Moving mesh system and method for finite element/finite volume simulations

Roughly described, the invention involves detecting the presence of features on the boundary mesh which are likely to hamper regeneration of a bulk mesh with high quality elements, and upon finding such features, performing a repair operation on the boundary mesh prior to bulk mesh regeneration. The repair operation can include smoothing knife edge features and/or handling topological changes that have occurred during the simulation time increment. Preferably the repair operation includes a multi-level set smoothing step and a Delaunay refinement step for piecewise smooth complex.