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######################################################## |
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# |
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# Copyright (c) 2003-2009 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) 2003-2009 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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from esys.escript import * |
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from esys.escript.pdetools import Locator |
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from esys.escript.linearPDEs import LinearPDE |
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from esys.finley import Brick |
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from numpy import identity,zeros,ones |
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import matplotlib.pyplot as plt |
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ne=32 # number of cells in x_0 and x_1 directions |
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width=10000. # length in x_0 and x_1 directions |
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lam=3.462e9 |
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mu=3.462e9 |
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rho=1154. |
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tend=10. # to ran a full simulation change tend to 60. |
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alpha=0.7 |
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t0=3. |
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U0=1. # maximum displacement |
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mkDir("data") # create directory data if it does not exist already. |
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def wavePropagation(domain,h,tend,lam,mu,rho, xc, src_radius, U0): |
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# lists to collect displacement at point source |
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ts, u_pc0,u_pc1,u_pc2=[], [], [], [] |
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x=domain.getX() |
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# ... open new PDE ... |
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mypde=LinearPDE(domain) |
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mypde.getSolverOptions().setSolverMethod(mypde.getSolverOptions().LUMPING) |
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kronecker=identity(mypde.getDim()) |
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dunit=numpy.array([1.,0.,0.]) # defines direction of point source |
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mypde.setValue(D=kronecker*rho, q=whereNegative(length(x-xc)-src_radius)*dunit) |
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# ... set initial values .... |
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n=0 |
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# for first two time steps |
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u=Vector(0.,Solution(domain)) |
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u_last=Vector(0.,Solution(domain)) |
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t=0 |
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|
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# define the location of the point source |
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L=Locator(domain,xc) |
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# find potential at point source |
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u_pc=L.getValue(u) |
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print "u at point charge=",u_pc |
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ts.append(t); u_pc0.append(u_pc[0]), u_pc1.append(u_pc[1]), u_pc2.append(u_pc[2]) |
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while t<tend: |
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t+=h |
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# ... get current stress .... |
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g=grad(u) |
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stress=lam*trace(g)*kronecker+mu*(g+transpose(g)) |
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# ... get new acceleration .... |
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amplitude=U0*(4*(t-t0)**3/alpha**3-6*(t-t0)/alpha)*sqrt(2.)/alpha**2*exp(1./2.-(t-t0)**2/alpha**2) |
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mypde.setValue(X=-stress, r=dunit*amplitude) |
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a=mypde.getSolution() |
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# ... get new displacement ... |
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u_new=2*u-u_last+h**2*a |
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# ... shift displacements .... |
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u_last=u |
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u=u_new |
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n+=1 |
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print n,"-th time step t ",t |
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u_pc=L.getValue(u) |
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print "u at point charge=",u_pc |
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ts.append(t); u_pc0.append(u_pc[0]), u_pc1.append(u_pc[1]), u_pc2.append(u_pc[2]) |
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# ... save current acceleration in units of gravity and displacements |
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if n==1 or n%10==0: saveVTK("./data/usoln.%i.vtu"%(n/10),acceleration=length(a)/9.81, |
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displacement = length(u), tensor = stress, Ux = u[0] ) |
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return ts, u_pc0,u_pc1,u_pc2 |
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|
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# |
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# create domain: |
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# |
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mydomain=Brick(ne,ne,10,l0=width,l1=width,l2=10.*width/ne) |
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# |
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# sety time step size: |
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# |
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h=inf(1./5.)*inf(sqrt(rho/(lam+2*mu))*mydomain.getSize()) |
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print "time step size = ",h |
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# |
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# spherical source at middle of bottom face |
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# |
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xc=[width/2.,width/2.,0.] |
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# define small radius around point xc |
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src_radius = 0.03*width |
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print "src_radius = ",src_radius |
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# |
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# run it |
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# |
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ts, u_pc0,u_pc1,u_pc2 = wavePropagation(mydomain,h,tend,lam,mu,rho, xc, src_radius, U0) |
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# |
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# create a plot: |
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# |
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if getMPIRankWorld() == 0: |
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plt.title("Displacement at Point Source") |
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plt.plot(ts, u_pc0, '-', label="x_0", linewidth=1) |
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plt.plot(ts, u_pc1, '-', label="x_1", linewidth=1) |
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plt.plot(ts, u_pc2, '-', label="x_2", linewidth=1) |
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plt.xlabel('time') |
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plt.ylabel('displacement') |
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plt.legend() |
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plt.savefig('u_pc.png', format='png') |
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# or save displacement |
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u_pc_data=FileWriter('./data/U_pc.out') |
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for i in xrange(len(ts)) : |
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u_pc_data.write("%f %f %f %f\n"%(ts[i],u_pc0[i],u_pc1[i],u_pc2[i])) |
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u_pc_data.close() |
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