|Advanced Simulation Technologies, AVL, Austria
In this talk, we would like to discuss about an algorithm to numerically solve a normal flow equation in level set method on a polyhedron mesh in 3D. The equation has been extensively used in image processing and surface evolution. Unlike to commonly used a structured mesh in level set method, it is very challenging to obtain a high order scheme in a polyhedron mesh. We propose a cell-centered gradient defined by flux signs to design a robust scheme considered as an extension of well-known Rouy-Tourin scheme into 3D with the second order upwind difference. A high order of convergence, performance in parallel computation, and a recovery of signed distance function from a sparse data are illustrated in numerical examples.