Comparison of discrete BGK-Shakhov System with DSMC

Results obtained by numerically solving the discrete Boltzmann equation, using the Bhattnagar-Gross-Krook (BGK) relaxation approximation with Shakhov target distribution, are compared to those obtained by the Direct Simulation Monte-Carlo (DSMC) method. The relaxation dynamics of the BGK-Shakhov system are also compared to DSMC results. The method is of arbitrary order with velocity and physical space discretized according to truncated series of Hermite and Legendre polynomials respectively. The polynomial based physical space discretization is shown to allow the implementation of the relaxation operator in a continuous-in-space manner. Results show a high degree of similarity with DSMC solutions with little numerical dissipation and no statistical scatter