Abstract
Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of different components that require additional degrees of freedom for representation in computational fluid dynamics. It is challenging to construct an accurate and efficient numerical algorithm to faithfully represent multiscale flow physics across different regimes. In this paper, a unified gas-kinetic scheme (UGKS) is developed to study non-equilibrium multicomponent gaseous flows. Based on the Boltzmann kinetic equation, an analytical space-time evolving solution is used to construct the discretized equations of gas dynamics directly according to cell size and scales of time steps, i.e., the so-called direct modeling method. With the variation in the ratio of the numerical time step to the local particle collision time (or the cell size to the local particle mean free path), the UGKS automatically recovers all scale-dependent flows over the given domain and provides a continuous spectrum of the gas dynamics. The performance of the proposed unified scheme is fully validated through numerical experiments. The UGKS can be a valuable tool to study multiscale and multicomponent flow physics.
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Project supported by the National Natural Science Foundation of China (Nos. 11772281, 91530319, and 11521091) and the Hong Kong Research Grant Council (Nos. 16207715 and 16206617)
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Xiao, T., Xu, K. & Cai, Q. A unified gas-kinetic scheme for multiscale and multicomponent flow transport. Appl. Math. Mech.-Engl. Ed. 40, 355–372 (2019). https://doi.org/10.1007/s10483-019-2446-9
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DOI: https://doi.org/10.1007/s10483-019-2446-9