Three-dimensional lattice Boltzmann models for solid-liquid phase change

TL;DR

This paper introduces 3D lattice Boltzmann models, both MRT and SRT, for simulating solid-liquid phase change, demonstrating improved accuracy of the MRT model in capturing phase interfaces and analyzing effects of physical parameters.

Contribution

The paper develops and validates new 3D MRT and SRT lattice Boltzmann models for solid-liquid phase change, with the MRT model showing superior accuracy.

Findings

MRT model more accurately captures phase interfaces than SRT.

Validation against analytical and 2D numerical results confirms model reliability.

Influence of Rayleigh and Prandtl numbers on melting process analyzed.

Abstract

A three-dimensional (3 D) multiple-relaxation-time (MRT) and a 3 D single-relaxation-time (SRT) lattice Boltzmann (LB) models are proposed for the solid-liquid phase change. The enthalpy conservation equation can be recovered from the present models. The reasonable relationship of the relaxation times in the MRT model is discussed. Both One-dimensional (1 D) melting and solidification with analytical solutions are respectively calculated by the SRT and MRT models for validation. Compared with the SRT model, the MRT one is more accurate to capture the phase interface. The MRT model is also verified with other published two-dimensional (2 D) numerical results. The validations suggest that the present MRT approach is qualified to simulate the 3 D solid-liquid phase change process. Furthermore, the influences of Rayleigh number and Prandtl number on the 3 D melting are investigated.