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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,
Stéphane.