Lattice Boltzmann simulation of thermal flows with complex geometry using a single-node curved boundary condition

Abstract

Abstract Thermal curved boundary condition is proposed for lattice Boltzmann simulation of thermal flows with complex geometry. In this scheme, the unknown temperature distribution function at the boundary point is interpolated by the distribution functions at the interface and a further fluid point. The former one is decomposed into the equilibrium and non-equilibrium parts. The equilibrium part can be determined by the boundary conditions, while the anti-bounce back rule is applied to obtain the non-equilibrium part, i.e., the key point for the present scheme. On the other hand, the latter one streams directly from the boundary point. Since information of a single fluid point is needed, the computation involved in the present scheme is completely localized. Another advantage of the method is for the second-order convergence rate in simulations, preserving the overall accuracy of the lattice Boltzmann method. Four thermal problems are used to validate the present scheme. The first two cases, i.e., thermal Couette flow with wall injection, and natural convection in a square cavity are performed to verify the second-order accuracy. It is further applied to the other three thermal flows with complex geometries, including the natural convections in a cavity with a cylinder and in a concentric annulus, and a hot cylinder moving in a channel. Good agreement can be found between the present results and those available in the literature. The five test cases together demonstrate that the present method retains the property of local computation and second-order accuracy simultaneously in the simulations.