A robust numerical method for the R13 equations of rarefied gas dynamics: Application to lid driven cavity

Abstract

In this work we present a finite difference scheme to compute steady state solutions of the regularized 13 moment (R13) equations of rarefied gas dynamics. The scheme allows fast solutions for 2D and 3D boundary value problems (BVPs) with velocity slip and temperature jump boundary conditions. The scheme is applied to the lid driven cavity problem for Knudsen numbers up to 0.7. The results compare well with those obtained from more costly solvers for rarefied gas dynamics, such as the Integro Moment Method (IMM) and the Direct Simulation Monte Carlo (DSMC) method. The R13 equations yield better results than the classical Navier–Stokes–Fourier equations for this boundary value problem, since they give an approximate description of Knudsen boundary layers at moderate Knudsen numbers. The R13 based numerical solutions are computationally economical and may be considered as a reliable alternative mathematical model for complex industrial problems at moderate Knudsen numbers.