A hybrid level-set / embedded boundary method applied to solidification-melt problems
Abstract
In this paper, we introduce a novel way to represent the interface for two-phase flows with phase change. We combine a level-set method with a Cartesian embedded boundary method and take advantage of both. This is part of an effort to obtain a numerical strategy relying on Cartesian grids allowing the simulation of complex boundaries with possible change of topology while retaining a high-order representation of the gradients on the interface and the capability of properly applying boundary conditions on the interface. This leads to a two-fluid conservative second-order numerical method. The ability of the method to correctly solve Stefan problems, onset dendrite growth with and without anisotropy is demonstrated through a variety of test cases. Finally, we take advantage of the two-fluid representation to model a Rayleigh--B\'enard instability with a melting boundary.
Keywords
Cite
@article{arxiv.2202.08300,
title = {A hybrid level-set / embedded boundary method applied to solidification-melt problems},
author = {A. Limare and S. Popinet and C. Josserand and Z. Xue and A. Ghigo},
journal= {arXiv preprint arXiv:2202.08300},
year = {2022}
}