A coupled discrete unified gas-kinetic scheme for Boussinesq flows. (5th October 2015) - Wang, Peng; Tao, Shi; Guo, Zhaoli
Highlights: A coupled discrete unified gas-kinetic scheme for Boussinesq flows is developed. Kinetic boundary conditions for both velocity and temperature fields are proposed. The model is validated by the canonical Boussinesq flows with Rayleigh numbers up to. Present model has a remarkable numerical stability compared with the previous kinetic scheme. Abstract: Recently, the discrete unified gas-kinetic scheme (DUGKS) [Guo et al ., (2013) [6]] based on the Boltzmann equation is developed as a new multiscale kinetic method for isothermal flows. In this paper, a thermal and coupled discrete unified gas-kinetic scheme is derived for the Boussinesq flows, where the velocity and temperature fields are described independently. Kinetic boundary conditions for both velocity and temperature fields are also proposed. The proposed model is validated by simulating several canonical test cases, including the porous plate problem, the Rayleigh–Bénard convection, and the natural convection with Rayleigh number up to 10 10 in a square cavity. The results show that the coupled DUGKS is of second order accuracy in space and can well describe the convection phenomena from laminar to turbulent flows. Particularly, it is found that this new scheme has better numerical stability in simulating high Rayleigh number flows compared with the previous kinetic models.