/[escript]/trunk/finley/test/python/axisymm-splitB.py
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Annotation of /trunk/finley/test/python/axisymm-splitB.py

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Revision 1639 - (hide annotations)
Mon Jul 14 08:55:25 2008 UTC (12 years, 9 months ago) by gross
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1 gross 1562 #
2     # AXI-SYMMETRIC NEWTONIAN MODEL ; UPDATED LAGRANGIAN FORMULATION
3     #
4     #
5     # step 1 rho*(v_star-v) = dt * (sigma'_ij,j-teta3*p,i+f_i)
6     # step 2 dp=-dt*B*(v_j,j+teta1*v_star_j,j-dt*teta1*((1-teta3)*p_,jj+teta2*dp_,jj))
7     # step 3 rho*(v+-v) = -dt*((1-teta3)*p_,jj+teta2*dp_,jj)
8     # step 3b p+=1/2(p+dp+abs(p+dp))
9     # step 4 sigma'i+_ij,j=f(v+,p+,...)
10     #
11     #
12     from esys.escript import *
13     from esys.escript.linearPDEs import LinearSinglePDE, LinearPDESystem
14     from esys.finley import Rectangle
15    
16    
17     nel = 20
18     H = 0.5
19     L = 1.0
20    
21     eta = 1.0 # shear viscosity
22     ro = 1.0
23     g = 1.00
24    
25     alpha_w = 1.00
26     alpha = 1.00*1000000.
27     Pen=0.
28     B=100.
29    
30     nstep = 3000
31     dt = 1.
32     small = EPSILON
33     w_step=max(int(nstep/50),1)*0+1
34     toler = 0.001
35     teta1 = 0.5
36     teta2 = 0.5
37     teta3 = 1 # =0 split A; =1 split B
38    
39     # create domain:
40     dom=Rectangle(int(nel*L/min(L,H)),int(nel*H/min(L,H)),order=1, l0=L, l1=H)
41     x=dom.getX()
42    
43    
44     momentumStep1=LinearPDESystem(dom)
45     momentumStep1.setValue(q=whereZero(x[0])*[1.,0.]+whereZero(x[1])*[0.,1.]) # fix x0=0 and x1=0
46     face_mask=whereZero(FunctionOnBoundary(dom).getX()[1])
47    
48     pressureStep2=LinearSinglePDE(dom)
49     pressureStep2.setReducedOrderOn()
50     pressureStep2.setValue(q=whereZero(x[0]-L)+whereZero(x[1]-H))
51    
52     momentumStep3=LinearPDESystem(dom)
53     momentumStep3.setValue(q=whereZero(x[0])*[1.,0.]+whereZero(x[1])*[0.,1.])
54     #
55     # initial values:
56     #
57     U=Vector(0.,Solution(dom))
58     p=ro*g*(L-ReducedSolution(dom).getX()[0])*(H-ReducedSolution(dom).getX()[1])/3
59 gross 1639 p=ro*g*(H-ReducedSolution(dom).getX()[1])
60     dev_stress=Tensor(0.,Function(dom))
61 gross 1562
62     t=dt
63     istep=0
64     while istep < nstep:
65     istep=istep+1
66     print "time step :",istep," t = ",t
67     r=Function(dom).getX()[0]
68     r_b=FunctionOnBoundary(dom).getX()[0]
69     print " volume : ",integrate(r)
70     #
71     # step 1:
72     #
73     # calculate normal
74     n_d=dom.getNormal()
75     t_d=matrixmult(numarray.array([[0.,-1.],[1.,0]]),n_d)
76     sigma_d=(sign(inner(t_d,U))*alpha_w*t_d-n_d)*Pen*clip(inner(n_d,U),0.)
77     print " sigma_d =",inf(sigma_d),sup(sigma_d)
78    
79 gross 1639 momentumStep1.setValue(D=r*ro*kronecker(dom),
80     Y=r*ro*U+dt*r*[0.,-ro*g],
81     X=-dt*r*(dev_stress-teta3*p*kronecker(dom)),
82     y=sigma_d*face_mask*r_b)
83 gross 1562 U_star=momentumStep1.getSolution()
84 gross 1639 saveVTK("u.xml",u=U_star,u0=U)
85     1/0
86 gross 1562 #
87     # step 2:
88     #
89     # U2=U+teta1*(U_star-U)
90     U2=U+teta1*U_star
91     gg2=grad(U2)
92     div_U2=gg2[0,0]+gg2[1,1]+U2[0]/r
93    
94     grad_p=grad(p)
95    
96     pressureStep2.setValue(A=r*dt*B*teta1*teta2/ro*dt*kronecker(dom),
97     D=r,
98     Y=-dt*B*r*div_U2,
99     X=-r*B*dt**2/ro*teta1*(1-teta3)*grad_p)
100     dp=pressureStep2.getSolution()
101     #
102     # step 3:
103     #
104     p2=(1-teta3)*p+teta2*dp
105     grad_p2=grad(p2)
106     momentumStep3.setValue(D=r*ro*kronecker(dom),
107     Y=r*(ro*U_star-dt*teta2*grad_p2))
108     U_new=momentumStep3.getSolution()
109     #
110     # update:
111     #
112     p+=dp
113     U=U_new
114     print " U:",inf(U),sup(U)
115     print " P:",inf(p),sup(p)
116    
117    
118     p_pos=clip(p,small)
119     gg=grad(U)
120     vol=gg[0,0]+gg[1,1]+U[0]/r
121     gamma=sqrt(2*((gg[0,0]-vol/3)**2+(gg[1,1]-vol/3)**2+(U[0]/r-vol/3)**2+(gg[1,0]+gg[0,1])**2/2))
122     m=whereNegative(eta*gamma-alpha*p_pos)
123     eta_d=m*eta+(1.-m)*alpha*p_pos/(gamma+small)
124     print " viscosity =",inf(eta_d),sup(eta_d)
125 gross 1639 dev_stress=eta_d*(symmetric(gg)-2./3.*vol*kronecker(dom))
126 gross 1562 #
127     # step size control:
128     #
129     len=inf(dom.getSize())
130     dt1=inf(dom.getSize()/(length(U)+small))
131     dt2=inf(0.5*ro*(len**2)/eta_d)
132     dt=dt1*dt2/(dt1+dt2)
133     print " new step size = ",dt
134     #
135     # update geometry
136     #
137     dom.setX(dom.getX()+U*dt)
138     t=t+dt
139     if (istep-1)%w_step==0:saveVTK("u.%d.xml"%((istep-1)/w_step),p=p,eta=eta_d,U=U_star,U_star=U_star,gamma=gamma)
140     if istep == 3: 1/0

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