examples/geotutorial/forward_euler.py

########################################################
#
# Copyright (c) 2003-2008 by University of Queensland
# Earth Systems Science Computational Center (ESSCC)
# http://www.uq.edu.au/esscc
#
# Primary Business: Queensland, Australia
# Licensed under the Open Software License version 3.0
# http://www.opensource.org/licenses/osl-3.0.php
#
########################################################

__copyright__="""Copyright (c) 2003-2008 by University of Queensland
Earth Systems Science Computational Center (ESSCC)
http://www.uq.edu.au/esscc
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Open Software License version 3.0
http://www.opensource.org/licenses/osl-3.0.php"""
__url__="https://launchpad.net/escript-finley"

# import tools
from esys.escript import *
from esys.escript.linearPDEs import LinearPDE
from esys.finley import Rectangle
# end of simulation time
t_end=0.1
# dimensions:
L0=1.;L1=1.
# location, size and value of heat source
xc=[0.3,0.4]; r=0.1; Qc=3000
# material parameter
k=1.; rhocp=100; 
# bottom temperature:
T_bot=100
# generate domain:
mydomain=Rectangle(l0=L0,l1=L1,n0=20,n1=20)
x=mydomain.getX()
# set boundray temperature:
T_D=T_bot/L1*(L1-x[1])
# set heat source:
Q=Qc*whereNegative(length(x-xc)-r)
# time step size:
dt=0.01
# or use adaptive choice dt=0.05*inf(rhocp*mydomain.getSize()**2/k)
print "time step size = ",dt
# generate domain:
mypde=LinearPDE(mydomain)
mypde.setSymmetryOn()
# set PDE coefficients:
mypde.setValue(D=rhocp, 
               r=T_D, q=whereZero(x[1])+whereZero(x[1]-L1))
# initial temperature
T=T_D 
# step counter and time marker:
N=0; t=0
# stop when t_end is reached:
while t<t_end:
    print N,"-th time step t=",t," T_max=", Lsup(T)
    # update PDE coefficient:
    mypde.setValue(Y=rhocp*T+dt*Q, X=-k*dt*grad(T))
    # new temperature:
    T=mypde.getSolution()
    # save to vtk for mayavi:
    # saveVTK("u.%s.xml"%N,T=T)
    # increase counter and marker:
    N+=1; t+=dt
1	gross	2156	########################################################
2			#
3			# Copyright (c) 2003-2008 by University of Queensland
4			# Earth Systems Science Computational Center (ESSCC)
5			# http://www.uq.edu.au/esscc
6			#
7			# Primary Business: Queensland, Australia
8			# Licensed under the Open Software License version 3.0
9			# http://www.opensource.org/licenses/osl-3.0.php
10			#
11			########################################################
12
13			__copyright__="""Copyright (c) 2003-2008 by University of Queensland
14			Earth Systems Science Computational Center (ESSCC)
15			http://www.uq.edu.au/esscc
16			Primary Business: Queensland, Australia"""
17			__license__="""Licensed under the Open Software License version 3.0
18			http://www.opensource.org/licenses/osl-3.0.php"""
19	jfenwick	2344	__url__="https://launchpad.net/escript-finley"
20	gross	2156
21			# import tools
22			from esys.escript import *
23			from esys.escript.linearPDEs import LinearPDE
24			from esys.finley import Rectangle
25			# end of simulation time
26			t_end=0.1
27			# dimensions:
28			L0=1.;L1=1.
29			# location, size and value of heat source
30			xc=[0.3,0.4]; r=0.1; Qc=3000
31			# material parameter
32			k=1.; rhocp=100;
33			# bottom temperature:
34			T_bot=100
35			# generate domain:
36			mydomain=Rectangle(l0=L0,l1=L1,n0=20,n1=20)
37			x=mydomain.getX()
38			# set boundray temperature:
39			T_D=T_bot/L1*(L1-x[1])
40			# set heat source:
41			Q=Qc*whereNegative(length(x-xc)-r)
42			# time step size:
43			dt=0.01
44			# or use adaptive choice dt=0.05inf(rhocpmydomain.getSize()**2/k)
45			print "time step size = ",dt
46			# generate domain:
47			mypde=LinearPDE(mydomain)
48			mypde.setSymmetryOn()
49			# set PDE coefficients:
50			mypde.setValue(D=rhocp,
51			r=T_D, q=whereZero(x[1])+whereZero(x[1]-L1))
52			# initial temperature
53			T=T_D
54			# step counter and time marker:
55			N=0; t=0
56			# stop when t_end is reached:
57			while t<t_end:
58			print N,"-th time step t=",t," T_max=", Lsup(T)
59			# update PDE coefficient:
60			mypde.setValue(Y=rhocpT+dtQ, X=-kdtgrad(T))
61			# new temperature:
62			T=mypde.getSolution()
63			# save to vtk for mayavi:
64			# saveVTK("u.%s.xml"%N,T=T)
65			# increase counter and marker:
66			N+=1; t+=dt