Investigation on different discrete velocity quadrature rules in gas-kinetic unified algorithm solving Boltzmann model equation

Numerical simulations for the Sod and Lax shock-tube problems and the shock-density wave disturbing interaction problems are conducted by using GKUA with the above quadrature rules to make comparison. All quadrature rules can obtain nice accurate results with different number of the DVO points. The original and modified Gauss-Hermite quadrature rules, using the least DVO nodes to obtain results with enough computed precision, are the best options for GKUA to simulate low mach number flow regimes, while the Gauss-Chebyshev quadrature rule, which can obtain results with adequate and controllable precision for a wide integral interval using little DVO nodes, is the most appropriate quadrature rule for GKUA solving some complex and high mach number flows covering various flow regimes.