A coupled gas-kinetic BGK scheme for the finite volume lattice Boltzmann method for nearly incompressible thermal flows. (January 2021)

• Record Type: Journal Article
• Authors: Zhao, Zhangyan; Wen, Mengke; Li, Weidong
• Is Part Of: International journal of heat and mass transfer. Volume 164(2021)
• Publication Date: 2021-01
• Subjects: Gas kinetic scheme -- BGK -- Finite volume lattice Boltzmann method -- Thermal convective flows -- Natural convection; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2020.120584
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: A gas kinetic BGK scheme based thermal finite volume lattice Boltzmann method (GKSTFVLBM) is proposed. GKSTFVLBM achieves second order accuracy of both time and space in one step. GKSFVLBM is an accurate and reliable tool for incompressible thermal flows. Abstract: This work presents a coupled gas-kinetic Bhatnagar-Gross-Krook (BGK) scheme based finite volume lattice Boltzmann method (FVLBM) for nearly incompressible thermal flows. In the present formulation, a thermal lattice BGK model with double distribution functions coupled through the Boussinesq approximation is adopted. Compared with the conventional thermal finite volume/finite difference lattice Boltzmann schemes, the present method has two striking advantages. One is that the fluxes on cell interfaces are determined by the formal analytical solution of the lattice BGK equation rather than interpolation or solving the Riemann problem, which reduces numerical dissipation considerably. Another is that, an implicit collision of the lattice Boltzmann equations (LBE) is adopted to remove the time-step constrain from the relaxation time, which improves the efficiency for high Rayleigh number thermal flows. Additionally, the accuracy of the proposed scheme are validated by the numerical simulations of four test cases in two dimensions: (a) the thermal Couette flow with wall injection; (b) the natural convection in a square cavity with differently heated vertical walls; (c) the Rayleigh-Bénard convection in a rectangle heated from bottom; and (d) the turbulent Rayleigh-Bénard convection in a square cavity heated from bottom. The numerical results show that the present scheme has second-order accuracy and can be a reliable tool for incompressible thermal flows.