A Multiple-Grid Lattice Boltzmann Method for Natural Convection under Low and High Prandtl Numbers

Seyed Amin Nabavizadeh,Mohsen Eshraghi,Himel Barua,Sergio D Felicelli

doi:10.3390/fluids6040148

Seyed Amin Nabavizadeh, Mohsen Eshraghi + Show 2 more

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https://doi.org/10.3390/fluids6040148

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Abstract

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations.

Highlights

The lattice Boltzmann (LB) method is considered a robust numerical method to solve fluid flow [1]
The results obtained with the conventional single relaxation time (SRT)-LB model were validated against the results reported in references [40,42]
The streamlines and isotherms obtained with the LB model are plotted in Figure 3, which is in qualitative agreement with [40,42]

Summary

Introduction

The lattice Boltzmann (LB) method is considered a robust numerical method to solve fluid flow [1]. A distribution function f α (x, t) describes the motion and properties of the fluid, which represents the probability of finding a particle at lattice position x at time t in direction α. The particle motion is restricted to specific discrete directions that are necessary for modeling hydrodynamic behavior on the macroscopic scale [2]. The distribution functions of fluid particles propagate along with the discrete directions from one lattice node to another in the streaming step. The particle distribution function relaxes back towards the local equilibrium distribution function through the collision step [3]. The macroscopic fluid properties can be recovered through the summation of the distribution function [4]. The method becomes unstable at high Reynolds numbers [5,6,7]

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