Hello folks, I'm currently working on a 2D finite difference scheme of an unsteady flow problem. I'm trying to replicate the results of the original author as part of my PhD research.

In solving this unsteady 2D problem I have a tridiagonal set of equations to solve (and use standard thomas algorithm). I'm using a SLOR scheme to solve the equations, each set of equations corresponding to one column of my grid. The equations uses time marching to work out the new values from previous time values. The right hand side contains differences in both the x&y direction using values from the previous sweep. The mesh is a standard cartesian mesh.

I was wondering if there was a well documented method to analyse the stability of such a scheme - I've tried Von Neumann analysis but just get a load of garbage - I can't seem to work out the stability criteria of dt as a function of dx and dy.

The original authors claim it's unconditionally stable but I am finding otherwise - it'd be a big help if someone could help me work out why!

Many thanks, Frank

Take a look at

Hirt, C. W., "Heuristic Stability Theory for Finite-Difference Equations," JCP, vol.2 no. 4, June, 1968, pp. 339-355.

Your answer may not be directly in the article, but the pragmatic way of approaching stability can be extremely useful.

Good luck!

That's depend on the equations you're trying to resolve.

Generally, if there's no way of set a mathematical stability criteria we speak about numerical stability criteria.

It's a littl' bit hard to find because you have to performe a lot of simulation with different characteristics (dt, dx, dy) for the same case until you determine that the stability is unconditional or you find this criteria.

Good Luck