Dynamic mesh adaptation for multi-material simulations using weighted condition number relaxation

A mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from either a level set or volume fraction representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin (DG) projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. The method retains the excellent smoothing capabilities of condition number relaxation, while providing a method for clustering mesh cells near regions of interest requiring increased resolution. The algorithm has recently been implemented in one of LLNL’s arbitrary Lagrangian Eulerian (ALE) production codes. Results for a number of multi-material problems are presented, which will demonstrate the method’s great potential as a mesh relaxer for ALE simulations.