Analysis and reconstruction of the thermal lattice Boltzmann flux solver

Abstract

The thermal lattice Boltzmann flux solver (TLBFS) has been proposed as an alternative method to overcome the drawbacks of thermal lattice Boltzmann models. However, as a weakly compressible model, its mechanism of the good numerical stability for high Rayleigh number thermal flows is still unclear. To reveal the mechanism, the present article first derives the macroscopic equations of TLBFS (MEs-TLBFS) with actual numerical dissipation terms by approximating its computational process. By solving MEs-TLBFS with the finite volume method, the reconstructed TLBFS (RTLBFS) is proposed. Detailed analyzes prove that these actual numerical dissipation terms are the mechanism of the good numerical stability of TLBFS for high Rayleigh number thermal flows.More detailed numerical tests indicate RTLBFS has similar performances as TLBFS for stability, accuracy, and efficiency, which further validates the mechanism of the good numerical stability of TLBFS for high Rayleigh number thermal flows.

Development of a Fourier‐expansion based differential quadrature method with lattice Boltzmann flux solvers: Application to incompressible isothermal and thermal flows

“…The resulting solver inherits all the merits of both conventional N-S solvers and LBM, including flexility on computational meshes, simple boundary condition implementations, no need for pressure-velocity decoupling, convenient flux evaluation, and so forth. As shown by Lu et al, 4,5 the recovered macroscopic equations of LBFS and thermal LBFS (TLBFS) are weakly compressible models in the low-Mach number limits. Generally, numerical instabilities can occur when directly solving those weakly compressible models, so extra stabilization treatments are necessary.…”