| 1 |
# $Id$ |
| 2 |
|
| 3 |
__copyright__=""" Copyright (c) 2006 by ACcESS MNRF |
| 4 |
http://www.access.edu.au |
| 5 |
Primary Business: Queensland, Australia""" |
| 6 |
__license__="""Licensed under the Open Software License version 3.0 |
| 7 |
http://www.opensource.org/licenses/osl-3.0.php""" |
| 8 |
|
| 9 |
from esys.escript import * |
| 10 |
from esys.escript.modelframe import Model,IterationDivergenceError |
| 11 |
from esys.escript.linearPDEs import LameEquation |
| 12 |
|
| 13 |
class SteadyIncompressibleFlow(Model): |
| 14 |
""" |
| 15 |
|
| 16 |
M{-\left(\eta\left(v_{i,j}+v_{j,i}\right)\right)_{,j}+p_{,i}=F_i} |
| 17 |
|
| 18 |
M{\sigma_{ij}=2\eta D_{ij}-p\,\delta_{ij}} |
| 19 |
|
| 20 |
M{D_{ij}=\frac{1}{2}\left( v_{j,i} + v_{i,j }\right)} |
| 21 |
|
| 22 |
M{v_{k,k} = 0} |
| 23 |
|
| 24 |
""" |
| 25 |
|
| 26 |
def __init__(self,**kwargs): |
| 27 |
""" |
| 28 |
set up model |
| 29 |
""" |
| 30 |
Model.__init__(self,**kwargs) |
| 31 |
self.declareParameter(domain=None, \ |
| 32 |
velocity=0., \ |
| 33 |
pressure=0., \ |
| 34 |
viscosity=1., \ |
| 35 |
internal_force=0., \ |
| 36 |
location_prescribed_velocity=None, \ |
| 37 |
prescribed_velocity=None, \ |
| 38 |
rel_tol=1.e-3,abs_tol=0.,max_iter=10,relaxation=0.0001) |
| 39 |
self.__iter=0 |
| 40 |
|
| 41 |
def doInitialization(self): |
| 42 |
""" |
| 43 |
initialize model |
| 44 |
""" |
| 45 |
self.__p_old=None |
| 46 |
self.__p_very_old=None |
| 47 |
self.__dt_old=None |
| 48 |
self.__pde=LameEquation(self.domain) |
| 49 |
self.__pde.setSolverMethod(LameEquation.DIRECT) |
| 50 |
if self.location_prescribed_velocity == None: self.location_prescribed_velocit=Data() |
| 51 |
if self.prescribed_velocity == None: self.prescribed_velocity=Data() |
| 52 |
|
| 53 |
def stress(self): |
| 54 |
""" |
| 55 |
returns current stress""" |
| 56 |
return 2*self.viscosity*self.stretching-self.pressure*kronecker(self.domain) |
| 57 |
|
| 58 |
def stretching(self): |
| 59 |
""" |
| 60 |
returns stertching tensor |
| 61 |
""" |
| 62 |
g=grad(self.velocity) |
| 63 |
return (g+transpose(g))/2 |
| 64 |
|
| 65 |
def doStepPreprocessing(self,dt): |
| 66 |
""" |
| 67 |
step up pressure iteration |
| 68 |
|
| 69 |
if run within a time dependend problem extrapolation of pressure from previous time steps is used to |
| 70 |
get an initial guess (that needs some work!!!!!!!) |
| 71 |
""" |
| 72 |
self.__iter=0 |
| 73 |
self.__diff=1.e40 |
| 74 |
if not self.__p_old==None: |
| 75 |
if self.__p_very_old==None: |
| 76 |
self.pressure=self.__p_old |
| 77 |
else: |
| 78 |
self.pressure=(1.+dt/self.__dt_old)*self.__p_old-dt/self.__dt_old*self.__p_very_old |
| 79 |
|
| 80 |
def doStep(self,dt): |
| 81 |
""" |
| 82 |
|
| 83 |
performs an iteration step of the penalty method. |
| 84 |
IterationDivergenceError is raised if pressure error cannot be reduced or max_iter is reached. |
| 85 |
|
| 86 |
""" |
| 87 |
penalty=self.viscosity/self.relaxation |
| 88 |
self.__pde.setValue(lame_mu=self.viscosity, \ |
| 89 |
lame_lambda=penalty, \ |
| 90 |
F=self.internal_force, \ |
| 91 |
sigma=self.pressure*kronecker(self.__pde.getDomain()), \ |
| 92 |
r=self.prescribed_velocity, \ |
| 93 |
q=self.location_prescribed_velocity) |
| 94 |
self.__pde.setTolerance(self.rel_tol/10.) |
| 95 |
self.velocity=self.__pde.getSolution() |
| 96 |
update=penalty*div(self.velocity) |
| 97 |
self.pressure=self.pressure-update |
| 98 |
self.__diff,diff_old=Lsup(update),self.__diff |
| 99 |
self.__iter+=1 |
| 100 |
self.trace("velocity range %e:%e"%(inf(self.velocity),sup(self.velocity))) |
| 101 |
self.trace("pressure range %e:%e"%(inf(self.pressure),sup(self.pressure))) |
| 102 |
self.trace("pressure correction: %e"%self.__diff) |
| 103 |
if self.__iter>2 and diff_old<self.__diff: |
| 104 |
self.trace("Pressure iteration failed!") |
| 105 |
raise IterationDivergenceError,"no improvement in pressure iteration" |
| 106 |
if self.__iter>self.max_iter: |
| 107 |
raise IterationDivergenceError,"Maximum number of iterations steps reached" |
| 108 |
|
| 109 |
def terminateIteration(self): |
| 110 |
"""iteration is terminateIterationd if relative pressure change is less then rel_tol""" |
| 111 |
return self.__diff<=self.rel_tol*Lsup(self.pressure)+self.abs_tol |
| 112 |
|
| 113 |
def doStepPostprocessing(self,dt): |
| 114 |
self.__dt_old=dt |
| 115 |
self.__p_old,self.__p_very_old=self.pressure,self.__p_old |
Parent Directory
| 
Revision Log