Can anybody share their experience about reinitialization of level set on non-uniform, non-orthogonal grids? Since I have trouble implementing them. Any suggestion about reference is more than welcome.

Thanks a lot. Wu

I have never seen the level set method implemented on such grid. It is always implemented on Cartesian grid. Can you guide me to any Reference?

Are you using finite difference? When people do FD in curvilinear coordinates, they always use coordinate transformation. What you need is only some derivatives, so a transformation may help. Good luck.

Pete

why do you need to use a level set method for non uniform and non orthgonal mesh. I was under the impression that level sets are used for solving complex geometry in cartesian mesh. Can u plz give me an example ast why u r adopting such a method!!!

I'm not an expert on level set. I guess the use of non-uniform(orthogonal) mesh is because of some complex geometries.

If you want to use cartesian mesh for complex geometries, maybe immersed boundary method is the only choice? I think level set on cartesian mesh can't simulate complex geometries.

http://math.uci.edu/~lowengrb/RESEAR...ons/JCP05b.pdf

Hi

I am working in the field of Level Set Method, however, I am using Cartesin Grid, and Level Set Method is adopted because it can simulate very complex geometries and handle topological complexities while using cartesian mesh. People have used Cartesian Mesh with restructuring or refining of grid. I have Sethian's book, and a whole lot of papers on LSM, so, I will check out and let you know if there is any on Non-orthogonal mesh, or if Sethian has described something related to that, as I never cared if someone is using Non-orthogonal mesh or not.

Vinod Dhiman

Thank all of you. Yeah, that's what I'm doing. Using the fixed amount of grids, puting more grids around interface, solving coordinate transformed equations by FD, the problem came out after dozens of time steps, that's why I started to wonder what the problem is, due to the grid shape or errors associated with numerical methods.

I don't have paper about level set by using FD. Sorry for not showing the link.

Thanks Kim for the link.

Wu

This is probably what you are looking for:

Yue et al., 2003, "Numerical simulation of unsteady multidimensional free surface motions by level set method,", Int. J. Numer. Meth. Fluids, 42:853-884

many thanks