/[escript]/trunk/finley/test/python/FCT_test2.py
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Contents of /trunk/finley/test/python/FCT_test2.py

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Revision 1476 - (show annotations)
Mon Apr 7 23:38:50 2008 UTC (11 years, 5 months ago) by gross
File MIME type: text/x-python
File size: 3406 byte(s)
Jacobian-free Newton method added to Paso
1 #
2 # upwinding test moving a Gaussian hill around
3 #
4 # we solve U_,t - E *u_,ii + v_i u_,i =0 (E is small)
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 NE=64
29 DIM=2
30 THETA=0.5
31 OMEGA0=1.
32 ALPHA=pi/4
33 T0=0.5*pi
34 T_END=2.5*pi
35 dt=1e-3*10
36 E=1.e-3
37 TEST_SUPG=False or True
38
39
40 def getCenter(t):
41 if DIM==2:
42 x0=[cos(OMEGA0*t)*0.5,-sin(OMEGA0*t)*0.5]
43 x0=[-sin(OMEGA0*t)*0.5,cos(OMEGA0*t)*0.5]
44 else:
45 x0=[cos(ALPHA)*cos(OMEGA0*t)*0.5,-sin(OMEGA0*t)*0.5,-sin(ALPHA)*cos(OMEGA0*t)*0.5]
46 return x0
47 def QUALITY(t,u_h):
48 dom=u_h.getDomain()
49 x=dom.getX()
50 a=inf(u_h)
51 b=sup(u_h)*(4*pi*E*t)**(DIM/2.)-1.
52 c=integrate(u_h,Function(dom))-1.
53 x0=getCenter(t)
54 x0h=integrate(x*u_h,Function(dom))
55 d=length(x0-x0h)
56 sigma_h2=sqrt(integrate(length(x-x0h)**2 * u_h, Function(dom)))
57 if DIM == 3: sigma_h2*=sqrt(2./3.)
58 e=sigma_h2/sqrt(4*E*t)-1
59 # return a,b,c,e,1./(4*pi*E*t)**(DIM/2.)
60 return d,e
61 # return a,b,c,d,e
62
63
64
65
66 if DIM==2:
67 dom=Rectangle(NE,NE)
68 else:
69 dom=Brick(NE,NE,NE)
70 dom.setX(2*dom.getX()-1)
71
72 # set initial value
73 x=dom.getX()
74 u0=1/(4.*pi*E*T0)**(DIM/2.)*exp(-length(dom.getX()-getCenter(T0))**2/(4.*E*T0))
75
76 print "QUALITY ",QUALITY(T0,u0)
77
78 x=Function(dom).getX()
79 if DIM == 2:
80 V=OMEGA0*(x[0]*[0,-1]+x[1]*[1,0])
81 else:
82 V=OMEGA0*(x[0]*[0,cos(ALPHA),0]+x[1]*[-cos(ALPHA),0,sin(ALPHA)]+x[2]*[0.,-sin(ALPHA),0.])
83 #===================
84 fc=TransportPDE(dom,num_equations=1,theta=THETA)
85 x=Function(dom).getX()
86 fc.setValue(M=Scalar(1.,Function(dom)),C=V,A=-Scalar(E,Function(dom))*kronecker(dom))
87 #==============
88 if TEST_SUPG:
89 supg=LinearSinglePDE(dom)
90 supg.setValue(D=1.)
91 supg.setSolverMethod(supg.LUMPING)
92 dt_supg=1./(1./inf(dom.getSize()/length(V))+1./inf(dom.getSize()**2/E))*0.3
93 u_supg=u0*1.
94
95 c=0
96 saveVTK("u.%s.xml"%c,u=u0)
97 fc.setInitialSolution(u0)
98 t=T0
99 while t<T_END:
100 print "time step t=",t+dt
101 u=fc.solve(dt)
102 if TEST_SUPG:
103 #========== supg tests ================
104 nn=max(ceil(dt/dt_supg),1.)
105 dt2=dt/nn
106 nnn=0
107 while nnn<nn :
108 supg.setValue(X=-dt2/2*E*grad(u_supg),Y=u_supg+dt2/2*inner(V,grad(u_supg)))
109 u2=supg.getSolution()
110 supg.setValue(X=-dt2*E*grad(u2),Y=u_supg+dt2*inner(V,grad(u2)))
111 u_supg=supg.getSolution()
112 nnn+=1
113 c+=1
114 t+=dt
115 print "QUALITY FCT: time = %s pi"%(t/pi),QUALITY(t,u),
116 if TEST_SUPG:
117 print "QUALITY SUPG: ",QUALITY(t,u_supg)
118 # saveVTK("u.%s.xml"%c,u=u,u_supg=u_supg)
119 else:
120 # saveVTK("u.%s.xml"%c,u=u)
121 pass
122 # if c == 20: 1/0

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