A numerical analysis of an anisotropic phase-field model for binary-fluid mixtures in the presence of magnetic-field

Aziz Belmiloudi (1) , Amer Rasheed (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Mathematics, Lahore University of Management Sciences, , [e-mail],

In this paper we propose a numerical scheme and perform its numerical analysis devoted to an anisotropic phase-field model with convection under the influence of magnetic field for the isother-mal solidification of binary mixtures in two-dimensional geometry. Precisely, the numerical stability and error analysis of this approximation scheme which is based on mixed finite-element method are performed. The particular application of a nickelcopper (NiCu) binary alloy, with real physical parameters , is considered. The study substantiates a good agreement between the numerical and theoretical results, and demonstrates the efficiency of the presented method.

Mots clés: Mixed finite elements; stability and error analysis; anisotropic phase-field; dendritic so- lidification; binary alloys; uid ow; magnetic-field.

Domaines: Analyse numérique [math.NA]

Aziz Belmiloudi, Amer Rasheed. A numerical analysis of an anisotropic phase-field model for binary-fluid mixtures in the presence of magnetic-field. 2015. ⟨hal-01364872⟩