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# You can shorten the execution time by reducing variable tend from 60 to 0.5 |
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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 numarray import identity,zeros,ones |
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if not os.path.isdir("data"): |
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print "\nCreating subdirectory 'data'\n" |
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os.mkdir("data") |
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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=60 |
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h=(1./5.)*sqrt(rho/(lam+2*mu))*(width/ne) |
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print "time step size = ",h |
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U0=0.01 # amplitude of point source |
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def wavePropagation(domain,h,tend,lam,mu,rho,U0): |
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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.setSolverMethod(LinearPDE.LUMPING) |
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kronecker=identity(mypde.getDim()) |
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# spherical source at middle of bottom face |
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xc=[width/2.,width/2.,0.] |
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# define small radius around point xc |
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# Lsup(x) returns the maximum value of the argument x |
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src_radius = 0.1*Lsup(domain.getSize()) |
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print "src_radius = ",src_radius |
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dunit=numarray.array([1.,0.,0.]) # defines direction of point source |
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mypde.setValue(D=kronecker*rho) |
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# ... set initial values .... |
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n=0 |
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# initial value of displacement at point source is constant (U0=0.01) |
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# for first two time steps |
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u=U0*whereNegative(length(x-xc)-src_radius)*dunit |
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u_last=U0*whereNegative(length(x-xc)-src_radius)*dunit |
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t=0 |
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# define the location of the point source |
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L=Locator(domain,numarray.array(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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u_pc_x = u_pc[0] |
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u_pc_y = u_pc[1] |
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u_pc_z = u_pc[2] |
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# open file to save displacement at point source |
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u_pc_data=open('./data/U_pc.out','w') |
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u_pc_data.write("%f %f %f %f\n"%(t,u_pc_x,u_pc_y,u_pc_z)) |
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while t<tend: |
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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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mypde.setValue(X=-stress) |
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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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t+=h |
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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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u_pc_x=u_pc[0] |
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u_pc_y=u_pc[1] |
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u_pc_z=u_pc[2] |
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# save displacements at point source to file for t > 0 |
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u_pc_data.write("%f %f %f %f\n"%(t,u_pc_x,u_pc_y,u_pc_z)) |
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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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u_pc_data.close() |
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mydomain=Brick(ne,ne,10,l0=width,l1=width,l2=10.*width/32.) |
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wavePropagation(mydomain,h,tend,lam,mu,rho,U0) |
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