二维波浪数学模型的验证与应用

根据水深修正的二维非线性Boussinesq方程,建立波浪数学模型,通过模拟单突堤绕射及圆形浅滩折射现象,证明该模型是可行的,在科美纳河口的波浪变形计算中得到应用,效果较好.     

Geometrical design of blade＇s surface and boundary control of Navier-Stokes equations

In this article a new principle of geometric design for blade＇s surface of an impeller is provided. This is an optimal control problem for the boundary geometric shape of flow and the control variable is the surface of the blade. We give a minimal functional depending on the geometry of the blade＇s surface and such that the flow＇s loss achieves minimum. The existence of the solution of the optimal control problem is proved and the Euler-Lagrange equations for the surface of the blade are derived. In addition, under a new curvilinear coordinate system, the flow domain between the two blades becomes a fixed hexahedron, and the surface as a mapping from a bounded domain in R2 into R3 , is explicitly appearing in the objective functional. The Navier-Stokes equations, which include the mapping in their coefficients, can be computed by using operator splitting algorithm. Furthermore, derivatives of the solution of Navier- Stokes equations with respect to the mapping satisfy linearized Navier-Stokes equations which can be solved by using operator splitting algorithms too. Hence, a conjugate gradient method can be used to solve the optimal control problem.     

三峡库区汛期日调节通航水流条件一维数学模型

采用圣维南方程组建立三峡库区日调节通航水流条件一维数学模型,利用三峡枢纽淤积平衡地形日调节物理模型试验成果对数学模型进行验证。研究表明,24h日调节过程中,流量变化的时候,上游引航道通航水流条件最不利。随着泥沙淤积年份增加,汛期日调节通航水流条件逐渐恶化。电站机组错时开启或关闭可以减小口门处的流速。     

Improvement of two inequalities in the stationary Navier-Stokes equations

Two inequalities in the book Navier-Stokes Equations Theory and Numerical Analysis written by Roger Temam are improved via Schwarz＇s inequality and Young＇s inequality, and the coefficients of them are simplified from 2^1/4 · 3^1/2 and 2^1/2 · 3^3/4to 2^1/4 and 2^3/4 , respectively. Therefore, to some extent the approximating error can be reduced and the accuracy of approximation can be improved.     

船舶管线流体荷载与支座反力计算

建立了船舶与海洋平台舱内管线流体荷载与局部应力的直接计算方法 ,应用总流能量方程法计算整个管系的流体压力分布 ,应用NS方程与二模式湍流方程法计算管系局部压力分布 ,最终应用有限元分析法确定管线、支座以及接头、端头、法兰与阀门的应力分布