On improvements of simplified and highly stable lattice Boltzmann method: Formulations, boundary treatment, and stability analysis

Summary In this paper, we present a detailed report on a revised form of simplified and highly stable lattice Boltzmann method (SHSLBM) and its boundary treatment as well as stability analysis. The SHSLBM is a recently developed scheme within lattice Boltzmann framework, which utilizes lattice properties and relationships given by Chapman‐Enskog expansion analysis to reconstruct solutions of macroscopic governing equations recovered from lattice Boltzmann equation and resolved in a predictor‐corrector scheme. Formulations of original SHSLBM are slightly adjusted in the present work to facilitate implementation on body‐fitted mesh. The boundary treatment proposed in this paper offers an analytical approach to interpret no‐slip boundary condition, and the stability analysis in this paper fixes flaws in previous works and reveals a very nice stability characteristic in high Reynolds number scenarios. Several benchmark tests are conducted for comprehensive evaluation of the boundary treatment and numerical validation of stability analysis. It turns out that by adopting the modifications suggested in this work, lower numerical error can be expected. This paper presents a revised version of simplified and highly stable lattice Boltzmann method (SHSLBM). Compared to the original scheme of SHSLBM, the revised scheme is more compact in form, more efficient in computation, more accurate in handling body‐fitted mesh, and more robust in interpreting physical boundary conditions. The revised von Neumann stability analysis of SHSLBM reveals that the method is highly stable at high Reynolds number scenario, which makes it more competitive than conventional lattice Boltzmann method (LBM).