My main question is: How to implement a matrix dissipation method on an unstructured FV, cell centred, Runge-Kutta sheme?

Can anyone give me some references on matrix dissipation applied with unstructured grids?

Thanks

I assume you are talking about a central discretization + a matrix dissipation term.

I don't know any papers, unfortunately.

Isn't any upwind scheme a matrix dissipation scheme as well?

For example the Roe scheme across an interface can be written as:

F = 1/2*(F(Q_l) + F(Q_r)) - 1/2*|A|*(Q_r - Q_l)

with Q_l and Q_r beeing the extrapolated values from the left and right side and |A| the Roe matrix. In this case the matrix is based on physical considerations (direction of influence, eigenvalues). I think that you could in principle use any other matrix as well. How you extrapolate Q_l and Q_r defines the order of your scheme.

'hope this helps, or did I miss anything out??

Thanks.

Yes I mean "central discretization + a matrix dissipation". My main concern is the implementation/calculation of |A| in an unstructured framework? How does the lack of direction of the grid influences the calculation of |A|?

You do have a direction. If you compute the flux across an interface than the interface has a normal and thus you can differentiate between an upwind and a downwind side. But it is true that things can be awkward. Something like the next neighbour in upwind direction is impossible on triangular grids. Unfortunately I have no experience with matrix dissipation schemes. For upwind schemes you can formulate something by using a local direction (e.g. interface normal) and the gradients in the two cells adjacent to your interface (for more than 1st order).

If you find/found a good paper on this, I'd be interested in the reference.

This is classic, it should answer all you questions:

http://hdl.handle.net/2002/13559

which should be the same as:

http://library-dspace.larc.nasa.gov/...dle/2002/13559

Cheers

Andy

That describes a very classic upwind solver.