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

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Revision 868 - (show annotations)
Tue Oct 10 22:32:13 2006 UTC (13 years, 5 months ago) by gross
File MIME type: text/x-python
File size: 5816 byte(s)
new benchmark problem
1 ################################################
2 ## ##
3 ## October 2006 ##
4 ## ##
5 ## 3D Rayleigh-Taylor instability benchmark ##
6 ## by Laurent Bourgouin ##
7 ## ##
8 ################################################
9
10
11 ### IMPORTS ###
12 from esys.escript import *
13 import esys.finley
14 from esys.finley import finley
15 from esys.escript.linearPDEs import LinearPDE
16 from esys.escript.pdetools import Projector
17 import sys
18 import math
19
20 ### DEFINITION OF THE DOMAIN ###
21 l0=1.
22 l1=1.
23 n0=20 # IDEALLY 80...
24 n1=20 # IDEALLY 80...
25 mesh=esys.finley.Brick(l0=l0, l1=l1, l2=l0, order=2, n0=n0, n1=n1, n2=n0)
26
27 ### PARAMETERS OF THE SIMULATION ###
28 rho1 = 1.0e3 # DENSITY OF THE FLUID AT THE BOTTOM
29 rho2 = 1.01e3 # DENSITY OF THE FLUID ON TOP
30 eta1 = 1.0e2 # VISCOSITY OF THE FLUID AT THE BOTTOM
31 eta2 = 1.0e2 # VISCOSITY OF THE FLUID ON TOP
32 penalty = 1.0e3 # PENALTY FACTOR FOT THE PENALTY METHOD
33 g=10. # GRAVITY
34 t_step = 0
35 t_step_end = 2000
36 reinit_max = 30 # NUMBER OF ITERATIONS DURING THE REINITIALISATION PROCEDURE
37 reinit_each = 3 # NUMBER OF TIME STEPS BETWEEN TWO REINITIALISATIONS
38 h = Lsup(mesh.getSize())
39 numDim = mesh.getDim()
40 smooth = h*2.0 # SMOOTHING PARAMETER FOR THE TRANSITION ACROSS THE INTERFACE
41
42 ### DEFINITION OF THE PDE ###
43 velocityPDE = LinearPDE(mesh, numEquations=3)
44 velocityPDE.setSolverMethod(solver=LinearPDE.DIRECT)
45 advectPDE = LinearPDE(mesh)
46 advectPDE.setReducedOrderOn()
47 advectPDE.setValue(D=1.0)
48 advectPDE.setSolverMethod(solver=LinearPDE.DIRECT)
49 reinitPDE = LinearPDE(mesh, numEquations=1)
50 reinitPDE.setReducedOrderOn()
51 reinitPDE.setSolverMethod(solver=LinearPDE.LUMPING)
52 my_proj=Projector(mesh)
53
54 ### BOUNDARY CONDITIONS ###
55 xx = mesh.getX()[0]
56 yy = mesh.getX()[1]
57 zz = mesh.getX()[2]
58 top = whereZero(zz-l1)
59 bottom = whereZero(zz)
60 left = whereZero(xx)
61 right = whereZero(xx-l0)
62 front = whereZero(yy)
63 back = whereZero(yy-l0)
64 b_c = (bottom+top)*[1.0, 1.0, 1.0] + (left+right)*[1.0,0.0, 0.0] + (front+back)*[0.0, 1.0, 0.0]
65 velocityPDE.setValue(q = b_c)
66
67 pressure = Scalar(0.0, ContinuousFunction(mesh))
68
69 ### INITIALISATION OF THE INTERFACE ###
70 func = -(-0.1*cos(math.pi*xx/l0)*cos(math.pi*yy/l0)-zz+0.4)
71 phi = func.interpolate(ReducedSolution(mesh))
72
73
74 def advect(phi, velocity, dt):
75 ### SOLVES THE ADVECTION EQUATION ###
76
77 Y = phi.interpolate(Function(mesh))
78 for i in range(numDim):
79 Y -= (dt/2.0)*velocity[i]*grad(phi)[i]
80 advectPDE.setValue(Y=Y)
81 phi_half = advectPDE.getSolution()
82
83 Y = phi
84 for i in range(numDim):
85 Y -= dt*velocity[i]*grad(phi_half)[i]
86 advectPDE.setValue(Y=Y)
87 phi = advectPDE.getSolution()
88
89 print "Advection step done"
90 return phi
91
92 def reinitialise(phi):
93 ### SOLVES THE REINITIALISATION EQUATION ###
94 s = sign(phi.interpolate(Function(mesh)))
95 w = s*grad(phi)/length(grad(phi))
96 dtau = 0.3*h
97 iter =0
98 previous = 100.0
99 mask = whereNegative(abs(phi)-1.2*h)
100 reinitPDE.setValue(q=mask, r=phi)
101 while (iter<=reinit_max):
102 prod_scal =0.0
103 for i in range(numDim):
104 prod_scal += w[i]*grad(phi)[i]
105 coeff = s - prod_scal
106 ps2=0
107 for i in range(numDim):
108 ps2 += w[i]*grad(my_proj(coeff))[i]
109 reinitPDE.setValue(D=1.0, Y=phi+dtau*coeff-0.5*dtau**2*ps2)
110 phi = reinitPDE.getSolution()
111 error = Lsup((previous-phi)*whereNegative(abs(phi)-3.0*h))/h
112 print "Reinitialisation iteration :", iter, " error:", error
113 previous = phi
114 iter +=1
115 return phi
116
117 def update_phi(phi, velocity, dt, t_step):
118 ### CALLS THE ADVECTION PROCEDURE AND THE REINITIALISATION IF NECESSARY ###
119 phi=advect(phi, velocity, dt)
120 if t_step%reinit_each ==0:
121 phi = reinitialise(phi)
122 return phi
123
124 def update_parameter(phi, param_neg, param_pos):
125 ### UPDATES THE PARAMETERS TABLE USING THE SIGN OF PHI, A SMOOTH TRANSITION IS DONE ACROSS THE INTERFACE ###
126 mask_neg = whereNonNegative(-phi-smooth)
127 mask_pos = whereNonNegative(phi-smooth)
128 mask_interface = whereNegative(abs(phi)-smooth)
129 param = param_pos*mask_pos + param_neg*mask_neg + ((param_pos+param_neg)/2 +(param_pos-param_neg)*phi/(2.*smooth))*mask_interface
130 return param
131
132 def solve_vel(rho, eta, pressure):
133 ### SOLVES THE VELOCITY PROBLEM USING A PENALTY METHOD FOR THE INCOMPRESSIBILITY ###
134 error = 1.0
135 ref = pressure*1.0
136 p_iter=0
137 while (error >= 1.0e-2):
138
139 A=Tensor4(0.0, Function(mesh))
140 for i in range(numDim):
141 for j in range(numDim):
142 A[i,j,i,j] += eta
143 A[i,j,j,i] += eta
144 A[i,i,j,j] += penalty*eta
145
146 Y = Vector(0.0,Function(mesh))
147 Y[1] -= rho*g
148
149 X = Tensor(0.0, Function(mesh))
150 for i in range(numDim):
151 X[i,i] += pressure
152
153 velocityPDE.setValue(A=A, X=X, Y=Y)
154 velocity_new = velocityPDE.getSolution()
155 p_iter +=1
156 if p_iter >=500:
157 print "You're screwed..."
158 sys.exit(1)
159
160 pressure -= penalty*eta*(trace(grad(velocity_new)))
161 error = penalty*Lsup(trace(grad(velocity_new)))/Lsup(grad(velocity_new))
162 print "\nPressure iteration number:", p_iter
163 print "error", error
164 ref = pressure*1.0
165
166 return velocity_new, pressure
167
168 ### MAIN LOOP, OVER TIME ###
169 while t_step <= t_step_end:
170
171 rho = update_parameter(phi, rho1, rho2)
172 eta = update_parameter(phi, eta1, eta2)
173
174 velocity_new, pressure = solve_vel(rho, eta, pressure)
175 dt = 0.3*Lsup(mesh.getSize())/Lsup(velocity_new)
176 phi = update_phi(phi, velocity_new, dt, t_step)
177
178 ### PSEUDO POST-PROCESSING ###
179 print "########## Saving image", t_step, " ###########"
180 phi.saveVTK("/home/laurent/results2006/instability/phi3D.%2.2i.vtk" % t_step)
181
182 print "######################"
183 print "Time step:", t_step
184 print "######################"
185 t_step += 1

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