I'm working on numerical solutions of free surface problems for imcompressible Newtonian fluids in two dimensions using finite diferences.

I'm implementing a semi-implicit method for working with problems with a low Reynold's number (Re<1), but I'm having problems of numerical unstability for some values of the time step. I'd like to know how I should work with the time step for avoiding such unstability or references about this problem.

Obs. I'm following the stabilty condition CFL.

Thanks in advance Cassio Oishi

Other terms such as the diffusion term also have restrictions to the time step. CFL number only serves as a time step restriction to the convection term.

Employing a better time integeration method can help get a bigger time step.

Linfeng.