二维明渠非恒定水流BGK数值模型

本文根据BGK波尔兹曼方程及明渠水流中波尔兹曼变量与宏观变量之间的基本关系，导出了明渠水流运动方程，验证了BGK波尔兹曼方程与明渠水流运动方程的一致性，并从理论上证明，圣维南方程是BGK明渠水流模型在局部平衡状态下的一个特例。以BGK波尔兹曼方程为基本方程，利用有限体积离散方法，建立了满足熵原理的二维明渠非恒定水流的BGK数值模型。通过对典型的明渠水流现象的模拟，并与其它计算方法获得的解以及实验结果相比较，表明BGK模型勿须人为的熵修正，能准确地模拟存在不连续运动的明渠水流运动，是一种较好的明渠非恒定水流模型。

2-D Bhatnagar-Gross-Krook numerical model for unsteady open channel flow

According to the Boltzmann equation and basic relationshipbetween the microscopic and macroscopic variables, the Bhatnagar Gross Krook(BGK) equations governing open channel flow are derived and the consistency between the BGK Boltzmann equations and open channel flow equations is verified. The theoretical derivation shows that St. Venant equation is the special case of theBGK model under the local equilibrium state. Based on the BGK Boltzmann equation, a 2-D numerical model for open channel flows, which satisfies the entropy condition, is established by employing the finite volume method. The proposed model is applied to solve typical open channel flow problems. The comparison betweenthe numerical results and the solutions obtained from other models and experimental data show that the BGK model does not need any entropy fixes and it can accurately simulate the open channel problems in which discontinuous flows exist.