An efficient discrete unified gas-kinetic scheme for compressible thermal flows

In this paper, an efficient discrete unified gas-kinetic scheme (DUGKS) is developed for compressible thermal flows based on the total energy kinetic model for natural convection with a large relative temperature difference. A double distribution function model is designed with the second distribution representing the total energy. This efficient DUGKS enables the simulation of compressible thermal flows, governed by the compressible Navier-Stokes-Fourier system, using only a seventh-order, off-lattice Gauss-Hermite quadrature (GHQ) D3V27A7 combined with a fifth-order GHQ D3V13A5. The external force is included by truncated Hermite expansions. Based on the Chapman-Enskog approximation and Hermite projection, we propose a systematic approach to derive the discrete kinetic boundary conditions for the density and total energy distribution functions. The discrete kinetic boundary treatments are provided for the no-slip boundary condition, Dirichlet boundary condition and Neumann boundary condition. To validate our scheme, we perform simulations of steady natural convection ( R a = 10(3) - 10(6)) in two- and three-dimensional cavities with differentially heated sidewalls and a large temperature difference ( epsilon = 0.6), where the Oberbeck-Boussinesq approximation is invalid. The results demonstrate that the current efficient DUGKS is robust and accurate for thermal compressible flow simulations. With the D3V27A7 and D3V13A5 off-lattice discrete particle velocity model, the computational efficiency of the DUGKS is improved by a factor of 3.09 when compared to the previous partial energy kinetic model requiring the ninth-order Gauss-Hermite quadrature.