[mbfranklin@gmail.com]

Hello everybody,

I am working on implementing the conservative level set method presented by Olsson & Kreiss in their 2005 paper "A conservative level set method for two phase flow". I am currently using Scipy/Numpy for all of my numerical calculations.

I have been banging my head against the wall for months trying to debug my codes, and have yet to find any issues that are obviously incorrect, which brings me to this forum.

Has anybody else successfully implemented the level set method? I would love to have some conversation with anybody who is familiar with calculating normals, gradients, curvatures, etc. to bounce some ideas around, and perhaps share some numerical advice.

The first question that I have is this:

When calculating normal vectors from the gradients, one must divide by the magnitude of the gradient. In regions where the phase function is smooth, the gradients/magnitudes should go to zero, so dividing by this magnitude presents some numerical difficulty. Would you suggest

(1) adding a small number to the denominator (e.g. normal = gradient/(magnitude+eps) to avoid division by zero errors, or

(2) perform a check (e.g. if magnitude == 0: normal = 0)

More to come...any help would be MUCH appreciated!