Accuracy and efficiency comparison of the fluid flow and heat transfer simulations by discrete velocity models of LBM and FDLBM regardless of grid clustering

This paper is dedicated to the comparison of discrete velocity models (DVM) used for the simulation of heat transfer and fluid flows in the lattice Boltzmann method (LBM). In this study, the discrete velocity models of D2Q9 and D2Q8 in which particle velocity vectors are eight are used in simulating four benchmark problems. An enhancement in the stability of the single relaxation time (SRT) model for problems is facilitated by solving the continuous Boltzmann equation, and its application in efficiently addressing conductive heat transfer/fluid flow benchmark problems is expanded by utilizing the finite difference methods paired with the lattice Boltzmann method (FDLBM). To generalize the paper’s conclusion more accurately, the LBM with two-relaxation time (TRT-LBM) is included in all comparisons. A D2Q5 scheme is also considered to understand how it would address heat transfer problems compared to the ones presented. Moreover, an improvement in the accuracy of the FDLBM for some cases is assisted through the integration of the finite differentiation mechanism with the Runge–Kutta method. A series of unsteady and steady problems were numerically solved to validate the introduced methods. The outcomes affirmed that the proposed FDLBM algorithm procures more stable and robust results compared to those derived from the DVMs of SRT-LBM devoid of filtering techniques. Notably, the FDLBM method achieves this increased accuracy without introducing additional complexity to the SRT model by resorting to nonuniform grids. The decision to exclude more complex methods stems from their requirement for refined computational grids. To ascertain the numerical stability and accuracy of the devised algorithm, a comparative analysis was performed with analytical results or other numerical methods. The simulations underscored the efficacy of the current method, showcasing commendable harmony with analytical solutions and other numerical strategies.