examples/geotutorial/forward_euler.py

##############################################################################
#
# Copyright (c) 2003-2018 by The University of Queensland
# http://www.uq.edu.au
#
# Primary Business: Queensland, Australia
# Licensed under the Apache License, version 2.0
# http://www.apache.org/licenses/LICENSE-2.0
#
# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
# Development 2012-2013 by School of Earth Sciences
# Development from 2014 by Centre for Geoscience Computing (GeoComp)
#
##############################################################################
from __future__ import division, print_function

__copyright__="""Copyright (c) 2003-2018 by The University of Queensland
http://www.uq.edu.au
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Apache License, version 2.0
http://www.apache.org/licenses/LICENSE-2.0"""
__url__="https://launchpad.net/escript-finley"

# import tools
from esys.escript import *
from esys.escript.linearPDEs import LinearPDE
try:
    from esys.dudley import Rectangle
    HAVE_DUDLEY = True
except ImportError:
    HAVE_DUDLEY = False
from esys.weipa import saveVTK

if not HAVE_DUDLEY:
    print("Dudley module not available")
else:
    # 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 = %s"%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("time step %d, t=%s, T_max=%s"%(N, t, Lsup(T)))
        # update PDE coefficient:
        mypde.setValue(Y=rhocp*T+dt*Q, X=-k*dt*grad(T))
        # 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	jfenwick	3981	##############################################################################
2	gross	2156	#
3	jfenwick	6651	# Copyright (c) 2003-2018 by The University of Queensland
4	jfenwick	3981	# http://www.uq.edu.au
5	gross	2156	#
6			# Primary Business: Queensland, Australia
7	jfenwick	6112	# Licensed under the Apache License, version 2.0
8			# http://www.apache.org/licenses/LICENSE-2.0
9	gross	2156	#
10	jfenwick	3981	# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
11	jfenwick	4657	# Development 2012-2013 by School of Earth Sciences
12			# Development from 2014 by Centre for Geoscience Computing (GeoComp)
13	jfenwick	3981	#
14			##############################################################################
15	sshaw	5707	from __future__ import division, print_function
16	gross	2156
17	jfenwick	6651	__copyright__="""Copyright (c) 2003-2018 by The University of Queensland
18	jfenwick	3981	http://www.uq.edu.au
19	gross	2156	Primary Business: Queensland, Australia"""
20	jfenwick	6112	__license__="""Licensed under the Apache License, version 2.0
21			http://www.apache.org/licenses/LICENSE-2.0"""
22	jfenwick	2344	__url__="https://launchpad.net/escript-finley"
23	gross	2156
24			# import tools
25			from esys.escript import *
26			from esys.escript.linearPDEs import LinearPDE
27	sshaw	5288	try:
28			from esys.dudley import Rectangle
29			HAVE_DUDLEY = True
30			except ImportError:
31			HAVE_DUDLEY = False
32	caltinay	3346	from esys.weipa import saveVTK
33	caltinay	3953
34	sshaw	5288	if not HAVE_DUDLEY:
35			print("Dudley module not available")
36			else:
37			# end of simulation time
38			t_end=0.1
39			# dimensions:
40			L0=1.;L1=1.
41			# location, size and value of heat source
42			xc=[0.3,0.4]; r=0.1; Qc=3000
43			# material parameter
44			k=1.; rhocp=100;
45			# bottom temperature:
46			T_bot=100
47			# generate domain:
48			mydomain=Rectangle(l0=L0,l1=L1,n0=20,n1=20)
49			x=mydomain.getX()
50			# set boundray temperature:
51			T_D=T_bot/L1*(L1-x[1])
52			# set heat source:
53			Q=Qc*whereNegative(length(x-xc)-r)
54			# time step size:
55			dt=0.01
56			# or use adaptive choice dt=0.05inf(rhocpmydomain.getSize()**2/k)
57			print("time step size = %s"%dt)
58			# generate domain:
59			mypde=LinearPDE(mydomain)
60			mypde.setSymmetryOn()
61			# set PDE coefficients:
62			mypde.setValue(D=rhocp,
63			r=T_D, q=whereZero(x[1])+whereZero(x[1]-L1))
64			# initial temperature
65			T=T_D
66			# step counter and time marker:
67			N=0; t=0
68			# stop when t_end is reached:
69			while t<t_end:
70			print("time step %d, t=%s, T_max=%s"%(N, t, Lsup(T)))
71			# update PDE coefficient:
72			mypde.setValue(Y=rhocpT+dtQ, X=-kdtgrad(T))
73			# new temperature:
74			T=mypde.getSolution()
75			# save as VTK for visualisation:
76			# saveVTK("u.%s.vtu"%N,T=T)
77			# increase counter and marker:
78			N+=1; t+=dt
79