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 diaw June 14, 2005 09:06

Does a 2D finite volume triangular mesh

Hi,

I was having a discussion today with a Senior Lecturer whose speciality is the Finite Element Technique & the following question emerged.

Does a 2D finite volume triangular mesh technique exist? Not a depricated quadritaleral, but a true 2D triangle. Is solid theory in place?

All books I have seen for FV seem to focus on structured quad meshes, or unstructured quad meshes.

diaw...

 Hrvoje Jasak June 14, 2005 11:44

Re: Does a 2D finite volume triangular mesh

Unstructured (well, arbitrarily unstructured) solvers exist today and have been around for ages. They can work on arbitrary polyhedral cells, and a 2-D triangle is (obviously) included.

The FVM theory does not change at all (you just throw the compass away); as for code implementation, this is a question of opinion - I consider it easier to work with polyhedra.

Enjoy,

Hrv

 diaw June 14, 2005 16:06

Re: Does a 2D finite volume triangular mesh

Thanks Hrvoje... I was hoping that you would answer that one...

Do you have any links I could pursue?

Many thanks, diaw...

 Robert June 15, 2005 03:00

Re: Does a 2D finite volume triangular mesh

Always remember this: In the FVM fluxes (convective and diffusive) are computed across control volume faces. A control volume is a general volume defined by a finite number of planar faces. Any polyhedral cell could therefore be used (including triangle). Convective and diffusive fluxes are expressed in terms of CELL values on either side of a face. In the process jou loop through FACES and not CELLS to generate your linearized algebraic equations. Each face then contributes to the coefficients and source terms of the cells on either side of it. Just keep in mind the orientation of a face area vector relative to a cell. It points outwards!! In other words if you have a face shared by two cells you need to change face area vector sign when summing across the neighbour cell of that face. For the neighbour cell the face area vector points inwards.

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