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.

本研究的目的是建立一种统一的计算稳定流和非稳定流的方法，即基于时间线插值的特征法，这是基于弹性水柱模型的数值方法之一。为此，通过研究波浪特征、网格、插值和边界条件之间的关系，从理论上分析插值误差。有限差分方程的线性稳定性分析得到扩展，使其适用于具有指定边界条件的有限区域。新的稳定性分析中引入多项式传递矩阵，通过复杂的放大因子来分析误差特征，即与边界条件相关的多项式的解。整个系统的多项式传递矩阵反映了连接、分支等边界条件，通过施加质量和能量连续性条件很容易导出。它使我们能够准确分析系统中的数值误差。插值误差的非粘性分析表明，在简单管道中，误差随着频率的增加而单调增加，而对于串联管道、分支管道系统等一般管道系统则不一定成立。通过没有任何插值的粘性分析，离散化误差有可能将最低频率模式的过阻尼添加到最高频率模式，尽管数值精度的顺序确实会产生显着影响。数值模拟正确地检验了所分析的误差特性。稳定流时间步进方法的理论基础也得到了论证，该方法通过最大化离散化误差来快速抑制所有频率模态，并提出了一种计算大型管网管道稳定流的实用方法。