/[escript]/trunk/doc/examples/cookbook/example01b.py
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Contents of /trunk/doc/examples/cookbook/example01b.py

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1 from __future__ import division, print_function
2 ##############################################################################
3 #
4 # Copyright (c) 2009-2018 by The University of Queensland
5 # http://www.uq.edu.au
6 #
7 # Primary Business: Queensland, Australia
8 # Licensed under the Apache License, version 2.0
9 # http://www.apache.org/licenses/LICENSE-2.0
10 #
11 # Development until 2012 by Earth Systems Science Computational Center (ESSCC)
12 # Development 2012-2013 by School of Earth Sciences
13 # Development from 2014 by Centre for Geoscience Computing (GeoComp)
14 #
15 ##############################################################################
16
17 __copyright__="""Copyright (c) 2009-2018 by The University of Queensland
18 http://www.uq.edu.au
19 Primary Business: Queensland, Australia"""
20 __license__="""Licensed under the Apache License, version 2.0
21 http://www.apache.org/licenses/LICENSE-2.0"""
22 __url__="https://launchpad.net/escript-finley"
23
24 """
25 Author: Antony Hallam antony.hallam@uqconnect.edu.au
26 """
27 ############################################################FILE HEADER
28 # example01b.py
29 # Model temperature diffusion between two granite blocks of unequal
30 # initial temperature. Solve for total energy in the system. Use
31 # matplotlib to visualise the answer.
32 import sys
33 #######################################################EXTERNAL MODULES
34 # To solve the problem it is necessary to import the modules we require.
35 #For interactive use, you can comment out the next two lines
36 import matplotlib
37 matplotlib.use('agg') #It's just here for automated testing
38 from esys.escript import * # This imports everything from the escript library
39 from esys.escript.unitsSI import *
40 from esys.escript.linearPDEs import LinearPDE # This defines LinearPDE as LinearPDE
41 import pylab as pl #Plotting package.
42 import numpy as np #Array package.
43 import os, sys #This package is necessary to handle saving our data.
44 try:
45 from esys.finley import Rectangle
46 HAVE_FINLEY = True
47 except ImportError:
48 print("Finley module not available")
49 HAVE_FINLEY = False
50
51 if HAVE_FINLEY:
52 #################################################ESTABLISHING VARIABLES
53 #Domain related.
54 mx = 500*m #meters - model length
55 my = 100*m #meters - model width
56 ndx = 100 # mesh steps in x direction
57 ndy = 1 # mesh steps in y direction - one dimension means one element
58 boundloc = mx/2 # location of boundary between the two blocks
59 #PDE related
60 rho = 2750. *kg/m**3 #kg/m{3} density of iron
61 cp = 790.*J/(kg*K) # J/Kg.K thermal capacity
62 rhocp = rho*cp
63 kappa = 2.2*W/m/K # watts/m.Kthermal conductivity
64 qH=0 * J/(sec*m**3) # J/(sec.m{3}) no heat source
65 T1=20 * Celsius # initial temperature at Block 1
66 T2=2273. * Celsius # base temperature at Block 2
67
68 ################################################ESTABLISHING PARAMETERS
69 t=0 * day # our start time, usually zero
70 tend=50 * yr # - time to end simulation
71 outputs = 200 # number of time steps required.
72 h=(tend-t)/outputs #size of time step
73 #user warning statement
74 print("Expected Number of time outputs is: ", (tend-t)/h)
75 i=0 #loop counter
76 #the folder to put our outputs in, leave blank "" for script path
77 save_path= os.path.join("data","example01")
78 #ensure the dir exists
79 mkDir(save_path, os.path.join(save_path,"tempT"))
80
81 ####################################################DOMAIN CONSTRUCTION
82 blocks = Rectangle(l0=mx,l1=my,n0=ndx, n1=ndy)
83
84 ###############################################ESCRIPT PDE CONSTRUCTION
85 #... open PDE and set coefficients ...
86 mypde=LinearPDE(blocks)
87 mypde.setSymmetryOn()
88 A=zeros((2,2))
89 A[0,0]=kappa
90 mypde.setValue(A=A,D=rhocp/h)
91 # ... set initial temperature ....
92 x=Solution(blocks).getX()
93 T= T1*whereNegative(x[0]-boundloc)+T2*(1-whereNegative(x[0]-boundloc))
94
95 # ... open a collector for the time marks and corresponding total energy
96 t_list=[]
97 E_list=[]
98 ########################################################START ITERATION
99 while t<tend:
100 i+=1
101 t+=h
102 mypde.setValue(Y=qH+rhocp/h*T)
103 T=mypde.getSolution()
104 totE=integrate(rhocp*T)
105 print("time step %s at t=%e days completed. total energy = %e."%(i,t/day,totE))
106 t_list.append(t)
107 E_list.append(totE)
108
109 ###############################################################PLOTTING
110 # plot the total energy over time:
111 if getMPIRankWorld() == 0:
112 pl.plot(t_list,E_list)
113 pl.title("Total Energy")
114 pl.axis([0,max(t_list),0,max(E_list)*1.1])
115 pl.ylabel('Temperature (K)')
116 pl.xlabel("Length (m)")
117 pl.savefig(os.path.join(save_path,"totE_ex01b.png"))

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