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[ff3d-users] Extraction of the unit normal vector, or normal/tangential

From: Mykola Tasinkevych
Subject: [ff3d-users] Extraction of the unit normal vector, or normal/tangential derivatives.
Date: Mon, 20 Oct 2008 15:34:20 +0200

      Dear ff3d Users,

 I would like to solve the Stokes problem around an obstacle, which imposes
 a non-uniform slip boundary conditions on its surface.

 The slip velocity is determined by the gradient of a solute concentration, "RHO"
 around the obstacle. More precisely, by the projection of the gradient along the
 obstacle surface:

           V_{slip}  =   grad_{tangent}(RHO) = grad(RHO) - n.(n.grad(RHO))
 where "n" is the unit normal vector on the obstacle surface.

   Does it make any sense to define  this slip boundary conditions as I did in the
 line 11, below?  Or may be the tangential gradient is already implemented in

    With the best regards,
    M. Tasinkevych.

1             mesh M = read(medit,"MESH.mesh");
2             function RHO = read(medit,"concentration.bb",M);
4             solve(u1,u2,u3,p)  in  M
5             {
6                  test(U1,U2,U3,P)
7                       int ( ...... )  = 0;
9            // slip boundary condition of obstacle
11          u1 = dx(RHO) - nx*(nx*dx(RHO) +ny*dy(RHO)+nz*dz(RHO) )  on obstacle ;
12         " and similar equations on  u2 and u3"


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