/[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 1410 - (show annotations)
Thu Feb 7 04:24:00 2008 UTC (12 years ago) by gross
File MIME type: text/x-python
File size: 3402 byte(s)
a new version of the algebric upwinding a. flux limiter
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 DIM=2
29 THETA=0.5
30 OMEGA0=1.
31 ALPHA=pi/4
32 T0=0.5*pi
33 T_END=2.5*pi
34 dt=1e-3*10
35 E=1.e-3
36 TEST_SUPG=False # or True
37
38
39 def getCenter(t):
40 if DIM==2:
41 x0=[cos(OMEGA0*t)*0.5,-sin(OMEGA0*t)*0.5]
42 x0=[-sin(OMEGA0*t)*0.5,cos(OMEGA0*t)*0.5]
43 else:
44 x0=[cos(ALPHA)*cos(OMEGA0*t)*0.5,-sin(OMEGA0*t)*0.5,-sin(ALPHA)*cos(OMEGA0*t)*0.5]
45 return x0
46 def QUALITY(t,u_h):
47 dom=u_h.getDomain()
48 x=dom.getX()
49 a=inf(u_h)
50 b=sup(u_h)*(4*pi*E*t)**(DIM/2.)-1.
51 c=integrate(u_h,Function(dom))-1.
52 x0=getCenter(t)
53 x0h=integrate(x*u_h,Function(dom))
54 d=length(x0-x0h)
55 sigma_h2=sqrt(integrate(length(x-x0h)**2 * u_h, Function(dom)))
56 if DIM == 3: sigma_h2*=sqrt(2./3.)
57 e=sigma_h2/sqrt(4*E*t)-1
58 # return a,b,c,e,1./(4*pi*E*t)**(DIM/2.)
59 return b, d
60 # return a,b,c,d,e
61
62
63
64
65 if DIM==2:
66 dom=Rectangle(NE,NE)
67 else:
68 dom=Brick(NE,NE,NE)
69 dom.setX(2*dom.getX()-1)
70
71 # set initial value
72 x=dom.getX()
73 u0=1/(4.*pi*E*T0)**(DIM/2.)*exp(-length(dom.getX()-getCenter(T0))**2/(4.*E*T0))
74
75 print "QUALITY ",QUALITY(T0,u0)
76
77 x=Function(dom).getX()
78 if DIM == 2:
79 V=OMEGA0*(x[0]*[0,-1]+x[1]*[1,0])
80 else:
81 V=OMEGA0*(x[0]*[0,cos(ALPHA),0]+x[1]*[-cos(ALPHA),0,sin(ALPHA)]+x[2]*[0.,-sin(ALPHA),0.])
82 #===================
83 fc=TransportPDE(dom,num_equations=1,theta=THETA)
84 x=Function(dom).getX()
85 fc.setValue(M=Scalar(1.,Function(dom)),C=V,A=-Scalar(E,Function(dom))*kronecker(dom))
86 #==============
87 if TEST_SUPG:
88 supg=LinearSinglePDE(dom)
89 supg.setValue(D=1.)
90 supg.setSolverMethod(supg.LUMPING)
91 dt_supg=1./(1./inf(dom.getSize()/length(V))+1./inf(dom.getSize()**2/E))*0.3
92 u_supg=u0*1.
93
94 c=0
95 saveVTK("u.%s.xml"%c,u=u0)
96 fc.setInitialSolution(u0)
97 t=T0
98 while t<T_END:
99 print "time step t=",t+dt
100 u=fc.solve(dt)
101 if TEST_SUPG:
102 #========== supg tests ================
103 nn=max(ceil(dt/dt_supg),1.)
104 dt2=dt/nn
105 nnn=0
106 while nnn<nn :
107 supg.setValue(X=-dt2/2*E*grad(u_supg),Y=u_supg+dt2/2*inner(V,grad(u_supg)))
108 u2=supg.getSolution()
109 supg.setValue(X=-dt2*E*grad(u2),Y=u_supg+dt2*inner(V,grad(u2)))
110 u_supg=supg.getSolution()
111 nnn+=1
112 c+=1
113 t+=dt
114 print "QUALITY FCT: time = %s pi"%(t/pi),QUALITY(t,u)
115 if TEST_SUPG:
116 print "QUALITY SUPG: ",QUALITY(t,u_supg)
117 # saveVTK("u.%s.xml"%c,u=u,u_supg=u_supg)
118 else:
119 # saveVTK("u.%s.xml"%c,u=u)
120 pass
121 # if c == 20: 1/0

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