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######################################################## |
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# |
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# Copyright (c) 2009 by University of Queensland |
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# Earth Systems Science Computational Center (ESSCC) |
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# http://www.uq.edu.au/esscc |
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# |
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# Primary Business: Queensland, Australia |
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# Licensed under the Open Software License version 3.0 |
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# http://www.opensource.org/licenses/osl-3.0.php |
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# |
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######################################################## |
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__copyright__="""Copyright (c) 2009 by University of Queensland |
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Earth Systems Science Computational Center (ESSCC) |
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http://www.uq.edu.au/esscc |
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Primary Business: Queensland, Australia""" |
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__license__="""Licensed under the Open Software License version 3.0 |
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http://www.opensource.org/licenses/osl-3.0.php""" |
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__url__="https://launchpad.net/escript-finley" |
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|
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""" |
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Author: Antony Hallam antony.hallam@uqconnect.edu.au |
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""" |
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############################################################FILE HEADER |
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# example01b.py |
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# Model temperature diffusion between two granite blocks of unequal |
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# initial temperature. Solve for total energy in the system. Use |
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# matplotlib to visualise the answer. |
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|
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#######################################################EXTERNAL MODULES |
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# To solve the problem it is necessary to import the modules we require. |
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from esys.escript import * # This imports everything from the escript library |
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from esys.escript.unitsSI import * |
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from esys.escript.linearPDEs import LinearPDE # This defines LinearPDE as LinearPDE |
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from esys.finley import Rectangle # This imports the rectangle domain function |
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#For interactive use, you can comment out the next two lines |
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import matplotlib |
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matplotlib.use('agg') #It's just here for automated testing |
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import pylab as pl #Plotting package. |
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import numpy as np #Array package. |
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import os, sys #This package is necessary to handle saving our data. |
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|
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#################################################ESTABLISHING VARIABLES |
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#Domain related. |
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mx = 500*m #meters - model length |
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my = 100*m #meters - model width |
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ndx = 100 # mesh steps in x direction |
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ndy = 1 # mesh steps in y direction - one dimension means one element |
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boundloc = mx/2 # location of boundary between the two blocks |
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#PDE related |
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rho = 2750. *kg/m**3 #kg/m{3} density of iron |
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cp = 790.*J/(kg*K) # J/Kg.K thermal capacity |
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rhocp = rho*cp |
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kappa = 2.2*W/m/K # watts/m.Kthermal conductivity |
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qH=0 * J/(sec*m**3) # J/(sec.m{3}) no heat source |
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T1=20 * Celsius # initial temperature at Block 1 |
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T2=2273. * Celsius # base temperature at Block 2 |
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|
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################################################ESTABLISHING PARAMETERS |
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t=0 * day # our start time, usually zero |
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tend=50 * yr # - time to end simulation |
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outputs = 200 # number of time steps required. |
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h=(tend-t)/outputs #size of time step |
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#user warning statement |
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print "Expected Number of time outputs is: ", (tend-t)/h |
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i=0 #loop counter |
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#the folder to put our outputs in, leave blank "" for script path |
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save_path= os.path.join("data","example01") |
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#ensure the dir exists |
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mkDir(save_path, os.path.join(save_path,"tempT")) |
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|
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####################################################DOMAIN CONSTRUCTION |
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blocks = Rectangle(l0=mx,l1=my,n0=ndx, n1=ndy) |
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|
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###############################################ESCRIPT PDE CONSTRUCTION |
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#... open PDE and set coefficients ... |
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mypde=LinearPDE(blocks) |
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mypde.setSymmetryOn() |
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A=zeros((2,2)) |
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A[0,0]=kappa |
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mypde.setValue(A=A,D=rhocp/h) |
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# ... set initial temperature .... |
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x=Solution(blocks).getX() |
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T= T1*whereNegative(x[0]-boundloc)+T2*(1-whereNegative(x[0]-boundloc)) |
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|
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# ... open a collector for the time marks and corresponding total energy |
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t_list=[] |
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E_list=[] |
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########################################################START ITERATION |
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while t<tend: |
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i+=1 |
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t+=h |
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mypde.setValue(Y=qH+rhocp/h*T) |
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T=mypde.getSolution() |
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totE=integrate(rhocp*T) |
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print "time step %s at t=%e days completed. total energy = %e."%(i,t/day,totE) |
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t_list.append(t) |
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E_list.append(totE) |
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|
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###############################################################PLOTTING |
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# plot the total energy over time: |
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if getMPIRankWorld() == 0: |
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pl.plot(t_list,E_list) |
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pl.title("Total Energy") |
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pl.axis([0,max(t_list),0,max(E_list)*1.1]) |
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pl.ylabel('Temperature (K)') |
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pl.xlabel("Length (m)") |
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pl.savefig(os.path.join(save_path,"totE_ex01b.png")) |
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