Conserved method for specified heat flux boundary in UGKS simulation of microscale gas flow

Abstract

The unified gas kinetic scheme (UGKS) is a powerful method to simulate microscale gas flows. However, due to the lack of corresponding specified heat flux boundary (SHFB) treatment, there is great difficulty for UGKS to simulate problem with SHFB. In this paper, a SHFB treatment for UGKS is proposed based on gas kinetic theory. In the proposed boundary treatment, the heat flux term is directly added into the gas kinetic conservation equation of heat flux on boundary. In this conservation equation, the heat flux transferring from gas to the boundary is calculated using an extrapolated distribution function of inside gas, and the heat flux transferring form boundary to the gas is calculated using an equilibrium rebounding distribution function. Using the conservation equation of mass on boundary to close conservation equations, the gas density and temperature terms for rebounding gas distribution function can be calculated simultaneously. Distribution function on SHFB is reconstructed using rebounding gas distribution function and extrapolated distribution function of inside gas. Fluxes of gas distribution function and macro variables on SHFB is calculated with the reconstructed distribution function. Typical benchmark cases including steady and unsteady Fourier flow, steady Couette flow, pressure-driven flow, cavity flow and supersonic flow around square cylinder are tested to validate the proposed boundary treatment. The validations prove the accuracy, reliability and universality of the proposed method.