A ghost-cell discrete unified gas kinetic scheme for thermal flows with heat flux at curved interface

Abstract

The discrete unified gas kinetic scheme (DUGKS) is advanced for simulating thermal convections with curved heat flux condition using the ghost-cell (GC) approach. The fluid flow and temperature field combined under the Boussinesq approximation are solved by the double-population model. The ghost-cell immersed boundary method is applied to the curved heat-flux interface, where fictitious cells are set in the solid domain. The information at the centers of those cells is extrapolated from the fluid-solid interface and the neighboring flow. The heat-flux boundary condition at the interface can then be incorporated into the solution of the entire thermal flow. Note that the extrapolation/interpolation involved in the GC-DUGKS is accomplished through a sharp interface manner. Therefore, the difficulty in handling the heat-flux boundary condition for the diffuse-type immersed boundary methods due to the cross contamination is removed. Furthermore, the thermal buoyancy force is conveniently combined with the governing equation by the Strang-splitting scheme. Simulations of several well-established convection-diffusion flow problems with heat flux at the curved interface are performed to validate the present GC-DUGKS. The results demonstrate the accuracy and feasibility of the method.