A Diffuse-Interface Lattice Boltzmann Method for the Dendritic Growth with Thermosolutal Convection

Abstract

In this work, we proposed a diffuse-interface model for the dendritic growth with thermosolutal convection. In this model, the sharp boundary between the fluid and solid dendrite is firstly replaced by a thin but nonzero thickness diffuse interface, which is described by the order parameter, and the diffuse-interface based governing equations for the dendritic growth are presented. To solve the model for the dendritic growth with thermosolutal convection, we also developed a diffuse-interface multi-relaxation-time lattice Boltzmann (LB) method. In this method, the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction, and the treatment on the complex fluid-solid interface can be avoided. In addition, four LB models are designed for the phase-field equation, concentration equation, temperature equation and the Navier-Stokes equations in a unified framework. Finally, we performed some simulations of the dendritic growth to test the present diffuse-interface LB method, and found that the numerical results are in good agreements with some previous works.