Two‐Dimensional Bulk Microflow Simulations Based on Regularized Grad’s 13‐Moment Equations

Abstract

The newly derived fluid model named regularized 13‐moment system (R13) is capable of describing rarefied/microflows with high accuracy due to special modeling of the nonequilibrium dissipation. Explicit two‐dimensional equations are presented and discussed and a specialized numerical method derived. In two dimensions evolution equations for nine basic variables need to be solved, including directional temperatures, shear stress, and heat flux. The governing partial differential equations are given in balance law form with relaxation and parabolic dissipation. The numerical method is formulated as a practical and straightforward extension of standard finite volume methods. It focuses on bulk simulations with no boundary in order to provide a building block. As a microflow example the interaction of a shock front with a dense microbubble is considered in which the bubble’s diameter is a few mean free paths. The results are compared to the solution of the Navier–Stokes–Fourier system demonstrating the releva...