Lattice Boltzmann simulation of incompressible thermal convection using a cumulant-based double distribution function model

This study proposes a novel cumulant-based double distribution function (DDF) lattice Boltzmann method (LBM) for simulating incompressible thermal flows. Building on recent advances in cumulant collision operators, the proposed framework addresses the inherent accuracy limitations of the original cumulant LBM (CuLBM) in convective heat transfer simulations. The D2Q9 CuLBM integrates an improved forcing scheme that systematically adjusts higher-order cumulants to reduce numerical errors. A new D2Q5 CuLBM is concurrently developed for the temperature field and rigorously validated through asymptotic analysis, demonstrating its ability to recover the governing equation for thermal transport. Systematic numerical verification shows that the proposed D2Q9 CuLBM yields lower errors than the original formulation. Benchmark tests further indicate that the proposed D2Q5 CuLBM achieves improved accuracy compared with the original D2Q5 CuLBM. The coupled fluid-thermal model is validated through benchmark cases including thermal channel flow with wall injection and Rayleigh–Bénard convection, confirming its accuracy and stability. Moreover, the model exhibits notable numerical stability at a Reynolds number of 3.2 × 1 0 8 in thermal flows around square cylinders, with numerical accuracy at high Reynolds numbers confirmed using the two-dimensional lid-driven cavity flow. This work presents a novel cumulant-based framework for convective heat transfer simulations, positioning the CuLBM as a useful tool for thermal flow problems.