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Journal Articles Journal of Computational Physics Year : 2022

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-Bénard instability with a melting boundary.
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Dates and versions

hal-03889680 , version 1 (08-12-2022)

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Alexandre Limare, Stéphane Popinet, Christophe Josserand, Zhonghan Xue, Arthur R. Ghigo. A hybrid level-set / embedded boundary method applied to solidification-melt problems. Journal of Computational Physics, 2022, ⟨10.1016/j.jcp.2022.111829⟩. ⟨hal-03889680⟩
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