Hi, everyone

I am writing an 3-D unstructured grid solver using median-dual cell-vertex scheme. I got confused when I tried to compute the median-dual volume. Here is my question.

(1) If I used a mean unit normal vector and a total face area associated with each edge, then should the dual volume associated with each node be calculated with the mean surface on each adjacent edge or all partial surfaces on each adjacent edge?

(2)If all partial surfaces on each adjacent edge has to be accounted for, does that mean a integration of the fluxes on each partial surfaces?

Thanks in advance for any advice. Ricky

Which cell types do you intend to use?

For simplex elements only (triangles, tetrahedra) an averaged interface vector should be fine for the fluxes.

For hexas only the averaged vector should do as well (similar formulation compared to structured FV).

If, however, you mix the elements you are in trouble ...

In theory (as far as I understand it!!), it is difficult to formulate a consistent scheme with an averaged interface vector. If you evaluate the fluxes on all partial surfaces it should be ok ... but that is a lot of fluxes!

Did you think about a cell centred scheme? I remember coming across all kinds of problems with boundary conditions for a node centred (dual mesh) type of solver ...

I am afraid that the cell-vertex scheme is inevitable for me since my professor has already made up his mind ^-^

I am just using triangle and tetrahedra elements so an mean face vector should be fine..

One friend suggets that I should just use 1/4 of all the adjacent tetrahedron volumes around a vertex as the dual volume , any better suggestion?

Thanks Ricky

I am afraid that is not correct - unless your are only interested in steady state solutions. In that case the volume doesn't matter too much.

What's wrong with adding up all the partial volumes? You can do that once at the beginning and then store the volume per node. For the fluxes you only store the sum of all the little faces (middle of edge -> middle of tetra -> middle of face). Reconstruction of the variables should be done onto the middle of the edge.

Good luck!

I do need transient solutions. I will use the partial volume as you suggested.

Thanks.