A diffuse-interface lattice Boltzmann method for the dendritic growth with thermosolutal convection

TL;DR

This paper introduces a diffuse-interface lattice Boltzmann method for simulating dendritic growth with thermosolutal convection, simplifying interface treatment and accurately capturing complex solid-liquid interactions.

Contribution

It develops a novel diffuse-interface LB method that unifies phase-field, concentration, temperature, and fluid flow models for dendritic growth simulation.

Findings

Numerical results agree well with previous studies.

The method effectively models complex fluid-solid interfaces.

Simulations demonstrate accurate dendritic growth patterns.

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 replaced by a thin but nonzero thickness diffuse interface, which is described by the order parameter governed by the phase-field equation for the dendritic growth. The governing equations for solute and heat transfer are modified such that the previous special treatments for source term can be avoided. 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 developed for the phase-field equation, concentration equation, temperature equation and the Navier-Stokes equations in a unified framework. Finally, to test the present diffuse-interface LB method, we performed some simulations of the dendritic growth, and found that the numerical results are in good agreements with some previous works.