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Development and numerical validations of a two-dimensional cumulant-driven thermal lattice Boltzmann method

Year: 2025
Type: article
Abstract: A novel cumulant-based lattice Boltzmann method (CuLBM) has been developed for the two-dimensional (2D) D2Q9 lattice model to analyze velocity and the D2Q5 lattice model for temperature fields. The computer code has been bench-marked for natural convection in fluid flow and heat transfer within a side-heated square cavity for the Newtonian and non-Newtonian power-law and Bingham fluids, utilizing compute unified device architecture (CUDA) C/C++ through graphics processing unit (GPU) computing. This study details the mathematical formulation of the cumulant-based 2D lattice Boltzmann method for the velocity and passive scalar fields. A wide range of flow Rayleigh numbers, from R a = 10 3 to R a = 10 9 , has been employed for the Newtonian fluids, for the non-Newtonian fluids the maximum R a = 10 6 for the various power-law index n = 0.6 to 1.4 and the Bingham numbers B n = 0 to 15, and results are presented in terms of streamlines, isotherms, velocity, temperature, local and average rate of heat transfer, and flow entropy generation. These validations demonstrate that the current two-dimensional CuLBM will be a superior option for solving convective heat transfer problems for the Newtonian and non-Newtonian complex fluids.
DOI: 10.1016/j.rineng.2025.106225
Language: English
Open Access status: gold
Estimated APC paid: $1,940
OpenAlex ID: W4412480510
FWCI: 2.666
Cites: 42
Cited by: 6
Related to: 10