The reconstructed thermal lattice Boltzmann flux solver and its applications for simulations of thermal flows

TL;DR

This paper introduces a reconstructed thermal lattice Boltzmann flux solver (RTLBFS) that clarifies its stability mechanism for high Rayleigh number thermal flows, demonstrating comparable performance to the original TLBFS with improved understanding.

Contribution

The paper derives macroscopic equations for TLBFS, proposes RTLBFS via finite volume method, and elucidates the stability mechanism for high Rayleigh number thermal flows.

Findings

RTLBFS has similar stability, accuracy, and efficiency as TLBFS.

Numerical dissipation terms are key to stability in high Rayleigh flows.

RTLBFS provides a clear mechanism for numerical stability.

Abstract

The thermal lattice Boltzmann flux solver (TLBFS) has been proposed to overcome the drawbacks of the thermal lattice Boltzmann models. However, as a weakly compressible model, its mechanism of good numerical stability for high Rayleigh number thermal flows is still unclear. To reveal the mechanism, the present paper firstly 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 analyses 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. Moreover, the present RTLBFS shows a clear mechanism to achieve good numerical stability for high Rayleigh number flows.