# Contents of /trunk/finley/test/python/axisymm-splitB.py

Revision 1562 - (show annotations)
Wed May 21 13:04:40 2008 UTC (12 years, 10 months ago) by gross
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```The algebraic upwinding with MPI. The case of boundary constraint needs still some attention.

```
 1 # 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 53 54 momentumStep3=LinearPDESystem(dom) 55 momentumStep3.setValue(q=whereZero(x[0])*[1.,0.]+whereZero(x[1])*[0.,1.]) 56 # 57 # initial values: 58 # 59 U=Vector(0.,Solution(dom)) 60 p=ro*g*(L-ReducedSolution(dom).getX()[0])*(H-ReducedSolution(dom).getX()[1])/3 61 # p=ro*g*(H-ReducedSolution(dom).getX()[1]) 62 stress=Tensor(0.,Function(dom)) 63 64 t=dt 65 istep=0 66 while istep < nstep: 67 istep=istep+1 68 print "time step :",istep," t = ",t 69 r=Function(dom).getX()[0] 70 r_b=FunctionOnBoundary(dom).getX()[0] 71 print " volume : ",integrate(r) 72 # 73 # step 1: 74 # 75 # calculate normal 76 n_d=dom.getNormal() 77 t_d=matrixmult(numarray.array([[0.,-1.],[1.,0]]),n_d) 78 sigma_d=(sign(inner(t_d,U))*alpha_w*t_d-n_d)*Pen*clip(inner(n_d,U),0.) 79 print " sigma_d =",inf(sigma_d),sup(sigma_d) 80 81 momentumStep1.setValue(D=ro*kronecker(dom), 82 Y=ro*U+dt*((stress[:,0]-p*teta3*kronecker(dom)[:,0])/r+[0.,-ro*g]), 83 # Y=r*ro*U+dt*r*[0.,-ro*g], 84 X=-dt*(stress-teta3*p*kronecker(dom)), 85 y=sigma_d*face_mask) 86 U_star=momentumStep1.getSolution() 87 # 88 # step 2: 89 # 90 # U2=U+teta1*(U_star-U) 91 U2=U+teta1*U_star 92 gg2=grad(U2) 93 div_U2=gg2[0,0]+gg2[1,1]+U2[0]/r 94 95 grad_p=grad(p) 96 97 pressureStep2.setValue(A=r*dt*B*teta1*teta2/ro*dt*kronecker(dom), 98 D=r, 99 Y=-dt*B*r*div_U2, 100 X=-r*B*dt**2/ro*teta1*(1-teta3)*grad_p) 101 dp=pressureStep2.getSolution() 102 # 103 # step 3: 104 # 105 p2=(1-teta3)*p+teta2*dp 106 grad_p2=grad(p2) 107 momentumStep3.setValue(D=r*ro*kronecker(dom), 108 Y=r*(ro*U_star-dt*teta2*grad_p2)) 109 U_new=momentumStep3.getSolution() 110 # 111 # update: 112 # 113 p+=dp 114 U=U_new 115 print " U:",inf(U),sup(U) 116 print " P:",inf(p),sup(p) 117 118 119 p_pos=clip(p,small) 120 gg=grad(U) 121 vol=gg[0,0]+gg[1,1]+U[0]/r 122 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)) 123 m=whereNegative(eta*gamma-alpha*p_pos) 124 eta_d=m*eta+(1.-m)*alpha*p_pos/(gamma+small) 125 print " viscosity =",inf(eta_d),sup(eta_d) 126 stress=eta_d*(symmetric(gg)-2./3.*vol*kronecker(dom)) 127 # 128 # step size control: 129 # 130 len=inf(dom.getSize()) 131 dt1=inf(dom.getSize()/(length(U)+small)) 132 dt2=inf(0.5*ro*(len**2)/eta_d) 133 dt=dt1*dt2/(dt1+dt2) 134 print " new step size = ",dt 135 # 136 # update geometry 137 # 138 dom.setX(dom.getX()+U*dt) 139 t=t+dt 140 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) 141 if istep == 3: 1/0

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