Adaptive anisotropic meshing and Level Set for free surface and interface flow problems
November 17, 2010
3:00 p.m.
Thierry Coupez
Abstract
In this presentation a level set representation of moving free surfaces and interfaces is combined with anisotropic mesh adaptation. We introduce first the convected Level Set method using a convective time derivative with the redistancing Hamilton Jacobi equation. Then, the anisotropic mesh adaptation framework will be introduced in the context of a local mesh generation method based on mesh topology modification and a minimal volume principle. In this case one needs to account for a metric field when length and volume evaluations are required. Convincing results have been already obtained in the past years by deriving the metric field from a posteriori interpolation error analysis. We propose here a different route to get a metric field directly at the node of the mesh, by introducing the length distribution tensor and an edge based error analysis. Applications combine a stabilised Finite Element flow solver with the Level Set for multiphase flow calculation within a monolithic approach. The a posteriori error estimation is applied to a modification of the Level Set scalar field, giving automatically the anisotropic mesh refinement in the interface region. The potential of this approach will be shown on several geometrical interpolation examples and new results of free surface calculation will be proposed in fluid buckling simulation, fluid structure interaction and moving interface problems.