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James July 14, 2005 16:29

Far field boudary conditions in FDM

I have a simple shear flow with complicated interface conditions and am struggling to formulate far field boundary conditions for a staggered type grid. Applying du/dx=dv/dx=0 on the boundary I still have an unknown pressure term outside my domain. Any ideas?

Also at the boundaries should I apply the boundary conditions above to the equations (Stokes) or simply disretise them and use them instead of the normal equations?



agg July 15, 2005 12:19

Re: Far field boudary conditions in FDM
This is for incompressible flow"

For velocities just set u(N) = u(N-1) {along X) v(N) = v(N-1) (along X)

For pressure set pressure such that pressure at boundary to be zero P(N+1) = - P(N-1) Where N+1 is pressure point just ouside of domain and N-1 is point just inside domain (for staggered grid)

james July 15, 2005 12:47

Re: Far field boudary conditions in FDM
Thanks, thats great.

One final thing, would you substitute u(N)=u(N-1) into the discretised Stokes equations (so that dp/dx=d2u/dy2 etc) or would you simply use u(N)=u(N-1) instead of the bulk equations?

Also do you know of any good books/sites on FDM and in particular staggered grid arrangements as on the whole I have found the literature average.

Thanks again


yuan July 20, 2005 02:44

Re: Far field boudary conditions in FDM
At outflow boundary the zero-gradient condition for (u,v,p) may work well. But you need fix something of the inflow.

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