LI, Minghui; AZAIEZ, Mejdi; XU, Chuanju

doi:10.1016/j.camwa.2022.01.017

AZAIEZ, Mejdi
Institut de Mécanique et d'Ingénierie [I2M]

XU, Chuanju

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Article de revue

Ce document a été publié dans

Computers & Mathematics with Applications. 2022-03-01, vol. 109, p. 204-215

Résumé en anglais

In this paper, we propose and analyze a first-order and a second-order time-stepping schemes for the anisotropic phase-field dendritic crystal growth model. The proposed schemes are based on an auxiliary variable approach for the Allen-Cahn equation and delicate treatment of the terms coupling the Allen-Cahn equation and temperature equation. The idea of the former is to introduce suitable auxiliary variables to facilitate construction of high order stable schemes for a large class of gradient flows. We propose a new technique to treat the coupling terms involved in the crystal growth model, and introduce suitable stabilization terms to result in totally decoupled schemes, which satisfy a discrete energy law without affecting the convergence order. A delicate implementation demonstrates that the proposed schemes can be realized in a very efficient way. That is, it only requires solving four linear elliptic equations and a simple algebraic equation at each time step. A detailed comparison with existing schemes is given, and the advantage of the new schemes is emphasized. As far as we know this is the first second-order scheme that is totally decoupled, linear, unconditionally stable for the dendritic crystal growth model with variable mobility parameter.< Réduire

Mots clés en anglais

Dendritic crystal growth

Phase-field

Time-stepping schemes

Unconditional stability

URI

https://oskar-bordeaux.fr/handle/20.500.12278/172364

DOI

http://dx.doi.org/10.1016/j.camwa.2022.01.017

Unités de recherche

Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295

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New efficient time-stepping schemes for the anisotropic phase-field dendritic crystal growth model

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Résumé en anglais

Mots clés en anglais

URI

DOI

Unités de recherche