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

A new low-Mach algorithm based on thermal Lattice Boltzmann method (LBM) is proposed aiming at reducing the computational cost of thermal flow simulations in low Mach number limit.Considering the time-step restriction of fully compressible solvers, the Low Mach Number Approximation (LMNA) allows to accelerate significantly the simulations by re-scaling the acoustic speed to the same order of the velocity of the fluid motion when calculating the time-step.The proposed method is inspired by the similarity between the artificial compressibility method and isothermal LBM, and is further extended to thermal counterpart.It must be emphasized that this kind of low-Mach acceleration strategy is a general form and can be easily applied to other thermal LB methods.The present method overcomes the drawback of classical PGS (Pressure Gradient Scaling) method due to the pressure gradient changing. The new algorithm is validated by benchmarking the code on various well-documented academic test cases in laminar (1D gravity column, 2D rising thermal bubble, 2D differentially heated square cavity) and turbulent (Taylor Green Vortex and 3D heated cylinder) regimes.All the results show excellent agreement with reference data of the literature and demonstrate high computational efficiency.