Year: 2014
Communications in Computational Physics, Vol. 15 (2014), Iss. 4 : pp. 996–1011
Abstract
This paper generalizes the exponential Runge-Kutta asymptotic preserving (AP) method developed in [G. Dimarco and L. Pareschi, SIAM Numer. Anal., 49 (2011), pp. 2057–2077] to compute the multi-species Boltzmann equation. Compared to the single species Boltzmann equation that the method was originally applied to, this set of equation presents a new difficulty that comes from the lack of local conservation laws due to the interaction between different species. Hence extra stiff nonlinear source terms need to be treated properly to maintain the accuracy and the AP property. The method we propose does not contain any nonlinear nonlocal implicit solver, and can capture the hydrodynamic limit with time step and mesh size independent of the Knudsen number. We prove the positivity and strong AP properties of the scheme, which are verified by two numerical examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.010113.160813s
Communications in Computational Physics, Vol. 15 (2014), Iss. 4 : pp. 996–1011
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
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