NDSolve with Oblique Boundary Conditions

Questions
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1

Hi everyone,

I have a question concerning the solution of PDEs with NDSolve in Mathematica 10. I am trying to solve a PDE in 2D with oblique boudary conditions. Specifically, I want the gradient of the solution in a given direction to be zero at the boundary, namely:

d.Grad[u[x,y],{x,y}]=0

with d a given unit vector, say {1,1}/Sqrt[2].

However, with NeumannValue I can only demand that the gradient be zero in the direction perpendicular to the boundary:

n.Grad[u[x,y],{x,y}]=0

at the boundary with n an outgoing normal to the boundary.

Does anybody know how to extend this to a general direction d rather than the normal to the boundary n?

Thanks!

Ofri Telem

2

I wanted to ask the same question! Did you find any answer elsewhere? We need the source code of NeumannValue function and want to modify it.