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

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. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper presents a numerical strategy for solving convection-coupled phase-transition problems, specifically focusing on solidification and melting. The authors track the position of the phase-change interface using a level-set method and compute the heat-flux jump using an extended ghost-cell approach. Verification cases are provided for 1D and 2D phase-transition problems.