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A coupled discrete unified gas-kinetic scheme for Boussinesq flows. (English) Zbl 1390.76775
Summary: Recently, the discrete unified gas-kinetic scheme (DUGKS) [the third author et al., “Discrete unified gas kinetic scheme for all Knudsen number flows: low-speed isothermal case”, Phys. Rev. E (3) 88, No. 3, Article ID 033305, 11 p. (2013; doi:10.1103/physreve.88.033305)] 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.

MSC:
76M28 Particle methods and lattice-gas methods
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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