Abstract
Based on the lattice Boltzmann method (LBM), the lattice Boltzmann flux solver (LBFS), which combines the advantages of conventional Navier–Stokes solvers and lattice Boltzmann solvers, was proposed recently. Specifically, LBFS applies the finite volume method to solve the macroscopic governing equations which provide solutions for macroscopic flow variables at cell centers. In the meantime, numerical fluxes at each cell interface are evaluated by local reconstruction of LBM solution. In other words, in LBFS, LBM is only locally applied at the cell interface for one streaming step. This is quite different from the conventional LBM, which is globally applied in the whole flow domain. This paper shows three different versions of LBFS respectively for isothermal, thermal and compressible flows and their relationships with the standard LBM. In particular, the performance of isothermal LBFS in terms of accuracy, efficiency and stability is investigated by comparing it with the standard LBM. The thermal LBFS is simplified by using the D2Q4 lattice velocity model and its performance is examined by its application to simulate natural convection with high Rayleigh numbers. It is demonstrated that the compressible LBFS can be effectively used to simulate both inviscid and viscous flows by incorporating non-equilibrium effects into the process for inviscid flux reconstruction. Several numerical examples, including lid-driven cavity flow, natural convection in a square cavity at Rayleigh numbers of 107 and 108 and transonic flow around a staggered-biplane configuration, are tested on structured or unstructured grids to examine the performance of three LBFS versions. Good agreements have been achieved with the published data, which validates the capability of LBFS in simulating a variety of flow problems.
Highlights
The lattice Boltzmann method (LBM) was developed from the lattice gas cellular automata (LGCA) method, aiming to remove its statistical noise and limitation to use Boolean numbers
As the equilibrium distribution function is the function of conservative variables, we just need to calculate the conservative variables at the cell interface first
The LBM is applied locally in one streaming time step, which is different from the global application of the conventional LBM
Summary
Has been developed into an effective and efficient solver for simulating a variety of complex fluid flow problems, such as isothermal and thermal flows [9,10,12], multi-phase and multi-component flows [8,13,14,15], compressible flows [16,17,18] and micro non-equilibrium flows [19,20,21] To effectively study these problems, a large number of LBE-based methods have been continuously proposed and refined [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Both single relaxation time (SRT) model (lattice Bhatnagar–Gross–Krook (LBGK) model) [4] and multiple-relaxation-time (MRT) model [22]
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