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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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# heatrefraction001.py |
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# Model steady state temperature distribution in two block model, mesh |
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# from heatrefraction_mesher001.py |
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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 |
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# require. |
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|
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|
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# This imports everything from the escript library |
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from esys.escript import * |
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# This defines LinearPDE as LinearPDE |
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from esys.escript.linearPDEs import LinearPDE, Poisson |
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# smoothing operator |
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from esys.escript.pdetools import Projector |
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# This imports the rectangle domain function from finley |
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from esys.finley import Rectangle, ReadMesh, Domain |
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# This package is necessary to handle saving our data. |
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import os |
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# A useful unit handling package which will make sure all our units |
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# match up in the equations. |
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from esys.escript.unitsSI import * |
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# numpy for array handling |
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import numpy as np |
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|
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import matplotlib |
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#For interactive use, you can comment out the next line |
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matplotlib.use('agg') #It's just here for automated testing |
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|
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# pylab for matplotlib and plotting |
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import pylab as pl |
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# cblib functions |
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from cblib import toQuivLocs, toXYTuple, needdirs, toRegGrid, gradtoRegGrid |
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|
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########################################################MPI WORLD CHECK |
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if getMPISizeWorld() > 1: |
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import sys |
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print "This example will not run in an MPI world." |
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sys.exit(0) |
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|
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#################################################ESTABLISHING VARIABLES |
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qin=70*Milli*W/(m*m) #our heat source temperature is now zero |
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Ti=290.15*K # Kelvin #the starting temperature of our iron bar |
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width=5000.0*m |
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depth=-6000.0*m |
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|
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# the folder to gett our outputs from, leave blank "" for script path - |
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# note these depen. are generated from heatrefraction_mesher001.py |
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saved_path = save_path= os.path.join("data","heatrefrac001" ) |
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needdirs([saved_path]) |
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|
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################################################ESTABLISHING PARAMETERS |
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## DOMAIN |
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mymesh=ReadMesh(os.path.join(saved_path,"heatrefraction_mesh001.fly")) |
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tpg = np.loadtxt(os.path.join(saved_path,"toppg")) |
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tpgx = tpg[:,0] |
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tpgy = tpg[:,1] |
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bpg = np.loadtxt(os.path.join(saved_path,"botpg")) |
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bpgx = bpg[:,0] |
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bpgy = bpg[:,1] |
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|
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# set up kappa (thermal conductivity across domain) using tags |
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kappa=Scalar(0,Function(mymesh)) |
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kappa.setTaggedValue("top",2.0) |
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kappa.setTaggedValue("bottom",4.0) |
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|
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#... generate functionspace... |
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#... open PDE ... |
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mypde=LinearPDE(mymesh) |
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#define first coefficient |
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mypde.setValue(A=kappa*kronecker(mymesh)) |
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|
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# ... set initial temperature .... |
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x=mymesh.getX() |
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qH=Scalar(0,FunctionOnBoundary(mymesh)) |
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qH.setTaggedValue("linebottom",qin) |
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mypde.setValue(q=whereZero(x[1]),r=Ti) |
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mypde.setValue(y=qH) |
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|
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###########################################################GET SOLUTION |
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T=mypde.getSolution() |
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|
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##########################################################VISUALISATION |
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# calculate gradient of solution for quiver plot |
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qu=-kappa*grad(T) |
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quT=qu.toListOfTuples() |
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|
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#Projector is used to smooth the data. |
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proj=Projector(mymesh) |
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smthT=proj(T) |
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#move data to a regular grid for plotting |
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xi,yi,zi = toRegGrid(smthT,mymesh,200,200,width,depth) |
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#Temperature Depth Profile along x[50] |
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cut=int(len(xi)/2) |
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pl.clf() |
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pl.plot(zi[:,cut],yi) |
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pl.title("Heat Refraction Temperature Depth Profile") |
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pl.xlabel("Temperature (K)") |
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pl.ylabel("Depth (m)") |
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if getMPIRankWorld() == 0: #check for MPI processing |
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pl.savefig(os.path.join(saved_path,"heatrefraction001_tdp.png")) |
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|
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# Heat flow depth profile. |
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pl.clf() |
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# grid the data. |
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qu=proj(-kappa*grad(T)) |
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xiq,yiq,ziq = gradtoRegGrid(qu,mymesh,200,200,width,depth,1) |
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cut=int(len(xiq)/2) |
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pl.plot(ziq[:,cut]*1000.,yiq) |
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pl.title("Heat Flow Depth Profile") |
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pl.xlabel("Heat Flow (mW/m^2)") |
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pl.ylabel("Depth (m)") |
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if getMPIRankWorld() == 0: #check for MPI processing |
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pl.savefig(os.path.join(saved_path,"heatrefraction001_hf.png")) |
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|
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# Temperature Gradient Depth Profile at x[50] |
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pl.clf() |
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zT=proj(-grad(T)) |
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xt,yt,zt=gradtoRegGrid(zT,mymesh,200,200,width,depth,1) |
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cut=int(len(xt)/2) |
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pl.plot(zt[:,cut]*1000.,yt) |
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pl.title("Heat Refraction Temperature Gradient \n Depth Profile") |
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pl.xlabel("Temperature (K/Km)") |
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pl.ylabel("Depth (m)") |
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if getMPIRankWorld() == 0: #check for MPI processing |
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pl.savefig(os.path.join(saved_path,"heatrefraction001_tgdp.png")) |
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# Thermal Conditions Depth Profile |
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pl.clf() |
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xk,yk,zk = toRegGrid(kappa,mymesh,200,200,width,depth) |
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cut=int(len(xk)/2) |
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pl.plot(zk[:,cut],yk) |
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pl.title("Heat Refraction Thermal Conductivity Depth Profile") |
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pl.xlabel("Conductivity (W/K/m)") |
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pl.ylabel("Depth (m)") |
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pl.axis([1,5,-6000,0]) |
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if getMPIRankWorld() == 0: #check for MPI processing |
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pl.savefig(os.path.join(saved_path,"heatrefraction001_tcdp.png")) |
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# contour the gridded data, |
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# plotting dots at the randomly spaced data points. |
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quivshape = [20,20] #quivers x and quivers y |
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# function to calculate quiver locations |
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qu,qulocs = toQuivLocs(quivshape,width,depth,qu) |
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|
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# select colour |
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pl.matplotlib.pyplot.autumn() |
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pl.clf() |
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# plot polygons for boundaries |
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CKL = pl.fill(tpgx,tpgy,'brown',label='2 W/m/k',zorder=-1000) |
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CKM = pl.fill(bpgx,bpgy,'red',label='4 W/m/k',zorder=-1000) |
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# contour temperature |
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CS = pl.contour(xi,yi,zi,5,linewidths=0.5,colors='k') |
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# labels and formatting |
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pl.clabel(CS, inline=1, fontsize=8) |
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pl.title("Heat Refraction across a clinal structure.") |
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pl.xlabel("Horizontal Displacement (m)") |
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pl.ylabel("Depth (m)") |
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pl.legend() |
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if getMPIRankWorld() == 0: #check for MPI processing |
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pl.savefig(os.path.join(saved_path,"heatrefraction001_cont.png")) |
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#Quiver Plot qulocs -> tail location, qu -> quiver length/direction |
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QUIV=pl.quiver(qulocs[:,0],qulocs[:,1],qu[:,0],qu[:,1],\ |
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angles='xy',color="white") |
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pl.title("Heat Refraction across a clinal structure\n with\ |
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gradient quivers.") |
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if getMPIRankWorld() == 0: #check for MPI processing |
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pl.savefig(os.path.join(saved_path,"heatrefraction001_contqu.png")) |
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