WBK方程稳态解的保结构分析  

STRUCTURE-PRESERVING ANALYSIS FOR STEADY-STATE SOLUTION OF WBK EQUATION

作　　者：韩磊 胡伟鹏 Han Lei;Hu Weipeng(Xianyang Research Institute Water Conservancy and Hydropower Planning and Design,Xianyang 712000,China;School of Civil Engineering and Architecture,Xi′an University of Technology,Xi′an 710048,China)

机构地区：[1]咸阳市水利水电规划勘测设计研究院,咸阳712000 [2]西安理工大学土木建筑工程学院,西安710048

出　　处：《动力学与控制学报》2019年第4期313-317,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11672241);大连理工大学工业装备结构分析国家重点实验室开放基金资助项目(GZ1605)~~

摘　　要：水动力学系统稳定状态下的总能量与系统初始能量之差直观反映了水力系统的水头损失.本文基于保结构思想,以色散浅水波WBK模型为例,推导了其对称形式及空间辛结构等守恒性质.随后,采用EulerBox差分离散方法构造对称形式的保结构差分格式,并推导其离散空间辛结构,为数值格式保结构性能检验提供理论依据.最后,通过数值实验,考察数值格式的保结构性能,并将数值格式用于研究不同相对扩散系数条件下,WBK方程保结构稳态水质点系统的总能量,为水力系统水头损失的分析提供参考.The difference between the initial energy and the ending energy of the hydrodynamics system reflects the head loss of the hydraulic system directly.Based on the structure-preserving idea,the symmetric form with the spatial symplectic structure,the energy flux conservation law and the momentum flux conservation law were deduced firstly.And then,the Euler Box scheme as well as its discrete spatial symplectic structure for the symmetric form were constructed to simulated the steady-state solution of the WBK equation.In the numerical experiments,the structure-preserving properties of the Euler Box scheme were verified.In addition,the total energies for the WBK system in the steady state with different relative diffusion coefficients were studied in detail,which will provide a reference for calculating the head loss in a hydraulic system.

关 键 词：WBK方程 保结构 稳态解 动量通量 辛结构 

分 类 号：O175[理学—数学]