Lattice Boltzmann Method Simulation of 3-D Natural Convection with Double MRT Model

TL;DR

This paper introduces a novel three-dimensional double MRT model within the Lattice Boltzmann Method to simulate natural convection, demonstrating high accuracy across various Rayleigh numbers and complex boundary conditions.

Contribution

It is the first to propose a 3D double MRT model for fluid flow and heat transfer in natural convection, expanding LBM capabilities for complex 3D problems.

Findings

Results agree well with benchmark solutions and experiments.

The model captures complex 3D natural convection behaviors.

Demonstrates robustness across different boundary conditions.

Abstract

Multiple-relaxation-time model (MRT) has more advantages than the many others approaches in the Lattice Boltzmann Method (LBM). Three-dimensional double MRT model is proposed for the first time for fluid flow and heat transfer simulation. Three types of cubic natural convection problems are solved with proposed method at various Rayleigh numbers. Two opposite vertical walls on the left and right are kept at different temperatures for all three types, while the remained four walls are either adiabatic or have linear temperature variations. For the first two types of cubic natural convections that four walls are either adiabatic or vary linearly, the present results agreed very well with the benchmark solutions or experimental results in the literature. For the third type of cubic natural convection, the front and back surfaces has linearly variable temperature while the bottom and top surface are adiabatic. The results from the third type exhibited more general three-dimensional characters.