examples/geotutorial/backward_euler.py

########################################################
#
# Copyright (c) 2003-2009 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
# time step size:
dt=0.01
# 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)
# generate domain:
mypde=LinearPDE(mydomain)
mypde.setSymmetryOn()
# set PDE coefficients:
mypde.setValue(A=dt*k*kronecker(mydomain), D=dt*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
    # update PDE coefficient:
    mypde.setValue(Y=dt*rhocp*T+dt*Q)
    # new temperature:
    T=mypde.getSolution()
    # save as VTK for visualisation:
    saveVTK("u.%s.vtu"%N,T=T)
    # increase counter and marker:
    N+=1; t+=dt
1	########################################################
2	#
3	# Copyright (c) 2003-2009 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	__url__="https://launchpad.net/escript-finley"
20
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	# time step size:
28	dt=0.01
29	# dimensions:
30	L0=1.;L1=1.
31	# location, size and value of heat source
32	xc=[0.3,0.4]; r=0.1; Qc=3000
33	# material parameter
34	k=1; rhocp=100;
35	# bottom temperature:
36	T_bot=100
37	# generate domain:
38	mydomain=Rectangle(l0=L0,l1=L1,n0=20,n1=20)
39	x=mydomain.getX()
40	# set boundray temperature:
41	T_D=T_bot/L1*(L1-x[1])
42	# set heat source:
43	Q=Qc*whereNegative(length(x-xc)-r)
44	# generate domain:
45	mypde=LinearPDE(mydomain)
46	mypde.setSymmetryOn()
47	# set PDE coefficients:
48	mypde.setValue(A=dtkkronecker(mydomain), D=dt*rhocp,
49	r=T_D, q=whereZero(x[1])+whereZero(x[1]-L1))
50	# initial temperature
51	T=T_D
52	# step counter and time marker:
53	N=0; t=0
54	# stop when t_end is reached:
55	while t<t_end:
56	print N,"-th time step t=",t
57	# update PDE coefficient:
58	mypde.setValue(Y=dtrhocpT+dt*Q)
59	# new temperature:
60	T=mypde.getSolution()
61	# save as VTK for visualisation:
62	saveVTK("u.%s.vtu"%N,T=T)
63	# increase counter and marker:
64	N+=1; t+=dt