Study of the shock wave structure by regularized Grad’s set of equations

Abstract

In this work, we continue to study the possibility of applying moment equations for strongly nonequilibrium flows by an example of the problem of the shock wave structure in a monatomic gas in a wide range of Mach numbers for various models of molecular interaction. The object of the study is the so-called regularized 13-moment Grad’s system (R13). First time, both linear and nonlinear versions of this system of equations were considered for the problem at such wide range of parameters. The Godunov method with increased accuracy is used as a numerical tool for solving the R13 system. The numerical results for the R13 system are analyzed by using data obtained by the Direct Simulation Monte Carlo (DSMC) method, experimental data, and analytical results. As a whole, the R13 system provides an adequate description of the shock wave structure in a wide range of Mach numbers. For Mach numbers around 2, good agreement with experimental and DSMC results is observed for both linear and nonlinear versions of the system. For high Mach numbers, the result strongly depends on the molecular interaction model used: shock wave structure predictions of the nonlinear R13 system are better for Maxwell molecules and worse for hard spheres as compared to the linear version. Particular attention in this work is paid to studying nonmonotonicity of the total temperature profile (temperature overshoot) in the structure of a strong shock wave. It is shown that the moment equations correctly predict the existence of the temperature overshoot. At the same time, the solution of the moment equations overpredicts the temperature overshoot at least two-fold for Mach number M = 8, and the nonlinear version of the R13 system yields a better result for this parameter than the linear version.