A BGK‐penalization‐based asymptotic‐preserving scheme for the multispecies Boltzmann equation |
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| Authors: | Shi Jin Qin Li |
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| Affiliation: | 1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China;2. Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China;3. Ministry of Education Key Lab of Scientific and Engineering Computing, Shanghai Jiau Tong University, Shanghai 200240, China;4. Department of Mathematics, University of Wisconsin‐Madison, Madison, Wisconsin 53706 |
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| Abstract: | An asymptotic‐preserving (AP) scheme is efficient in solving multiscale problems where kinetic and hydrodynamic regimes coexist. In this article, we extend the BGK‐penalization‐based AP scheme, originally introduced by Filbet and Jin for the single species Boltzmann equation (Filbet and Jin, J Comput Phys 229 (2010) 7625–7648), to its multispecies counterpart. For the multispecies Boltzmann equation, the new difficulties arise due to: (1) the breaking down of the conservation laws for each species and (2) different convergence rates to equilibria for different species in disparate masses systems. To resolve these issues, we find a suitable penalty function—the local Maxwellian that is based on the mean velocity and mean temperature and justify various asymptotic properties of this method. This AP scheme does not contain any nonlinear nonlocal implicit solver, yet it can capture the fluid dynamic limit with time step and mesh size independent of the Knudsen number. Numerical examples demonstrate the correct asymptotic‐behavior of the scheme. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013 |
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| Keywords: | asymptotic‐preserving schemes multispecies Boltzmann equations fluid dynamic limit |
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