Far field boudary conditions in FDM
Hi,
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? Thanks James 
Re: Far field boudary conditions in FDM
This is for incompressible flow"
For velocities just set u(N) = u(N1) {along X) v(N) = v(N1) (along X) For pressure set pressure such that pressure at boundary to be zero P(N+1) =  P(N1) Where N+1 is pressure point just ouside of domain and N1 is point just inside domain (for staggered grid) 
Re: Far field boudary conditions in FDM
Thanks, thats great.
One final thing, would you substitute u(N)=u(N1) into the discretised Stokes equations (so that dp/dx=d2u/dy2 etc) or would you simply use u(N)=u(N1) 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 James 
Re: Far field boudary conditions in FDM
At outflow boundary the zerogradient condition for (u,v,p) may work well. But you need fix something of the inflow.

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