A ghost-cell discrete unified gas kinetic scheme for thermal flows with heat flux at curved interface. (December 2020) - Tao, Shi; He, Qing; Chen, Baiman; Qin, Frank G.F.; Lin, Yousheng
Highlights: The DUGKS is extended for simulating thermal flow with heat flux interface. Curved interface is well handled by the ghost-cell method. Strang-Splitting scheme is used to conveniently incorporate the buoyancy force. The method is applicable to the non-circular interface and Robin condition. 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.