/[escript]/trunk/finley/test/python/FCT_test1.py
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Contents of /trunk/finley/test/python/FCT_test1.py

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Revision 1411 - (show annotations)
Thu Feb 7 08:09:15 2008 UTC (11 years, 6 months ago) by gross
File MIME type: text/x-python
File size: 2665 byte(s)
second test for upwinding added
1 #
2 # upwinding test moving a Gaussian hill around
3 #
4 # we solve U_,t + v_i u_,i =0
5 #
6 # the solution is given as u(x,t)=1/(4*pi*E*t)^{dim/2} * exp ( - |x-x_0(t)|^2/(4*E*t) )
7 #
8 # where x_0(t) = [ cos(OMEGA0*T0)*0.5,-sin(OMEGA0*T0)*0.5 ] and v=[-y,x]*OMEGA0 for dim=2 and
9 #
10 # x_0(t) = [ cos(OMEGA0*T0)*0.5,-sin(OMEGA0*T0)*0.5 ] and v=[-y,x]*OMEGA0 for dim=3
11 #
12 # the solution is started from some time T0>0.
13 #
14 # We are using five quality messurements for u_h
15 #
16 # - inf(u_h) > 0
17 # - sup(u_h)/sup(u(x,t)) = sup(u_h)*(4*pi*E*t)^{dim/2} ~ 1
18 # - integrate(u_h) ~ 1
19 # - | x_0h-x_0 | ~ 0 where x_0h = integrate(x*u_h)
20 # - sigma_h/4*E*t ~ 1 where sigma_h=sqrt(integrate(length(x-x0h)**2 * u_h) * (DIM==3 ? sqrt(2./3.) :1 )
21 #
22 #
23 from esys.escript import *
24 from esys.escript.linearPDEs import LinearSinglePDE, TransportPDE
25 from esys.finley import Rectangle, Brick
26 from math import pi, ceil
27 NE=128
28 DIM=2
29 THETA=0.5
30 OMEGA0=1.
31 ALPHA=pi/4
32 T0=0
33 T_END=2.*pi
34 dt=1e-3*10*10
35 E=1.e-3
36 TEST_SUPG=False or True
37
38
39 if DIM==2:
40 dom=Rectangle(NE,NE)
41 else:
42 dom=Brick(NE,NE,NE)
43 dom.setX(2*dom.getX()-1)
44
45 # set initial value
46 x=dom.getX()
47 r=sqrt(x[0]**2+(x[1]-1./3.)**2)
48 u0=whereNegative(r-1./3.)*wherePositive(wherePositive(abs(x[0])-0.05)+wherePositive(x[1]-0.5))
49
50 x=Function(dom).getX()
51 if DIM == 2:
52 V=OMEGA0*(x[0]*[0,-1]+x[1]*[1,0])
53 else:
54 V=OMEGA0*(x[0]*[0,cos(ALPHA),0]+x[1]*[-cos(ALPHA),0,sin(ALPHA)]+x[2]*[0.,-sin(ALPHA),0.])
55 #===================
56 fc=TransportPDE(dom,num_equations=1,theta=THETA)
57 x=Function(dom).getX()
58 fc.setValue(M=Scalar(1.,Function(dom)),C=V)
59 #==============
60 if TEST_SUPG:
61 supg=LinearSinglePDE(dom)
62 supg.setValue(D=1.)
63 supg.setSolverMethod(supg.LUMPING)
64 dt_supg=inf(dom.getSize()/length(V))
65 u_supg=u0*1.
66
67 c=0
68 saveVTK("u.%s.xml"%c,u=u0)
69 fc.setInitialSolution(u0)
70 t=T0
71 print "QUALITY FCT: time = %s pi"%(t/pi),inf(u0),sup(u0),integrate(u0)
72 while t<T_END:
73 print "time step t=",t+dt
74 u=fc.solve(dt)
75 print "QUALITY FCT: time = %s pi"%(t+dt/pi),inf(u),sup(u),integrate(u)
76 if TEST_SUPG:
77 #========== supg tests ================
78 nn=max(ceil(dt/dt_supg),1.)
79 dt2=dt/nn
80 nnn=0
81 while nnn<nn :
82 supg.setValue(Y=u_supg+dt2/2*inner(V,grad(u_supg)))
83 u2=supg.getSolution()
84 supg.setValue(Y=u_supg+dt2*inner(V,grad(u2)))
85 u_supg=supg.getSolution()
86 nnn+=1
87 c+=1
88 t+=dt
89 if TEST_SUPG:
90 print "QUALITY SUPG: time = %s pi"%(t/pi),inf(u_supg),sup(u_supg),integrate(u_supg)
91 saveVTK("u2.%s.xml"%c,u=u,u_supg=u_supg)
92 else:
93 # saveVTK("u.%s.xml"%c,u=u)
94 pass
95 # if c == 20: 1/0

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