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# $Id$ |
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|
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from escript.escript import * |
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from escript.modelframe import Model,IterationDivergenceError |
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from escript.linearPDEs import LameEquation |
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|
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class SteadyIncompressibleFlow(Model): |
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""" |
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|
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\f[ |
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-\left(\eta\left(v_{i,j}+v_{j,i}\right)\right)_{,j}+p_{,i}=F_i |
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\f] |
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|
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\f[ |
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\sigma_{ij}=2\eta D_{ij}-p\,\delta_{ij} |
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\f[ |
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D_{ij}=\frac{1}{2}\left( v_{j,i} + v_{i,j }\right) \; . |
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\f] |
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|
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\f[ |
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-v_{k,k} = 0 \; . |
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\f] |
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|
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""" |
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|
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def __init__(self,debug=False): |
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"""set up model""" |
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Model.__init__(self,debug=debug) |
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self.declareParameter(domain=None, \ |
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velocity=0., \ |
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pressure=0., \ |
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viscosity=1., \ |
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internal_force=0., \ |
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location_prescribed_velocity=Data(), \ |
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prescribed_velocity=Data(), \ |
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rel_tol=1.e-3,abs_tol=0.,max_iter=10,relaxation=0.001) |
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self.__iter=0 |
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|
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def doInitialization(self): |
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"""initialize model""" |
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self.__p_old=None |
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self.__p_very_old=None |
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self.__dt_old=None |
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self.__pde=LameEquation(self.domain) |
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|
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def stress(self): |
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"""returns current stress""" |
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return 2*self.viscosity*self.stretching-self.pressure*kronecker(self.domain) |
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|
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def stretching(self): |
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"""returns stertching tensor""" |
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g=grad(self.velocity) |
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return (g+transpose(g))/2 |
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|
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def doStepPreprocessing(self,dt): |
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""" |
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step up pressure iteration |
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|
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if run within a time dependend problem extrapolation of pressure from previous time steps is used to |
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get an initial guess (that needs some work!!!!!!!) |
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""" |
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self.__iter=0 |
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self.__diff=1.e40 |
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if not self.__p_old==None: |
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if self.__p_very_old==None: |
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self.pressure=self.__p_old |
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else: |
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self.pressure=(1.+dt/self.__dt_old)*self.__p_old-dt/self.__dt_old*self.__p_very_old |
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|
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def doStep(self,dt): |
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""" |
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|
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performs an iteration step of the penalty method. |
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IterationDivergenceError is raised if pressure error cannot be reduced or max_iter is reached. |
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|
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""" |
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penalty=self.viscosity/self.relaxation |
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self.__pde.setValue(lame_mu=self.viscosity, \ |
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lame_lambda=penalty, \ |
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F=self.internal_force, \ |
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sigma=self.pressure*kronecker(self.__pde.getDomain()), \ |
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r=self.prescribed_velocity, \ |
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q=self.location_prescribed_velocity) |
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self.__pde.setTolerance(self.rel_tol/10.) |
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self.velocity=self.__pde.getSolution() |
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update=penalty*div(self.velocity) |
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print "f=",inf(update),sup(update) |
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self.pressure=self.pressure-update |
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self.__diff,diff_old=Lsup(update),self.__diff |
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self.__iter+=1 |
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self.trace("velocity range %e:%e"%(inf(self.velocity),sup(self.velocity))) |
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self.trace("pressure range %e:%e"%(inf(self.pressure),sup(self.pressure))) |
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self.trace("pressure correction: %e"%self.__diff) |
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if self.__iter>2 and diff_old<self.__diff: |
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self.trace("Pressure iteration failed!") |
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raise IterationDivergenceError,"no improvement in pressure iteration" |
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if self.__iter>self.max_iter: |
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raise IterationDivergenceError,"Maximum number of iterations steps reached" |
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|
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def terminateIteration(self): |
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"""iteration is terminateIterationd if relative pressure change is less then rel_tol""" |
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return self.__diff<=self.rel_tol*Lsup(self.pressure)+self.abs_tol |
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|
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def doStepPostprocessing(self,dt): |
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self.__dt_old=dt |
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self.__p_old,self.__p_very_old=self.pressure,self.__p_old |
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