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jgs |
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# $Id$ |
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from esys.escript import * |
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from esys.linearPDEs import * |
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from esys import finley |
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g=9.81 * 1e-3 # km/sec |
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C=2 # sqrt(km)/sec |
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g_c=1e-5 # Hz |
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H_level=1 |
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#===================================== |
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L=1000. #km |
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mydomain=finley.Rectangle(l0=L,l1=L,n0=100,n1=100) |
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#mydomain=finley.ReadMesh("test.msh") |
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e_size=mydomain.getSize() |
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#==================================== |
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# profile: |
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#=================================== |
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x=mydomain.getX() |
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H=H_level # *(1.-exp(-2.*x[0]/L)) |
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#==================================== |
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h_pde=LinearPDE(mydomain) |
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h_pde.setValue(D=1.) |
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h_pde.setSymmetryOn() |
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hv_pde=LinearPDE(mydomain) |
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hv_pde.setValue(D=kronecker(mydomain)) |
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hv_pde.setSymmetryOn() |
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#==================================== |
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def getDh(h_pde,h,v,hv,H): |
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h_pde.setValue(Y=-trace(grad(hv))) |
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return h_pde.getSolution() |
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def getDhv(hv_pde,h,v,hv,H): |
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F=trace(grad(outer(hv,v)+0.5*g*(h**2-H**2)*kronecker(hv_pde.getDomain()))) |
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Q=h*g_c*matrixmult(numarray.array([[0,-1],[1,0]]),v)-g*(h-H)*grad(H)+g*length(v)/(C*h**2)*v |
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hv_pde.setValue(Y=-F-Q) |
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return hv_pde.getSolution() |
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x=mydomain.getX() |
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h=H-0.015*exp(-0.1*length(x-[L/2.,L/2.])) |
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v=Vector(0.,ContinuousFunction(mydomain)) |
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hv=h*v |
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t=0 |
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dt=0.01 |
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t_count=0 |
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while t_count<200: |
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t_count+=1 |
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t+=dt |
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print "@ ",t_count,"-th time step t =",t," (step size = ",dt,")" |
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# Taylor Galerkin method |
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h_half=h+dt/2*getDh(h_pde,h,v,hv,H) |
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hv_half=hv+dt/2*getDhv(hv_pde,h,v,hv,H) |
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v_half=hv_half/(h_half+1.e-15) |
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h=h+dt*getDh(h_pde,h_half,v_half,hv_half,H) |
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hv=hv+dt*getDhv(hv_pde,h_half,v_half,hv_half,H) |
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v=hv/(h+1.e-15) |
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if t_count%10==0: |
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print "save ",t_count |
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dt=min(inf(e_size/(sqrt(g*h)+length(v)+1.e-15)),10.) |
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print "@v =",sup(v),inf(v) |
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print "@h =",sup(h),inf(h) |
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print "@c =",Lsup(sqrt(g*h)) |
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print "@dt =",inf(e_size/(sqrt(g*h)+length(v)+1.e-15)) |
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