CBC Talk on Extended finite element method applied to the two-phase Stefan problem with a sharp phase interface

Total number of participants: 7
Total number of guests outside of CBC: 1
Number of different nationalities represented: 4
Total number of speakers: 1
Total number of talks: 1

Title: Extended finite element method applied to the two-phase Stefan problem with a sharp phase interface

by Timo Klock, Uni Bremen, Germany.

Abstract:

Two-phase Stefan problems with sharp interfaces are often used as model foundations to describe phase change processes in real-world applications. Thereby the temperature and the phase decomposition that evolve during the process are of key interest. Conventional numerical approaches are based on manipulating the underlying grid to accurately resolve irregularities near the interface in the temperature distribution. These methods are computationally expensive such that a faster alternative is desired. Therefore, the talk covers an approach for Stefan problems based on the extended finite element method (XFEM). This method uses an enriched finite element basis to capture local irregularities in the solution, hence expensive grid manipulations are avoided.
In addition to XFEM, the level set method is introduced and employed to mathematically represent a sharp phase interface. Both components are combined and yield an accurate, converging Stefan problem solver. Benchmark examples show linear convergence rates with respect to the characteristic triangulation diameter and the time step. Therefore XFEM/level set approaches are a viable alternative to methods that involve grid manipulations.