The high-order Runge-Kutta discontinuous Galerkin (DG) method is extended to the 2D kinetic model equations describing rarefied gas flows. A DG-type discretization of the equilibrium velocity distributions is formulated for the Bhatnagar-Gross-Krook and ellipsoidal statistical models which enforce a weak conservation of mass, momentum and energy in the collision relaxation term. The RKDG solutions have up to 3rd-order spatial accuracy and up to 4th-order time accuracy. Verification is carried out for a steady 1D Couette flow and a 2D thermal conduction problem by comparison with DSMC and analytical solutions. The computational performance of the RKDG method is compared with a widely used second-order finite volume method.


Copyright (2012) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in (Wei Su*, A. Alexeenko, and Guobiao Cai, “A Runge-Kutta discontinuous Galerkin solver for 2D Boltzmann model equations: Verification and analysis of computational performance”, Proceedings of 28th International Symposium on Rarefied Gas Dynamics, 9–13 July 2012, Zaragoza, Spain. AIP Conf. Proc. Vol. 1501, pp. 381-388.) and may be found at http://dx.doi.org/10.1063/1.4769547. The following article has been submitted to/accepted by [American Institute of Physics]. After it is published, it will be found at (http://dx.doi.org/10.1063/1.4769547). Copyright (2012) Wei Su*, A. Alexeenko, and Guobiao Cai. This article is distributed under a Creative Commons Attribution 3.0 Unported License.

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