The eXtreme Mesh deformation approach (X-MESH) for the Stefan phase-change model

TL;DR

X-MESH is a novel mesh deformation method that tracks sharp interfaces in phase change models without remeshing, allowing topology changes by enabling elements to reach zero measure.

Contribution

The paper introduces X-MESH, a new approach that allows interface tracking with fixed topology meshes by permitting elements to reach zero measure, handling complex interface dynamics.

Findings

Successfully tracks interfaces with topology changes

Avoids remeshing, reducing computational complexity

Demonstrated on Stefan phase change model examples

Abstract

The eXtreme Mesh deformation approach (X-MESH) is a new paradigm to follow sharp interfaces without remeshing and without changing the mesh topology. Even though the mesh does not change its topology, it can follow interfaces that do change their topology (nucleation, coalescence, splitting). To make this possible, the key X-MESH idea is to allow elements to reach zero measure. This permits interface relaying between nodes as well as interface annihilation and seeding in a time continuous manner. The paper targets the Stefan phase change model in which the interface (front) is at a given temperature. Several examples demonstrate the capability of the approach.