Lattice Boltzmann Method Simulation of 3-D Melting Using Double MRT Model with Interfacial Tracking Method

TL;DR

This paper introduces a novel 3-D melting simulation method combining double MRT Lattice Boltzmann models with an interfacial tracking technique, validated against analytical solutions and applied to convection-controlled melting scenarios.

Contribution

First application of double MRT Lattice Boltzmann models with interfacial tracking for 3-D melting simulation, improving accuracy and stability in complex melting problems.

Findings

Numerical results agree well with analytical solutions.

The method effectively captures melting front dynamics under natural convection.

Rayleigh number significantly influences melting front velocity.

Abstract

Three-dimensional melting problems are investigated numerically with Lattice Boltzmann method (LBM). Regarding algorithm's accuracy and stability, Multiple-Relaxation-Time (MRT) models are employed to simplify the collision term in LBM. Temperature and velocity fields are solved with double distribution functions, respectively. 3-D melting problems are solved with double MRT models for the first time in this article. The key point for the numerical simulation of a melting problem is the methods to obtain the location of the melting front and this article uses interfacial tracking method. The interfacial tracking method combines advantages of both deforming and fixed grid approaches. The location of the melting front was obtained by calculating the energy balance at the solid-liquid interface. Various 3-D conduction controlled melting problems are solved firstly to verify the numerical method. Liquid fraction tendency and temperature distribution obtained from numerical methods agree with the analytical results well. The proposed double MRT model with interfacial tracking method is valid to solve 3-D melting problems. Different 3-D convection controlled melting problems are then solved with the proposed numerical method. Various locations of the heat surface have different melting front moving velocities, due to the natural convection effects. Rayleigh number's effects to the 3-D melting process is discussed.