NR$xx$ Simulation of Microflows with Shakhov Model

Abstract

In this paper, we propose a method to simulate the microflows with Shakhov model using the NR$xx$ method developed in [Z. Cai and R. Li, SIAM J. Sci. Comput., 32 (2010), pp. 2875-2907; Z. Cai, R. Li, and Y. Wang, Commun. Comput. Phys., 11 (2012), pp. 1415-1438; Z. Cai, R. Li, and Y. Wang, J. Sci. Comput., to appear]. The equation under consideration is the Boltzmann equation with force terms, and the Shakhov model is adopted to achieve the correct Prandtl number. As the focus of this paper, we derive a uniform framework for different order moment systems on the wall boundary conditions, which is a major difficulty in the moment methods. Numerical examples for both steady and unsteady problems are presented to show the convergence in the number of moments.