/[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 873 - (show annotations)
Mon Oct 16 04:07:33 2006 UTC (13 years, 9 months ago) by gross
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uszawa scheme runs with variable viscosity
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, SaddlePointProblem
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=numDim)
44
45 advectPDE = LinearPDE(mesh)
46 advectPDE.setReducedOrderOn()
47 advectPDE.setValue(D=1.0)
48 advectPDE.setSolverMethod(solver=LinearPDE.DIRECT)
49
50 reinitPDE = LinearPDE(mesh, numEquations=1)
51 reinitPDE.setReducedOrderOn()
52 reinitPDE.setSolverMethod(solver=LinearPDE.LUMPING)
53 my_proj=Projector(mesh)
54
55 ### BOUNDARY CONDITIONS ###
56 xx = mesh.getX()[0]
57 yy = mesh.getX()[1]
58 zz = mesh.getX()[2]
59 top = whereZero(zz-l1)
60 bottom = whereZero(zz)
61 left = whereZero(xx)
62 right = whereZero(xx-l0)
63 front = whereZero(yy)
64 back = whereZero(yy-l0)
65 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]
66 velocityPDE.setValue(q = b_c)
67
68 pressure = Scalar(0.0, ContinuousFunction(mesh))
69 velocity = Vector(0.0, ContinuousFunction(mesh))
70
71 ### INITIALISATION OF THE INTERFACE ###
72 func = -(-0.1*cos(math.pi*xx/l0)*cos(math.pi*yy/l0)-zz+0.4)
73 phi = func.interpolate(ReducedSolution(mesh))
74
75
76 def advect(phi, velocity, dt):
77 ### SOLVES THE ADVECTION EQUATION ###
78
79 Y = phi.interpolate(Function(mesh))
80 for i in range(numDim):
81 Y -= (dt/2.0)*velocity[i]*grad(phi)[i]
82 advectPDE.setValue(Y=Y)
83 phi_half = advectPDE.getSolution()
84
85 Y = phi
86 for i in range(numDim):
87 Y -= dt*velocity[i]*grad(phi_half)[i]
88 advectPDE.setValue(Y=Y)
89 phi = advectPDE.getSolution()
90
91 print "Advection step done"
92 return phi
93
94 def reinitialise(phi):
95 ### SOLVES THE REINITIALISATION EQUATION ###
96 s = sign(phi.interpolate(Function(mesh)))
97 w = s*grad(phi)/length(grad(phi))
98 dtau = 0.3*h
99 iter =0
100 previous = 100.0
101 mask = whereNegative(abs(phi)-1.2*h)
102 reinitPDE.setValue(q=mask, r=phi)
103 print "Reinitialisation started."
104 while (iter<=reinit_max):
105 prod_scal =0.0
106 for i in range(numDim):
107 prod_scal += w[i]*grad(phi)[i]
108 coeff = s - prod_scal
109 ps2=0
110 for i in range(numDim):
111 ps2 += w[i]*grad(my_proj(coeff))[i]
112 reinitPDE.setValue(D=1.0, Y=phi+dtau*coeff-0.5*dtau**2*ps2)
113 phi = reinitPDE.getSolution()
114 error = Lsup((previous-phi)*whereNegative(abs(phi)-3.0*h))/h
115 print "Reinitialisation iteration :", iter, " error:", error
116 previous = phi
117 iter +=1
118 print "Reinitialisation finalized."
119 return phi
120
121 def update_phi(phi, velocity, dt, t_step):
122 ### CALLS THE ADVECTION PROCEDURE AND THE REINITIALISATION IF NECESSARY ###
123 phi=advect(phi, velocity, dt)
124 if t_step%reinit_each ==0:
125 phi = reinitialise(phi)
126 return phi
127
128 def update_parameter(phi, param_neg, param_pos):
129 ### UPDATES THE PARAMETERS TABLE USING THE SIGN OF PHI, A SMOOTH TRANSITION IS DONE ACROSS THE INTERFACE ###
130 mask_neg = whereNonNegative(-phi-smooth)
131 mask_pos = whereNonNegative(phi-smooth)
132 mask_interface = whereNegative(abs(phi)-smooth)
133 param = param_pos*mask_pos + param_neg*mask_neg + ((param_pos+param_neg)/2 +(param_pos-param_neg)*phi/(2.*smooth))*mask_interface
134 return param
135
136 class StokesProblem(SaddlePointProblem):
137 """
138 simple example of saddle point problem
139 """
140 def __init__(self,domain):
141 super(StokesProblem, self).__init__(self)
142 self.domain=domain
143 self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
144 self.__pde_u.setSymmetryOn()
145
146 self.__pde_p=LinearPDE(domain)
147 self.__pde_p.setReducedOrderOn()
148 self.__pde_p.setSymmetryOn()
149
150 def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1):
151 self.eta=eta
152 A =self.__pde_u.createCoefficientOfGeneralPDE("A")
153 for i in range(self.domain.getDim()):
154 for j in range(self.domain.getDim()):
155 A[i,j,j,i] += self.eta
156 A[i,j,i,j] += self.eta
157 self.__pde_p.setValue(D=1./self.eta)
158 self.__pde_u.setValue(A=A,q=fixed_u_mask,Y=f)
159
160 def inner(self,p0,p1):
161 return integrate(p0*p1,Function(self.__pde_p.getDomain()))
162
163 def solve_f(self,u,p,tol=1.e-8):
164 self.__pde_u.setTolerance(tol)
165 g=grad(u)
166 self.__pde_u.setValue(X=self.eta*symmetric(g)+p*kronecker(self.__pde_u.getDomain()))
167 return self.__pde_u.getSolution()
168
169 def solve_g(self,u,tol=1.e-8):
170 self.__pde_p.setTolerance(tol)
171 self.__pde_p.setValue(X=-u)
172 dp=self.__pde_p.getSolution()
173 return dp
174
175 def solve_vel_uszawa(rho, eta, velocity, pressure):
176 ### SOLVES THE VELOCITY PROBLEM USING A PENALTY METHOD FOR THE INCOMPRESSIBILITY ###
177 sol=StokesProblem(velocity.getDomain())
178 Y = Vector(0.0,Function(mesh))
179 Y[1] -= rho*g
180 sol.initialize(fixed_u_mask=b_c,eta=eta,f=Y)
181 velocity,pressure=sol.solve(velocity,pressure,relaxation=1.,iter_max=50,tolerance=0.01)
182 return velocity, pressure
183
184 def solve_vel_penalty(rho, eta, velocity, pressure):
185 ### SOLVES THE VELOCITY PROBLEM USING A PENALTY METHOD FOR THE INCOMPRESSIBILITY ###
186 velocityPDE.setSolverMethod(solver=LinearPDE.DIRECT)
187 error = 1.0
188 ref = pressure*1.0
189 p_iter=0
190 while (error >= 1.0e-2):
191
192 A=Tensor4(0.0, Function(mesh))
193 for i in range(numDim):
194 for j in range(numDim):
195 A[i,j,i,j] += eta
196 A[i,j,j,i] += eta
197 A[i,i,j,j] += penalty*eta
198
199 Y = Vector(0.0,Function(mesh))
200 Y[1] -= rho*g
201
202 X = Tensor(0.0, Function(mesh))
203 for i in range(numDim):
204 X[i,i] += pressure
205
206 velocityPDE.setValue(A=A, X=X, Y=Y)
207 velocity = velocityPDE.getSolution()
208 p_iter +=1
209 if p_iter >=500:
210 print "You're screwed..."
211 sys.exit(1)
212
213 pressure -= penalty*eta*(trace(grad(velocity)))
214 error = penalty*Lsup(trace(grad(velocity)))/Lsup(grad(velocity))
215 print "\nPressure iteration number:", p_iter
216 print "error", error
217 ref = pressure*1.0
218
219 return velocity, pressure
220
221 ### MAIN LOOP, OVER TIME ###
222 while t_step <= t_step_end:
223 print "######################"
224 print "Time step:", t_step
225 print "######################"
226 rho = update_parameter(phi, rho1, rho2)
227 eta = update_parameter(phi, eta1, eta2)
228
229 velocity, pressure = solve_vel_uszawa(rho, eta, velocity, pressure)
230 dt = 0.3*Lsup(mesh.getSize())/Lsup(velocity)
231 phi = update_phi(phi, velocity, dt, t_step)
232
233 ### PSEUDO POST-PROCESSING ###
234 print "########## Saving image", t_step, " ###########"
235 saveVTK("phi3D.%2.2i.vtk"%t_step,layer=phi)
236
237 t_step += 1
238
239 # vim: expandtab shiftwidth=4:

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