垂直二維具移動性邊界Navier-Stokes方程式流場之有限元素分析

Finite Element Method for Vertical 2-D Navier-Stokes Equations with Moving Boundaries

林寬心(Quain-Hsin Lin) ； 楊德良(Der-Liang Young)

《中華水土保持學報》 26卷2期 (1995/06) Pp. 79-88

https://doi.org/10.29417/JCSWC.199506_26(2).0002

摘要

近年來，隨著電子計算機容量及運算速率的進步，以數值方法分析各種流體運動力學問題，已顯得愈來愈便利。本文，對於具移動性邊界而控制方程式爲Navier-Stokes方程式的流場，發展一套垂直面二維的數值分析方法。文中，對複雜的Navier-Stokes構建具數值精確性及效率性的求解體制，並構建便利的演算及控制格網移動之方法，以處理移動性邊界所引起的困難性。由於，在水利、海洋及水土保持學上，具移動性邊界的流體運動力學爲數頗多，而Navier-Stokes方程式爲流體運動的基本方程式。因此，其數值分析方法頗有些應用及參考性。

關鍵字

移動邊界 ； Navier-Stokes方程式 ； 有限元素法 ； ALE法

並列摘要

In recent years, the numerical analysis of fluid mechanics is very convenient, by the advantage of computer advance. This study developes a vertical 2-D numerical method to analyse the problems with moving boundaries and governing by the Navier-Stokes equations. By using the finite element method, the ALE method and some numerical theories or techniques, the Nevier-Stokes equations will be solved by an accurate and efficient scheme. In the meantime, a convenient method for mesh motion will be constructed to solve the difficulty of moving boundaries. Finally, the dam breaking flow and a flow accelerating by a vertical plate will be analysed to verify this numerical method. In hydraulics, ocean engineering as well as the soil and water conservation engineering, there are several problems of flows with moving boundaries. And, the Navier-Stokes equations are the basic governing equations of fluid mechanics. Therefore, this numerical method is an usefull and helpfull tool to analyse these concerned flow problems.

並列關鍵字

Moving Boundaries ； Navier-Stokes Equations ； FE Method ； ALE Method