.-1./self.domain.getDim())*n_v*self.getTolerance(): |
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if self.verbose: print "PCG terminated after %s steps."%self.iter |
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return True |
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else: |
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return False |
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def stoppingcriterium_GMRES(self,norm_r,norm_b): |
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if self.verbose: print "GMRES step %s: L2(r) = %s, L2(b)*TOL=%s"%(self.iter,norm_r,norm_b*self.getTolerance()) |
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self.iter+=1 |
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if norm_r <= norm_b*self.getTolerance(): |
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if self.verbose: print "GMRES terminated after %s steps."%self.iter |
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return True |
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else: |
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return False |
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