Different variants of R13 moment equations applied to the shock-wave structure

Various versions of the regularized 13-moment system (R13) are applied to the problem of the shock wave structure in a monatomic Maxwell gas for Mach numbers up to M = 10. Numerical solutions are compared to direct simulation Monte Carlo results computed by the SMILE++ software system, in order to identify applicability and limitations of the variants. Over time, several versions of the R13 equations were presented, which differ in non-linear contributions for high-order moments but agree in asymptotic expansion to the third order in the Knudsen number. All variants describe typical subsonic microflows well, for which the non-linear contributions only play a minor role. The challenge of the present study is to determine the real boundaries of applicability of each variant of the moment equations as applied to non-equilibrium supersonic flows, depending on the Mach number and local Knudsen number.