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Abstract

Adequate modeling of transport processes is of key importance when studying phase transformation kinetics. In this context, convection can affect characteristics of the solidification process and lead to new phenomena such as formation of freckles [1] or influence the underlying length scale of the microstructure [2]. Due to its paramount importance, convection effect on solidification has been the subject of a number of studies (see, e.g., [3-5] and references therein).

In this work, fluid dynamical equations for systems with a diffuse solid liquid interface are obtained using a volume averaging approach [4]. These equations satisfy the Galilean invariance and naturally lend themselves for the study with the lattice Boltzmann method (LBM). The LBM is well known for its flexibility in dealing with complex geometries, omnipresent in solidification phenomena (Fig.1). We consider different ways of imposing the standard no-slip boundary condition in diffuse interface models and show the existence of an optimum solid-liquid coupling parameter which minimizes the mean standard deviations from the sharp interface solution. A criterion is proposed to best approximate the sharp interface limit in the presence of multiple length scales [6].

[1] M. Glicksman, S. Coriell, G. McFadden, Annual Review of Fluid Mechanics 18, 307 (1986).

[2] I. Steinbach, Acta Materialia 57, 2640 (2009).

[3] V. Emsellem, P. Tabeling, Journal of Crystal Growth 166, 251 (1996).

[4] C. Beckermann, H.-J. Diepers, I. Steinbach, A. Karma, X. Tong, Journal of Computational Physics 154, 468 (1999).

[5] D. Medvedev, K. Kassner, Physical Review E 72, 056703 (2005).

[6] A. Subhedar, I. Steinbach, F. Varnik, submitted.