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

This study is devoted to the analysis of applicability of moment equations to the shock wave structure problem in a wide range of Mach numbers. A modification of original Grad's 13-moment set of equations, so-called regularized Grad's set of equations (R13), is taken as a mathematical model. The numerical method for this set is formulated as a variant of the explicit high-order Godunov scheme with linear reconstruction of flow parameters. The degree of applicability of moment equations is determined by comparisons with Direct Simulation Monte Carlo (DSMC) predictions. Numerical results for hard sphere molecules show that the R13 set of equations describes well the internal structure of the shock wave in a wide range of Mach numbers. Nevertheless, R13 set significantly overpredicts the overall temperature overshoot (about 3 times for M=8), which is apparently related to nonlinearity of the dependence of the product of the transverse temperature component and density on normalized density.