應用平行運算於二維潰壩之模擬

A Study of a 2D Dam-break Problems by Using the Parallel Computation Algorithm

鄧志浩(Jyh-Haw Tang) ； 孫銘寬(Ming-Kuan Sun)

《先進工程學刊》 4卷2期 (2009/04) Pp. 171-178

https://doi.org/10.29948/JAE.200904.0012

摘要

本研究是利用平行運算技術於最小平方有限元素法來發展一套數值模式以有效的計算求解淺水波方程式(shallow water equation)以模擬具自由液面水體在壩體破壞後之運動情形。此研究利用平行運算技術將原有循序的最小平方有限元素法演算程式能以更快速而正確的方式加以模擬。計算將著重於平行運算模式建立後並用於模擬二維自由液面之演算驗證。二維潰壩問題將用於驗證之演算。藉由自由液面分布及不同幾何形狀之關係，同時藉由充分瞭解自由液面分布進而達到控制流場的目的。計算結果發現平行運算後的程式運算較原來的最小平方有限元素法更為快速，這樣的結果符合預期，同時研究結果顯示平行化後並非越多的電腦參與平行運算就可以得到越快的計算成果，平行計算之最大效益有其極限。

關鍵字

二維潰壩 ； 最小平方有限元素法 ； 平行運算 ； 自由液面流 ； 數值模擬

並列摘要

This study is to develop a numerical model associated with the parallel computation algorithm for solving the shallow-water equations. The least-squares finite element method (LSFEM) is applied for solving the two-dimensional shallow-water equations to investigate the free-surface movement phenomena on the river beds due to the dam broken. In addition, the parallel computation techniques for solving the complicated and time consuming problems will also be studied in this project. We focus on the establishment and investigation of the parallel computation numerical model for the simulation of two-dimensional dam-break free-surface flows on the channel beds. A typical dam break simulation will be used as a benchmark verification. According the free-surface distribution on the river beds, the numerical model will be used for the prediction of the possible flood control and design of the hydraulic structures. In this study, the simulation results of the original LSFEM take more time than those of the paralleled algorithm, this result meets the expected requirement, however, that more computers used in parallel computational scheme does not guarantee the computational efficiency will be better.

並列關鍵字

two-dimensional dam-break ； least-squares finite element method ； parallel computation ； free-surface flow ； numerical simulation