A two-dimensional numerical model of vertical jet scour was developed based on the turbulent flow theory and jet scour mechanism. In this model, drag force acts as the main reference variable and the critical Shields ...A two-dimensional numerical model of vertical jet scour was developed based on the turbulent flow theory and jet scour mechanism. In this model, drag force acts as the main reference variable and the critical Shields number acts as the incipient motion criteria of sediment. The morphological change in the bed caused by bed-load transport is simulated using the moving mesh method and the suspended-load is not considered. An experiment investigating vertical clear water jet scour was conducted in the laboratory, and some effective experimental results, such as flow pattems and distribution characteristics of scour pits, were obtained. Numerical simulation of the 2D jet scour was conducted using the same parameters as were used in the flume experiment. The evolution process of the jet scour observed in the experiment was simulated by the new model; validation of the numerical model and the algorithm was conducted. Semi-empirical formulas of the characteristic length of the equi-librium scour hole were deduced based on the results of the experiment and simulation.展开更多
The bondage number b（G） of number of edges whose removal from G number greater than that of G. Denote a nonempty graph G is the smallest results in a graph with domination Pn × Pm the Cartesian product of two p...The bondage number b（G） of number of edges whose removal from G number greater than that of G. Denote a nonempty graph G is the smallest results in a graph with domination Pn × Pm the Cartesian product of two paths Pn and Pm. This paper determines the exact values of b（Pn × P2）, b（Pn × P3）, and b（Pn × P4） for n ≥ 2.展开更多
电大尺寸目标高频散射场的仿真一般使用物理光学(physical optics,PO)方法,该方法要求对目标使用尺寸为八分之一倍波长的三角网格进行剖分.然而,随着入射波频率增加,网格数目呈指数增长.本文提出基于一倍波长的二次曲面网格的快速PO(fas...电大尺寸目标高频散射场的仿真一般使用物理光学(physical optics,PO)方法,该方法要求对目标使用尺寸为八分之一倍波长的三角网格进行剖分.然而,随着入射波频率增加,网格数目呈指数增长.本文提出基于一倍波长的二次曲面网格的快速PO(fast PO,FPO)方法,该方法使用线性多项式拟合振幅函数,能够有效降低面片数目.与二次多项式拟合振幅函数的快速物理光学方法相比,本文方法避免了菲涅尔积分的求解,且计算速度快1.22倍.为了进一步降低网格数目,提出了自适应网格技术的快速物理光学(FPO based on the adaptive mesh technique,AFPO)方法,允许使用比标准奈奎斯特采样率更少的网格数目对目标进行离散.通过后验误差估计和数值算例对所提出算法的精度和速度进行了验证,结果表明与采用均匀网格剖分的方法相比,AFPO方法所需的面片数目降低89.58%.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.10972163,51079106))the Fundamental Research Funds for the Central Universities (Grant Nos.2104001,2103002)
文摘A two-dimensional numerical model of vertical jet scour was developed based on the turbulent flow theory and jet scour mechanism. In this model, drag force acts as the main reference variable and the critical Shields number acts as the incipient motion criteria of sediment. The morphological change in the bed caused by bed-load transport is simulated using the moving mesh method and the suspended-load is not considered. An experiment investigating vertical clear water jet scour was conducted in the laboratory, and some effective experimental results, such as flow pattems and distribution characteristics of scour pits, were obtained. Numerical simulation of the 2D jet scour was conducted using the same parameters as were used in the flume experiment. The evolution process of the jet scour observed in the experiment was simulated by the new model; validation of the numerical model and the algorithm was conducted. Semi-empirical formulas of the characteristic length of the equi-librium scour hole were deduced based on the results of the experiment and simulation.
文摘The bondage number b（G） of number of edges whose removal from G number greater than that of G. Denote a nonempty graph G is the smallest results in a graph with domination Pn × Pm the Cartesian product of two paths Pn and Pm. This paper determines the exact values of b（Pn × P2）, b（Pn × P3）, and b（Pn × P4） for n ≥ 2.
文摘电大尺寸目标高频散射场的仿真一般使用物理光学(physical optics,PO)方法,该方法要求对目标使用尺寸为八分之一倍波长的三角网格进行剖分.然而,随着入射波频率增加,网格数目呈指数增长.本文提出基于一倍波长的二次曲面网格的快速PO(fast PO,FPO)方法,该方法使用线性多项式拟合振幅函数,能够有效降低面片数目.与二次多项式拟合振幅函数的快速物理光学方法相比,本文方法避免了菲涅尔积分的求解,且计算速度快1.22倍.为了进一步降低网格数目,提出了自适应网格技术的快速物理光学(FPO based on the adaptive mesh technique,AFPO)方法,允许使用比标准奈奎斯特采样率更少的网格数目对目标进行离散.通过后验误差估计和数值算例对所提出算法的精度和速度进行了验证,结果表明与采用均匀网格剖分的方法相比,AFPO方法所需的面片数目降低89.58%.
