A new hybrid lattice-Boltzmann method for thermal flow simulations in low-Mach number approximation

Abstract

A new low-Mach algorithm for the thermal lattice Boltzmann method (LBM) is proposed aiming at reducing the computational cost of thermal flow simulations in the low Mach number limit. The well-known low Mach number approximation is adopted to accelerate the simulations by enlarging the time step through re-scaling the psuedoacoustic speed to the same order of the fluid motion velocity. This specific process is inspired by the similarity between the artificial compressibility method and the isothermal LBM and is further extended to its thermal counterpart. It must be emphasized that such low-Mach acceleration strategy is in a general form, thus can be easily applied to other compressible LB methods. The present method overcomes the drawback of the classical pressure gradient scaling method due to the pressure gradient changing. The new algorithm is validated by various well-documented academic test cases in laminar [one dimensional gravity column, 2D (two dimensional) rising thermal bubble, and 2D differentially heated square cavity] and turbulent [3D (three dimensional) Taylor–Green vortex and 3D heated cylinder] regimes. All the results show excellent agreement with the reference data and high computational efficiency.