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• W2795010147 abstract "Different discrete velocity quadrature rules are analyzed and applied in gas-kinetic unified algorithm (GKUA) for rarefied free-molecule transition to continuum flows, including the original and modified Gauss–Hermite quadrature rules, the composite Newton–Cotes integration methods, the multi-subinterval Gauss–Legendre numerical quadrature rule and the Gauss–Chebyshev integral rule. Mathematical description and basic procedures of GKUA are presented briefly in solving the gas flow problems covering various flow regimes on the basis of the direction solution to the unified kinetic model of the Boltzmann equation. The numerical analyses and the application conditions of these quadrature rules are given in detail, as well as the evaluating method for the discretized velocity ordinate (DVO) points and their corresponding weights of each rule. According to the comparisons for some Gauss-type function integrations, the original and modified Gauss–Hermite quadrature rules can obtain the integration results with enough accuracy by using least DVO points among these rules, while the impossibility of more nodes limits the application scope of these two quadrature rules. Other four rules can conduct the problems with a needful wide integral interval, even if they use more DVO points than the Gauss–Hermite rules. Besides, the multi-subinterval Gauss–Legendre and the Gauss–Chebyshev rules can use less DVO points to obtain accurate integration results than the other two rules, which demonstrate their advantage and are recommended to be applied in GKUA to solve the Boltzmann model equation efficiently. 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." @default.
• W2795010147 created "2018-04-06" @default.
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• W2795010147 date "2018-06-01" @default.
• W2795010147 modified "2023-10-16" @default.
• W2795010147 title "Investigation on different discrete velocity quadrature rules in gas-kinetic unified algorithm solving Boltzmann model equation" @default.
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• W2795010147 doi "https://doi.org/10.1016/j.camwa.2018.03.021" @default.
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