Computing arbitrary Lagrangian Eulerian maps for evolving surfaces

摘要

The good mesh quality of a discretized closed evolving surface is often compromised during time evolution. In recent years this phenomenon has been theoretically addressed in a few ways, one of them uses arbitrary Lagrangian Eulerian (ALE) maps. However, the numerical computation of such maps still remained an unsolved problem in the literature. An approach, using differential algebraic problems, is proposed here to numerically compute an arbitrary Lagrangian Eulerian map, which preserves the mesh properties over time. The ALE velocity is obtained by finding an equilibrium of a simple spring system, based on the connectivity of the nodes in the mesh. We also consider the algorithmic question of constructing acute surface meshes. We present various numerical experiments illustrating the good properties of the obtained meshes and the low computational cost of the proposed approach.