A coupled high-order implicit-explicit flux reconstruction lattice Boltzmann method for nearly incompressible thermal flows

Abstract

In this paper, based on the double distribution function (DDF) model and the Boussinesq approximation, a high-order implicit-explicit flux reconstruction thermal lattice Boltzmann method (FRTLBM) is proposed for simulating nearly incompressible thermal flows. Two discrete velocity Boltzmann equations (DVBEs), one governing the flow field and the other governing the temperature field, are solved by using a high-order flux reconstruction scheme for spatial discretization and a second-order implicit-explicit Runge-Kutta scheme (IMEX RK) for time discretization in the generalized curvilinear coordinates with uniform and non-uniform grids. Numerical validations of the proposed method are implemented by simulating (a) porous plate problem, (b) natural convection in a square cavity, (c) Rayleigh-Bénard convection, (d) natural convection in a concentric annulus and (e) mixed heat transfer from a heated circular cylinder. Numerical results demonstrate that the present method can achieve the high-order accuracy and it is stable and accurate even at the relatively high Rayleigh number (Ra = 107 and 108). The present method is efficient due to the small amount of mesh, the simple algorithm and the time step unlimited by the relaxation time. Since the rescontruction is conducted in a single cell, the present method is compact for parallel computing. Moreover, the present method has a good adaptability of complicated geometries.