Improved standard thermal lattice Boltzmann model with hybrid recursive regularization for compressible laminar and turbulent flows

Abstract

Based on recent work by Guo et al. [“An efficient lattice Boltzmann method for compressible aerodynamics on D3Q19 lattice,” J. Comput. Phys. 418, 109570 (2020)], an improved thermal hybrid recursive regularized lattice Boltzmann model (iHRR-ρ) on a regular lattice is developed for two- and three-dimensional compressible laminar and turbulent flows. To enhance the numerical stability in a broad range of Courant–Friedrichs–Lewy numbers and in under-resolved simulations, a new equilibrium density distribution function is proposed to enlarge its positivity region in the Mach–temperature plane. An embedded hybridizing procedure is introduced in the quasi-symmetry correction terms, which allow for a decoupled treatment of unphysical modes and physical under-resolved turbulent scales on coarse grids. To handle compressible turbulent flows, the under-resolved scales are modeled using the original hybrid recursive regularized collision model given by Jacob et al. [“A new hybrid recursive regularised Bhatnagar–Gross–Krook collision model for Lattice Boltzmann method-based large eddy simulation,” J. Turbul. 19, 1051–1076 (2018)] equipped with Vreman’s subgrid model for the large-eddy simulation. The validity and accuracy of the present method for laminar and turbulent compressible flows are assessed by considering six test cases: (I) viscous shock wave internal structure, (II) isentropic vortex convection in a supersonic regime, (III) non-isothermal acoustic pulse, (IV) vortex–shock wave interaction, (V) supersonic flow over NACA airfoil at Re = 10 000 and Ma = 1.5, and (VI) compressible Taylor–Green vortex at Ma = 0.29.