A level-set based space-time finite element approach to the modelling of solidification and melting processes

TL;DR

This paper introduces a novel space-time finite element method using level-set techniques to model phase-change processes like solidification and melting, effectively capturing interface dynamics without complex basis enrichment.

Contribution

It extends ghost-cell approaches to space-time finite elements for phase-change problems, simplifying implementation and improving interface tracking accuracy.

Findings

Successfully modeled 1D Stefan problem and cavity melting.

Demonstrated applicability to complex 2D melting scenarios.

Method integrates seamlessly with existing finite element codes.

Abstract

We present a strategy for the numerical solution of convection-coupled phase-transition problems, with focus on solidification and melting. We solve for the temperature and flow fields over time. The position of the phase-change interface is tracked with a level-set method, which requires knowledge of the heat-flux discontinuity at the interface. In order to compute the heat-flux jump, we build upon the ghost-cell approach and extend it to the space-time finite element method. This technique does not require a local enrichment of the basis functions, such as methods like extended finite elements, and it can be easily implemented in already existing finite element codes. Verification cases for the 1D Stefan problem and the lid-driven cavity melting problem are provided. Furthermore, we show a more elaborate 2D case in view of complex applications.