High-Resolution Flux-Based Level Set Method

A new high-resolution flux-based finite volume method for general advection equations in non-divergent form including a level set equation for moving interfaces is introduced. The method is applicable to the case of non-divergence free velocity and to general unstructured grids in higher dimensions. We show that the method is consistent and that the numerical solution fulfils discrete minimum/maximum principle. Numerical experiments show its second order accuracy for smooth solutions as well as for solutions with discontinuous derivatives and on general unstructured meshes. Numerical examples for passive transport and shrinking of dynamic interfaces, including examples with topological changes, are presented using locally adapted 2D and 3D grids.