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Abstract
One of the central problems in the study of rarefied gas dynamics is to find the steadystate solution of the Boltzmann equation quickly. When the Knudsen number is large, i.e. the system is highly rarefied, the conventional iterative scheme can lead to convergence within a few iterations. However, when the Knudsen number is small, i.e. the flow falls in the nearcontinuum regime, hundreds of thousands iterations are needed, and yet the “converged” solutions are prone to be contaminated by accumulated error and large numerical dissipation. Recently, based on the gas kinetic models, the implicit unified gas kinetic scheme (UGKS) and its variants have significantly reduced the number of iterations in the nearcontinuum flow regime, but still much higher than that of the highly rarefied gas flows. In this paper, we put forward a general synthetic iterative scheme (GSIS) to find the steadystate solutions of rarefied gas flows within dozens of iterations at any Knudsen number. The key ingredient of our scheme is that the macroscopic equations, which are solved together with the Boltzmann equation and help to adjust the velocity distribution function, not only asymptotically preserve the NavierStokes limit in the framework of ChapmanEnskog expansion, but also contain the Newton's law for stress and the Fourier's law for heat conduction explicitly. For this reason, like the implicit UGKS, the constraint that the spatial cell size should be smaller than the mean free path of gas molecules is removed, but we do not need the complex evaluation of numerical flux at cell interfaces. What's more, as the GSIS does not rely on the specific collision operator, it can be naturally extended to quickly find converged solutions for mixture flows and even flows involving chemical reactions. These two superior advantages are expected to accelerate the slow convergence in the simulation of nearcontinuum flows via the direct simulation Monte Carlo method and its lowvariance version.
Original language  English 

Article number  109245 
Number of pages  28 
Journal  Journal of Computational Physics 
Volume  407 
Early online date  9 Jan 2020 
DOIs  
Publication status  Published  15 Apr 2020 
Keywords
 asymptotic preserving
 fast convergence
 general synthetic iterative scheme
 linearized Boltzmann equation
 rarefied gas flow
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 1 Finished

Efficient PoreScale Kinetic Simulation of Gas Flows in UltraTight Porous Media (EPSKS) MSCAIF2017
Zhang, Y.
European Commission  Horizon 2020
15/07/18 → 14/07/20
Project: Research