Thermal lattice Boltzmann simulations of natural convection with complex geometry

Thermal boundary condition of lattice Boltzmann method to simulate natural convection embedded with complex solid object is proposed. This is achieved by denoting the closest nodes adjacent to the boundary in the fluid domain as boundary nodes of the flow domain. The temperature of the boundary node is obtained by linear interpolation between the temperature of the solid object and the second fluid node further away. Then distribution functions originates from the solid domain at the boundary nodes are modified using known distribution functions and correctors to satisfy the momentum and energy. The technique is examined by simulating thermal Couette flow with wall injection, transient thermal flow induced by an abruptly rotating heated ring and nature convection in an annulus between a square outer cavity and a circular inner cylinder. Numerical simulations indicate that this method is second order accurate, and all the numerical results are compatible with the benchmark solutions.

► Lattice Boltzmann method for natural convection with solid object is proposed.
► Two distribution functions are used to simulate dynamic and thermal fields.
► Boundary nodes are modified using known distribution functions and correctors.
► Transient and steady thermal flows are adopted to examine the present technique.
► Numerical simulations indicate that this method is second order accurate.