Computing arbitrary Lagrangian Eulerian maps for evolving surfaces

TL;DR

This paper introduces a new algorithm for computing arbitrary Lagrangian Eulerian maps on evolving surfaces, improving mesh quality preservation during surface evolution through a spring-based equilibrium approach.

Contribution

The paper presents a novel algorithm for numerically computing ALE maps without prior knowledge, enhancing mesh quality in evolving surface simulations.

Findings

Algorithm effectively preserves mesh quality over time.

Numerical experiments demonstrate the algorithm's robustness.

Spring-based equilibrium approach is successful in computing ALE maps.

Abstract

The good mesh quality of an evolving discretized surface or domain is often compromised during time evolution. In recent years this phenomena have been overcome in a couple of ways, one of them uses arbitrary Lagrangian Eulerian maps. However, the numerical computation of such maps, without a priori knowledge, still remained elusive. An algorithm is proposed here to numerically compute an arbitrary Lagrangian Eulerian map, which helps to preserve the mesh properties over time. The algorithm is based on finding an equilibrium state of a mechanical system of springs, which is determined by the connectivity of the nodes in the mesh. We present various numerical experiments illustrating the good properties of the algorithm.