Asymptotic analysis of high order IMEX-RK methods for ES-BGK model at Navier-Stokes level

초록

Implicit explicit Runge-Kutta (IMEX-RK) time discretization methods are very popular when solving stiff kinetic equations. In the work of Hu and Zhang in [J. Sci. Comput. 73 (2017) 797-818], an asymptotic analysis shows that a specific class of high-order IMEX-RK schemes can accurately capture the Navier-Stokes limit without needing to resolve the small scales dictated by the Knudsen number. In this work, we extend the asymptotic analysis to general IMEX-RK schemes, known in literature as Type I and Type II. We further introduce some IMEX-RK methods developed by Boscarino and Pareschi [J. Comput. Appl. Math. 316 (2017) 60-73 to attain uniform accuracy in the wide range of Knudsen numbers. Several numerical examples are presented to verify the validity of the obtained theoretical results and the effectiveness of the methods.

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