Implicit Discrete Unified Gas Kinetic Scheme for Steady Flows of Binary Gas Mixtures (Communications in Computational Physics, 2025)
An implicit discrete unified gas kinetic scheme (DUGKS) is developed formultiscale steady flows of binary gas mixtures by solving the Andries-Aoki-Perthamekinetic model (AAP). To ensure the high convergence efficiency for all flow regimes,the microscopic and macroscopic asynchronous iterative strategies are used, whereboth the macroscopic and microscopic equations are solved iteratively by the Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method. The macroscopic iteration is conducted to solve the macroscopic governing equations containing source terms as animplicit prediction step to evaluate the local equilibrium state of the microscopic evolution, and the macroscopic flux used in the macroscopic iteration is obtained by takingmoments of the distribution function. Besides, to keep the asymptotic preserving properties, the numerical flux across the cell interface is reconstructed by the characteristicsolution of the kinetic governing equations for both species like the explicit DUGKS fora single gas. Several numerical tests, including the Couette flow, the lid-driven cavityflow, and the flows through a slit of different mixtures, are simulated to verify the accuracy and efficiency of the present scheme for binary mixtures. Furthermore, comparedto the explicit DUGKS, the implicit scheme improves the computational efficiency by1-2 orders of magnitude.
Keywords: Implicit scheme; discrete unified gas kinetic scheme; binary gas mixtures; multiscale gas flows.