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Tangential derivative Cell-Based Finite Volume

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Old   July 15, 2010, 19:56
Default Tangential derivative Cell-Based Finite Volume
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Hi everyone,

I am searching a discretization method for the tangential derivative terms of the viscosity.
For example if we have two cells with exact same y coordinate, how do we calculate du/dy? Here dy is the direction tangential to the face.

As a solution, someone told me to use the derivative between the vertices of the face. Well, I didn't like this solution.

The equation in fact says div(div(V)) where V is the vector .

The outer divergence is solved with the Gauss(divergence theorem).
But unless there is another method, the inner one should be solved. That's why i am looking for the discretization of du/dy, using cell based method. (only the cell based properties, face normal and tangent vectors, and the distance between cells).

Or should I use the solution that I didn't like?

Thanks,

P.S: div(div(V)) problem exists also for the div(grad(V)). But I assume the solution of one, will also be the solution of the other.

Sorry for English,
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