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Revision 3789 - (show annotations)
Tue Jan 31 04:55:05 2012 UTC (7 years, 2 months ago) by caltinay
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Fast forward to latest trunk revision 3788.

1
2 ########################################################
3 #
4 # Copyright (c) 2003-2010 by University of Queensland
5 # Earth Systems Science Computational Center (ESSCC)
6 # http://www.uq.edu.au/esscc
7 #
8 # Primary Business: Queensland, Australia
9 # Licensed under the Open Software License version 3.0
10 # http://www.opensource.org/licenses/osl-3.0.php
11 #
12 ########################################################
13
14 __copyright__="""Copyright (c) 2003-2010 by University of Queensland
15 Earth Systems Science Computational Center (ESSCC)
16 http://www.uq.edu.au/esscc
17 Primary Business: Queensland, Australia"""
18 __license__="""Licensed under the Open Software License version 3.0
19 http://www.opensource.org/licenses/osl-3.0.php"""
20 __url__="https://launchpad.net/escript-finley"
21
22 #
23 # upwinding test moving a Gaussian hill around
24 #
25 # we solve U_,t - E *u_,ii + v_i u_,i =0 (E is small)
26 #
27 # the solution is given as u(x,t)=1/(4*pi*E*t)^{dim/2} * exp ( - |x-x_0(t)|^2/(4*E*t) )
28 #
29 # where x_0(t) = [ cos(OMEGA0*T0)*0.5,-sin(OMEGA0*T0)*0.5 ] and v=[-y,x]*OMEGA0 for dim=2 and
30 #
31 # x_0(t) = [ cos(OMEGA0*T0)*0.5,-sin(OMEGA0*T0)*0.5 ] and v=[-y,x]*OMEGA0 for dim=3
32 #
33 # the solution is started from some time T0>0.
34 #
35 # We are using five quality messurements for u_h
36 #
37 # - inf(u_h) > 0
38 # - sup(u_h)/sup(u(x,t)) = sup(u_h)*(4*pi*E*t)^{dim/2} ~ 1
39 # - integrate(u_h) ~ 1
40 # - | x_0h-x_0 | ~ 0 where x_0h = integrate(x*u_h)
41 # - sigma_h/4*E*t ~ 1 where sigma_h=sqrt(integrate(length(x-x0h)**2 * u_h) * (DIM==3 ? sqrt(2./3.) :1 )
42 #
43 #
44 from esys.escript import *
45 from esys.escript.linearPDEs import LinearSinglePDE, TransportPDE
46 from esys.dudley import Rectangle, Brick
47 from esys.weipa import saveVTK
48 from math import pi, ceil
49
50 NE=128
51 NE=64
52 DIM=2
53 THETA=0.5
54 OMEGA0=1.
55 ALPHA=pi/4
56 T0=0.5*pi
57 T_END=2.5*pi
58 dt=1e-3*10
59 E=1.e-3
60 TEST_SUPG=False or True
61
62
63 def getCenter(t):
64 if DIM==2:
65 x0=[cos(OMEGA0*t)*0.5,-sin(OMEGA0*t)*0.5]
66 x0=[-sin(OMEGA0*t)*0.5,cos(OMEGA0*t)*0.5]
67 else:
68 x0=[cos(ALPHA)*cos(OMEGA0*t)*0.5,-sin(OMEGA0*t)*0.5,-sin(ALPHA)*cos(OMEGA0*t)*0.5]
69 return x0
70 def QUALITY(t,u_h):
71 dom=u_h.getDomain()
72 x=dom.getX()
73 a=inf(u_h)
74 b=sup(u_h)*(4*pi*E*t)**(DIM/2.)-1.
75 c=integrate(u_h,Function(dom))-1.
76 x0=getCenter(t)
77 x0h=integrate(x*u_h,Function(dom))
78 d=length(x0-x0h)
79 sigma_h2=sqrt(integrate(length(x-x0h)**2 * u_h, Function(dom)))
80 if DIM == 3: sigma_h2*=sqrt(2./3.)
81 e=sigma_h2/sqrt(4*E*t)-1
82 # return a,b,c,e,1./(4*pi*E*t)**(DIM/2.)
83 return d,e
84 # return a,b,c,d,e
85
86
87
88
89 if DIM==2:
90 dom=Rectangle(NE,NE)
91 else:
92 dom=Brick(NE,NE,NE)
93 dom.setX(2*dom.getX()-1)
94
95 # set initial value
96 x=dom.getX()
97 u0=1/(4.*pi*E*T0)**(DIM/2.)*exp(-length(dom.getX()-getCenter(T0))**2/(4.*E*T0))
98
99 print("QUALITY ",QUALITY(T0,u0))
100
101 x=Function(dom).getX()
102 if DIM == 2:
103 V=OMEGA0*(x[0]*[0,-1]+x[1]*[1,0])
104 else:
105 V=OMEGA0*(x[0]*[0,cos(ALPHA),0]+x[1]*[-cos(ALPHA),0,sin(ALPHA)]+x[2]*[0.,-sin(ALPHA),0.])
106 #===================
107 fc=TransportPDE(dom,num_equations=1,theta=THETA)
108 x=Function(dom).getX()
109 fc.setValue(M=Scalar(1.,Function(dom)),C=V,A=-Scalar(E,Function(dom))*kronecker(dom))
110 #==============
111 if TEST_SUPG:
112 supg=LinearSinglePDE(dom)
113 supg.setValue(D=1.)
114 supg.setSolverMethod(supg.LUMPING)
115 dt_supg=1./(1./inf(dom.getSize()/length(V))+1./inf(dom.getSize()**2/E))*0.3
116 u_supg=u0*1.
117
118 c=0
119 saveVTK("u.%s.vtu"%c,u=u0)
120 fc.setInitialSolution(u0)
121 t=T0
122 while t<T_END:
123 print("time step t=",t+dt)
124 u=fc.solve(dt)
125 if TEST_SUPG:
126 #========== supg tests ================
127 nn=max(ceil(dt/dt_supg),1.)
128 dt2=dt/nn
129 nnn=0
130 while nnn<nn :
131 supg.setValue(X=-dt2/2*E*grad(u_supg),Y=u_supg+dt2/2*inner(V,grad(u_supg)))
132 u2=supg.getSolution()
133 supg.setValue(X=-dt2*E*grad(u2),Y=u_supg+dt2*inner(V,grad(u2)))
134 u_supg=supg.getSolution()
135 nnn+=1
136 c+=1
137 t+=dt
138 print("QUALITY FCT: time = %s pi"%(t/pi),QUALITY(t,u), end=' ')
139 if TEST_SUPG:
140 print("QUALITY SUPG: ",QUALITY(t,u_supg))
141 # saveVTK("u.%s.vtu"%c,u=u,u_supg=u_supg)
142 else:
143 # saveVTK("u.%s.vtu"%c,u=u)
144 pass
145 # if c == 20: 1/0

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