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Re: [ff3d-users] Extraction of the unit normal vector, or normal/tangent


From: Stephane Del Pino
Subject: Re: [ff3d-users] Extraction of the unit normal vector, or normal/tangential derivatives.
Date: Mon, 20 Oct 2008 23:29:12 +0200
User-agent: KMail/1.9.9

Dear Mykola.

A way that I already used for slip condition consists in penalizing the 
variational formula in order to impose
        u.n = 0
on the boundary.

On the variational point of view, we added 
        1/\epsilon*\int_{boundary}( u.n * v.n)
to the bilinear part.

in ff3d's language, it means something like that:
        +int[ref](u*nx/eps*U*nx + v*ny/eps*U*nx + w*nz/eps*U*nx)
        +int[ref](u*nx/eps*V*ny + v*ny/eps*V*ny + w*nz/eps*V*ny)
        +int[ref](u*nx/eps*W*nz + v*ny/eps*W*nz + w*nz/eps*W*nz)

where 'ref' is the reference of the boundary, eps is to be taken small and 
U,V,W are the test functions.

Best regards,
St├ęphane.




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