کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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472060 | 698685 | 2016 | 15 صفحه PDF | دانلود رایگان |

A lattice-Boltzmann (LB) scheme, based on the Bhatnagar–Gross–Krook (BGK) collision rules is developed for a phase-field model of alloy solidification in order to simulate the growth of dendrites. The solidification of a binary alloy is considered, taking into account diffusive transport of heat and solute, as well as the anisotropy of the solid–liquid interfacial free energy. The anisotropic terms in the phase-field evolution equation, the phenomenological anti-trapping current (introduced in the solute evolution equation to avoid spurious solute trapping), and the variation of the solute diffusion coefficient between phases, make it necessary to modify the equilibrium distribution functions of the LB scheme with respect to the one used in the standard method for the solution of advection–diffusion equations. The effects of grid anisotropy are removed by using the lattices D3Q15 and D3Q19 instead of D3Q7. The method is validated by direct comparison of the simulation results with a numerical code that uses the finite-difference method. Simulations are also carried out for two different anisotropy functions in order to demonstrate the capability of the method to generate various crystal shapes.
Journal: Computers & Mathematics with Applications - Volume 71, Issue 9, May 2016, Pages 1784–1798