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Exponential Runge-Kutta Methods for the Multispecies Boltzmann Equation

Published online by Cambridge University Press:  03 June 2015

Qin Li  and
Xu Yang
Qin Li*
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA
Xu Yang*
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106-3080, USA
*
Email:qinli@caltech.edu
Corresponding author.Email:xuyang@math.ucsb.edu
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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 on, 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.

Keywords

65C2065M0676D0582C40Multispecies Boltzmann equationexponential Runge-Kutta methodhydrodynamic limitasymptotic preserving propertypositivity preserving
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 4 , April 2014 , pp. 996 - 1011
Copyright
Copyright © Global Science Press Limited 2014

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