/[escript]/trunk/finley/test/python/seismic_wave.py
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Revision 866 - (hide annotations)
Mon Oct 9 03:50:20 2006 UTC (14 years, 6 months ago) by gross
File MIME type: text/x-python
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now GEAR scheme is used
1 gross 842 """
2     seismic wave propagation
3    
4     @var __author__: name of author
5     @var __licence__: licence agreement
6     @var __url__: url entry point on documentation
7     @var __version__: version
8     @var __date__: date of the version
9     """
10    
11     __copyright__=""" Copyright (c) 2006 by ACcESS MNRF
12     http://www.access.edu.au
13     Primary Business: Queensland, Australia"""
14     __license__="""Licensed under the Open Software License version 3.0
15     http://www.opensource.org/licenses/osl-3.0.php"""
16     __author__="Lutz Gross, l.gross@uq.edu.au"
17     __url__="http://www.iservo.edu.au/esys/escript"
18     __version__="$Revision$"
19     __date__="$Date$"
20    
21     from esys.escript import *
22     from esys.escript.linearPDEs import LinearPDE
23     from esys.finley import Brick
24 gross 843 import time
25 gross 842
26 gross 844 output=True
27     n_end=10000
28 gross 843
29 gross 865 resolution=1000. # number of elements per m in the finest region
30     o=1 # element order
31 gross 842
32 gross 865 l=100000. # width and length m (without obsorber)
33     h=30000. # height in m (without obsorber)
34     d_absorber=l*0.10 # thickness of absorbing layer
35 gross 842
36 gross 866 l_sand=20000. # thickness of sand region on surface
37     h_sand=5000. # thickness of sand layer under the water
38 gross 842
39 gross 865 l_x_water=10000. # length of water in x
40     l_y_water=10000. # length of water in y
41     h_water=2000. # depth of water region
42 gross 842
43 gross 865 x_sand=l/2-l_x_water/2-l_sand # x coordinate of location of sand region (without obsorber)
44     y_sand=l/2-l_y_water/2-l_sand # y coordinate of location of sand region (without obsorber)
45 gross 842
46    
47 gross 865 # origin
48     origin={"x": -d_absorber, "y" : -d_absorber , "z" : -h-d_absorber }
49     # location and geometrical size of event reltive to origin:
50     xc=[l*0.2,l*0.3,-h*0.7]
51 gross 862 src_radius = 2*resolution
52 gross 842 # direction of event:
53 gross 862 event=numarray.array([0.,0.,1.])*1.e6
54 gross 842 # time and length of the event
55 gross 865 tc=2.
56     tc_length=0.5
57    
58     # material properties:
59     bedrock=0
60     absorber=1
61     water=2
62     sand=3
63    
64     rho_tab={}
65     rho_tab[bedrock]=8e3
66     rho_tab[absorber]=rho_tab[bedrock]
67     rho_tab[water]=1e3
68     rho_tab[sand]=5e3
69    
70     mu_tab={}
71     mu_tab[bedrock]=1.7e11
72     mu_tab[absorber]=mu_tab[bedrock]
73     mu_tab[water]=0.
74     mu_tab[sand]=1.5e10
75    
76     lmbd_tab={}
77     lmbd_tab[bedrock]=1.7e11
78     lmbd_tab[absorber]=lmbd_tab[bedrock]
79     lmbd_tab[water]=1.e9
80     lmbd_tab[sand]=1.5e10
81    
82     eta_tab={}
83     eta_tab[absorber]=-log(0.05)*sqrt(rho_tab[absorber]*(lmbd_tab[absorber]+2*mu_tab[absorber]))/d_absorber
84     eta_tab[sand]=eta_tab[absorber]/40.
85     eta_tab[water]=eta_tab[absorber]/40.
86     eta_tab[bedrock]=eta_tab[absorber]/40.
87    
88 gross 866
89     # material properties:
90     bedrock=0
91     absorber=1
92     water=2
93     sand=3
94    
95     rho={}
96     rho[bedrock]=8e3
97     rho[absorber]=rho[bedrock]
98     rho[water]=1e3
99     rho[sand]=5e3
100    
101     mu={}
102     mu[bedrock]=1.7e11
103     mu[absorber]=mu[bedrock]
104     mu[water]=0.
105     mu[sand]=1.5e10
106    
107     lmbd={}
108     lmbd[bedrock]=1.7e11
109     lmbd_absorber=lmbd[bedrock]
110     lmbd[water]=1.e9
111     lmbd[sand]=1.5e10
112    
113     eta={}
114     eta[absorber]=-log(0.05)*sqrt(rho[absorber]*(lmbd_absorber+2*mu[absorber]))/d_absorber
115     eta[sand]=eta[absorber]/40.
116     eta[water]=eta[absorber]/40.
117     eta[bedrock]=eta[absorber]/40.
118    
119 gross 843 if output:
120     print "event location = ",xc
121     print "radius of event = ",src_radius
122     print "time of event = ",tc
123     print "length of event = ",tc_length
124     print "direction = ",event
125 gross 842
126 gross 862 t_end=30.
127 gross 865 dt_write=0.1
128 gross 842
129 gross 865
130 gross 842 def getDomain():
131     """
132     this defines a dom as a brick of length and width l and hight h
133    
134    
135     """
136 gross 843 global netotal
137 gross 844
138 gross 865 v_p={}
139     for tag in rho_tab.keys():
140     v_p[tag]=sqrt((2*mu_tab[tag]+lmbd_tab[tag])/rho_tab[tag])
141     v_p_ref=min(v_p.values())
142     print "velocities: bedrock = %s, sand = %s, water =%s, absorber =%s, reference =%s"%(v_p[bedrock],v_p[sand],v_p[water],v_p[absorber],v_p_ref)
143 gross 844
144 gross 865 sections={}
145     sections["x"]=[d_absorber, x_sand, l_sand, l_x_water, l_sand, l-x_sand-2*l_sand-l_x_water, d_absorber]
146     sections["y"]=[d_absorber, y_sand, l_sand, l_y_water, l_sand, l-y_sand-2*l_sand-l_y_water, d_absorber]
147     sections["z"]=[d_absorber,h-h_water-h_sand,h_sand,h_water]
148     if output:
149     print "sections x = ",sections["x"]
150     print "sections y = ",sections["y"]
151     print "sections z = ",sections["z"]
152 gross 844
153 gross 865 mats= [
154     [ [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
155     [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
156     [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
157     [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
158     [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
159     [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
160     [absorber, absorber, absorber, absorber, absorber, absorber, absorber] ],
161 gross 844
162 gross 865 [ [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
163     [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
164     [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
165     [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
166     [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
167     [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
168     [absorber, absorber, absorber, absorber, absorber, absorber, absorber] ],
169 gross 844
170 gross 865 [ [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
171     [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
172     [absorber, bedrock , sand , sand , sand , bedrock , absorber],
173     [absorber, bedrock , sand , sand , sand , bedrock , absorber],
174     [absorber, bedrock , sand , sand , sand , bedrock , absorber],
175     [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
176     [absorber, absorber, absorber, absorber, absorber, absorber, absorber] ],
177    
178     [ [absorber, absorber, absorber, absorber, absorber, absorber, absorber],
179     [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
180     [absorber, bedrock , sand , sand , sand , bedrock , absorber],
181     [absorber, bedrock , sand , water , sand , bedrock , absorber],
182     [absorber, bedrock , sand , sand , sand , bedrock , absorber],
183     [absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber],
184     [absorber, absorber, absorber, absorber, absorber, absorber, absorber] ] ]
185 gross 844
186 gross 865 num_elem={}
187     for d in sections:
188     num_elem[d]=[]
189     for i in range(len(sections[d])):
190     if d=="x":
191     v_p_min=v_p[mats[0][0][i]]
192     for q in range(len(sections["y"])):
193     for r in range(len(sections["z"])):
194     v_p_min=min(v_p[mats[r][q][i]],v_p_min)
195     elif d=="y":
196     v_p_min=v_p[mats[0][i][0]]
197     for q in range(len(sections["x"])):
198     for r in range(len(sections["z"])):
199     v_p_min=min(v_p[mats[r][i][q]],v_p_min)
200     elif d=="z":
201     v_p_min=v_p[mats[i][0][0]]
202     for q in range(len(sections["x"])):
203     for r in range(len(sections["y"])):
204     v_p_min=min(v_p[mats[i][r][q]],v_p_min)
205     num_elem[d].append(max(1,int(sections[d][i] * v_p_ref/v_p_min /resolution+0.5)))
206    
207     ne_x=sum(num_elem["x"])
208     ne_y=sum(num_elem["y"])
209     ne_z=sum(num_elem["z"])
210     netotal=ne_x*ne_y*ne_z
211     if output: print "grid : %s x %s x %s (%s elements)"%(ne_x,ne_y,ne_z,netotal)
212     dom=Brick(ne_x,ne_y,ne_z,l0=o*ne_x,l1=o*ne_y,l2=o*ne_z,order=o)
213     x_old=dom.getX()
214     x_new=0
215 gross 844
216 gross 865 for d in sections:
217     if d=="x":
218     i=0
219     f=[1,0,0]
220     if d=="y":
221     i=1
222     f=[0,1,0]
223     if d=="z":
224     i=2
225     f=[0,0,1]
226     x=x_old[i]
227 gross 844
228 gross 865 p=origin[d]
229     ne=0
230     s=0.
231    
232     for i in range(len(sections[d])-1):
233     msk=whereNonPositive(x-o*ne+0.5)
234     s=s*msk + (sections[d][i]/(o*num_elem[d][i])*(x-o*ne)+p)*(1.-msk)
235     ne+=num_elem[d][i]
236     p+=sections[d][i]
237     x_new=x_new + s * f
238     dom.setX(x_new)
239 gross 844
240 gross 842 fs=Function(dom)
241     x=Function(dom).getX()
242 gross 865 x0=x[0]
243     x1=x[1]
244     x2=x[2]
245     p_z=origin["z"]
246     for i in range(len(mats)):
247     f_z=wherePositive(x2-p_z)*wherePositive(x2-p_z+sections["z"][i])
248     p_y=origin["y"]
249     for j in range(len(mats[i])):
250     f_y=wherePositive(x1-p_y)*wherePositive(x1-p_z+sections["y"][j])
251     p_x=origin["x"]
252     for k in range(len(mats[i][j])):
253     f_x=wherePositive(x0-p_x)*wherePositive(x0-p_x+sections["x"][k])
254     fs.setTags(mats[i][j][k],f_x*f_y*f_z)
255     p_x+=sections["x"][k]
256     p_y+=sections["y"][j]
257     p_z+=sections["z"][i]
258 gross 842 return dom
259    
260     def getMaterialProperties(dom):
261 gross 865 rho =Scalar(rho_tab[bedrock],Function(dom))
262     eta =Scalar(eta_tab[bedrock],Function(dom))
263     mu =Scalar(mu_tab[bedrock],Function(dom))
264     lmbd=Scalar(lmbd_tab[bedrock],Function(dom))
265     tags=Scalar(bedrock,Function(dom))
266    
267     for tag in rho_tab.keys():
268     rho.setTaggedValue(tag,rho_tab[tag])
269     eta.setTaggedValue(tag,eta_tab[tag])
270     mu.setTaggedValue(tag,mu_tab[tag])
271     lmbd.setTaggedValue(tag,lmbd_tab[tag])
272     tags.setTaggedValue(tag,tag)
273     return rho,mu,lmbd,eta
274 gross 842
275 gross 865 def wavePropagation(dom,rho,mu,lmbd,eta):
276 gross 842 x=Function(dom).getX()
277     # ... open new PDE ...
278     mypde=LinearPDE(dom)
279     mypde.setSolverMethod(LinearPDE.LUMPING)
280     k=kronecker(Function(dom))
281     mypde.setValue(D=k*rho)
282    
283 gross 865 dt=(1./5.)*inf(dom.getSize()/sqrt((2*mu+lmbd)/rho))
284 gross 843 if output: print "time step size = ",dt
285 gross 842 # ... set initial values ....
286     n=0
287     t=0
288 gross 865 t_write=0.
289     n_write=0
290 gross 842 # initial value of displacement at point source is constant (U0=0.01)
291     # for first two time steps
292 gross 866 u=Vector(0.,Solution(dom))
293 gross 865 v=Vector(0.,Solution(dom))
294 gross 866 a=Vector(0.,Solution(dom))
295     a2=Vector(0.,Solution(dom))
296     v=Vector(0.,Solution(dom))
297 gross 842
298 gross 843 starttime = time.clock()
299     while t<t_end and n<n_end:
300     if output: print n+1,"-th time step t ",t+dt," max u and F: ",Lsup(u),
301 gross 866 # prediction:
302     u_pr=u+dt*v+(dt**2/2)*a+(dt**3/6)*a2
303     v_pr=v+dt*a+(dt**2/2)*a2
304     a_pr=a+dt*a2
305 gross 842 # ... get current stress ....
306 gross 866 eps=symmetric(grad(u_pr))
307 gross 865 stress=lmbd*trace(eps)*k+2*mu*eps
308 gross 842 # ... force due to event:
309 gross 866 if abs(t-tc)<5*tc_length:
310     F=exp(-((t-tc)/tc_length)**2)*exp(-(length(x-xc)/src_radius)**2)*event
311     if output: print Lsup(F)
312     else:
313     if output: print 0.
314 gross 842 # ... get new acceleration ....
315 gross 866 mypde.setValue(X=-stress,Y=F-eta*v_pr)
316 gross 842 a=mypde.getSolution()
317     # ... get new displacement ...
318 gross 866 da=a-a_pr
319     u=u_pr+(dt**2/12.)*da
320     v=v_pr+(5*dt/12.)*da
321     a2+=da/dt
322 gross 842 # ... save current acceleration in units of gravity and displacements
323 gross 843 if output:
324 gross 862 if t>=t_write:
325 gross 865 saveVTK("disp.%i.vtu"%n,displacement=u, amplitude=length(u))
326     t_write+=dt_write
327     n_write+=1
328 gross 842 t+=dt
329     n+=1
330    
331 gross 843 endtime = time.clock()
332     totaltime = endtime-starttime
333     global netotal
334     print ">>number of elements: %s, total time: %s, per time step: %s <<"%(netotal,totaltime,totaltime/n)
335 gross 842 if __name__ =="__main__":
336     dom=getDomain()
337 gross 865 rho,mu,lmbd,eta=getMaterialProperties(dom)
338     wavePropagation(dom,rho,mu,lmbd,eta)

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