Construction of Numerical Stability Analysis in Systems and Error Estimate on Water Hammer Analysis in Pipeline Systems

系统数值稳定性分析的构建及管道系统水锤分析的误差估计

基本信息

批准号：
14360140
负责人：
SHIMADA Masashi
金额：
$ 7.74万
依托单位：
THE UNIVERSITY OF TOKYO
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

项目摘要

The aim of this study is to establish a unified method of calculating steady and unsteady flows using the method of characteristics with time-line interpolations, which is one of numerical methods based on the elastic water column model. To do this the interpolation errors are theoretically analyzed by investigating the relationships among the wave characteristics, grids, interpolations, and boundary conditions. The linear stability analysis of finite difference equations is extended so that it holds for a finite region with specified boundary conditions. Within the new stability analysis the polynomial transfer matrix is introduced, and the error characteristics can be analyzed by the complex amplify factors, which is the solution of the polynomial associated with the boundary conditions. The polynomial transfer matrix of the total system, which reflects the boundary conditions such as connections, branches, and so on, is easily derived by imposing the mass and energy continuity conditions. It makes us possible to exactly analyses the numerical errors in systems. The non-viscous analysis of the interpolation errors reveals that the errors increases monotonously as the frequency increases in a simple pipe while it does not necessarily hold for general pipe system such as series pipes, branching piping systems, and so on. With the viscous analysis without any interpolations the discretization errors have a possibility of over-damping of the lowest frequency mode adding to the highest frequency one, though the order of numerical accuracy does influence significantly. The error characteristics analyzed are examined rightly by the numerical simulations. The theoretical basis of the time marching approach for steady flows is also justified, which quickly damps out all frequency modes by maximizing the discretization errors, and a practical method of calculating the steady flows in large network pipelines is proposed.

这项研究的目的是建立一种统一的方法，该方法使用特征与时线插值来计算稳定和不稳定的流量，这是基于弹性水柱模型的数值方法之一。为此，通过研究波特征，网格，插值和边界条件之间的关系，可以在理论上分析插值误差。有限差方程的线性稳定性分析被扩展，因此它适用于具有指定边界条件的有限区域。在新的稳定性分析中，引入了多项式转移矩阵，并且可以通过复杂的放大因子来分析误差特性，这是与边界条件相关的多项式的解决方案。总体系统的多项式传输矩阵反映了连接，分支等边界条件，可以通过强加质量和能量连续性条件来得出。它使我们有可能精确分析系统中的数值错误。对插值误差的非静态分析表明，随着简单管道中的频率增加，这些误差会单调增加，而该频率不一定适用于串联管道，分支管道系统等通用管道系统等。通过粘性分析而没有任何插值，离散误差可能会过度阻尼最低的频率模式，但数值准确性的顺序确实会产生重大影响，从而增加了最高频率。通过数值模拟正确检查了分析的误差特性。稳定流动流动方法的理论基础也是合理的，该方法通过最大化离散误差来迅速抑制所有频率模式，并提出了一种计算大型网络管道中稳定流量的实用方法。