A curved lattice Boltzmann boundary scheme for thermal convective flows with Neumann boundary condition. (April 2020)

• Record Type: Journal Article
• Authors: Tao, Shi; Xu, Ao; He, Qing; Chen, Baiman; Qin, Frank G.F.
• Is Part Of: International journal of heat and mass transfer. Volume 150(2020)
• Publication Date: 2020-04
• Subjects: Lattice Boltzmann method -- Thermal flows -- Curved boundary condition -- Heat flux at interface -- Second-order accuracy; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2020.119345
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: A Neumann boundary scheme is proposed for thermal flows with heat flux at the interface. Only lattice link interpolation involved contributes to an easy implementation procedure. Fully second-order accuracy can be achieved for complex geometries. Versatility and efficiency of present scheme is validated in the simulations. Abstract: We propose a curved lattice Boltzmann boundary scheme for thermal convective flows with Neumann boundary condition. The distribution function at the fluid-solid intersection node is obtained to accomplish the interpolation of unknown temperature distribution function at the boundary point. Specifically, the distribution function is first extrapolated from the fluid point along the lattice link; and then, the one in the opposite direction is evaluated by the anti-bounce back rule with wall temperature, which can be further determined by the specified Neumann boundary condition at the fluid-solid interface. The advantage of our scheme is that the involved inter/extrapolations are completely link-based, resulting in a quite efficient implementation procedure. Furthermore, our scheme has second-order spatial accuracy, and we verified in four numerical examples where analytical solutions are available: the heat transfer in a channel with a sinusoidal temperature gradient, the thermal diffusion in an annulus, and the conjugate heat transfer for these two cases. To further validate our scheme for thermal convective flow problems with complex geometries, we simulate the natural convection in an annulus, the thermal flow past a cylinder, and the mixed convection in a lid-driven cavity with a circular enclosure. The simulation results are consistent with existing benchmark data obtained by other methods.