1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
|
##############################################################################
#
# Copyright (c) 2003-2018 by The University of Queensland
# http://www.uq.edu.au
#
# Primary Business: Queensland, Australia
# Licensed under the Apache License, version 2.0
# http://www.apache.org/licenses/LICENSE-2.0
#
# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
# Development 2012-2013 by School of Earth Sciences
# Development from 2014 by Centre for Geoscience Computing (GeoComp)
#
##############################################################################
from __future__ import print_function, division
__copyright__="""Copyright (c) 2003-2018 by The University of Queensland
http://www.uq.edu.au
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Apache License, version 2.0
http://www.apache.org/licenses/LICENSE-2.0"""
__url__="https://launchpad.net/escript-finley"
#
# upwinding test moving a Gaussian hill around
#
# we solve U_,t + v_i u_,i =0
#
# the solution is given as u(x,t)=1/(4*pi*E*t)^{dim/2} * exp ( - |x-x_0(t)|^2/(4*E*t) )
#
# where x_0(t) = [ cos(OMEGA0*T0)*0.5,-sin(OMEGA0*T0)*0.5 ] and v=[-y,x]*OMEGA0 for dim=2 and
#
# x_0(t) = [ cos(OMEGA0*T0)*0.5,-sin(OMEGA0*T0)*0.5 ] and v=[-y,x]*OMEGA0 for dim=3
#
# the solution is started from some time T0>0.
#
# We are using five quality messurements for u_h
#
# - inf(u_h) > 0
# - sup(u_h)/sup(u(x,t)) = sup(u_h)*(4*pi*E*t)^{dim/2} ~ 1
# - integrate(u_h) ~ 1
# - | x_0h-x_0 | ~ 0 where x_0h = integrate(x*u_h)
# - sigma_h/4*E*t ~ 1 where sigma_h=sqrt(integrate(length(x-x0h)**2 * u_h) * (DIM==3 ? sqrt(2./3.) :1 )
#
#
from esys.escript import *
from esys.escript.linearPDEs import TransportPDE, SolverOptions
from esys.finley import Rectangle, Brick
#from esys.ripley import Rectangle, Brick
from esys.weipa import saveVTK
from math import pi, ceil
NE=128
#NE=4
DIM=2
THETA=0.5
OMEGA0=1.
ALPHA=pi/4
T0=0
T_END=2.*pi
dt=1e-3*10*10
E=1.e-3
dom=Rectangle(NE,NE)
u0=dom.getX()[0]
# saveVTK("u.%s.vtu"%0,u=u0)
# print "XX"*80
# set initial value
#dom.setX(2*dom.getX()-1)
#x=dom.getX()
#r=sqrt(x[0]**2+(x[1]-1./3.)**2)
#u0=whereNegative(r-1./3.)*wherePositive(wherePositive(abs(x[0])-0.05)+wherePositive(x[1]-0.5))
#x=Function(dom).getX()
#if DIM == 2:
# V=OMEGA0*(x[0]*[0,-1]+x[1]*[1,0])
#else:
# V=OMEGA0*(x[0]*[0,cos(ALPHA),0]+x[1]*[-cos(ALPHA),0,sin(ALPHA)]+x[2]*[0.,-sin(ALPHA),0.])
x=dom.getX()
R0=0.15
#cylinder:
X0=0.5
Y0=0.75
r=sqrt((x[0]-X0)**2+(x[1]-Y0)**2)/R0
u0=whereNegative(r-1)*wherePositive(wherePositive(abs(x[0]-X0)-0.025)+wherePositive(x[1]-0.85))
# cone:
X0=0.5
Y0=0.25
r=sqrt((x[0]-X0)**2+(x[1]-Y0)**2)/R0
u0=u0+wherePositive(1-r)*(1-r)
#hump
X0=0.25
Y0=0.5
r=sqrt((x[0]-X0)**2+(x[1]-Y0)**2)/R0
u0=u0+1./4.*(1+cos(pi*clip(r,maxval=1)))
x=Function(dom).getX()
V=OMEGA0*((0.5-x[0])*[0,1]+(0.5-x[1])*[-1,0])
#===================
fc=TransportPDE(dom,numEquations=1)
fc.getSolverOptions().setVerbosityOn()
#fc.getSolverOptions().setODESolver(SolverOptions.BACKWARD_EULER)
fc.getSolverOptions().setODESolver(SolverOptions.LINEAR_CRANK_NICOLSON)
fc.getSolverOptions().setODESolver(SolverOptions.CRANK_NICOLSON)
x=Function(dom).getX()
fc.setValue(M=1,C=V)
c=0
saveVTK("u.%s.vtu"%c,u=u0)
fc.setInitialSolution(u0)
dt=fc.getSafeTimeStepSize()
#dt=1.e-3
print("dt = ",dt)
t=T0
print("QUALITY FCT: time = %s pi"%(t/pi),inf(u0),sup(u0),integrate(u0))
#T_END=200*dt
while t<T_END:
print("time step t=",t+dt)
u=fc.getSolution(dt)
print("QUALITY FCT: time = %s pi"%(t+dt/pi),inf(u),sup(u),integrate(u))
saveVTK("u.%s.vtu"%(c+1,),u=u)
c+=1
t+=dt
|
