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

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. • A new cumulant-based thermal lattice Boltzmann method (CuLBM) has been developed. • The method is implemented in CUDA C/C++ and executed on GPUs. • The model is validated for both Newtonian and non-Newtonian fluids under natural convection. • Simulations span a wide range of Ra up to 10 9 for the Newtonian and up to 10 6 for non-Newtonian fluids. • Results include detailed flow and thermal field visualizations showcasing the accuracy and versatility of CuLBM.