變化斷面水質模式線性解析法之研究

The Linearized Analytical Method of Water Quality Model with Varied Cross Section

鄧祥威(Siang-Wei Deng)

指導教授 ： 王士紘

淡江大學/工學院/水資源及環境工程學系碩士班/碩士(2010年)

https://doi.org/10.6846/TKU.2010.00880

摘要

本文是以數學模式利用聖凡納之水流連續方程式、動量方程式及濃度擴散方程式，推求出流量及濃度擴散之解析解，再藉由數學模式計算，使解析解更加精確，進而以解析解模擬不同斷面流量及汙染質濃度擴散分布之情形。
將連續方程式和擴散波動量方程式代入濃度擴散方程式中，使其合併為一非線性偏微分方程式，由於是非線性方程式，欲從中獲得解析解非常之困難，所以必須利用微小擾動法代入運動波方程式將其非線性部分線性化方可求得其解。
線性解析法運用在實際洪流演算及水質模擬，若天然渠道各斷面資料齊全，且有精確之上游流量及濃度入流量，即可推估出任意斷面之流量及濃度分佈情況，可運用在河川水質整治上。

關鍵字

解析解 ； 水質模式 ； 變量流 ； 變化斷面 ； 數學模式

並列摘要

This article is based on mathematical models using De Saint Venant continuity equation, momentum equation and concentration routing problem to conclude the analytical of flow and concentration extension. After that, calculating with mathematical models to obtain more precise analytical. What’s more, using analytical to simulate the flow of different sections and the concentration spreading distribution of pollutants.
Substitution continuity equation and diffusion model equation into concentration routing problem to make it combine into a nonlinear partial differential equation. Since it is non-linear equations, which is extremely difficult to derive analytical from it. We have to substitution small perturbation into Kinematic Wave Model to linear the nonlinear part, and will reach the solution.
Linearized Analytical Method is applied to the actual flood routing and water quality. We can calculate and estimate the situation of flow and concentration-spreading against any sections, if the information of natural channel in all sections is complete and we are aware of the accurate upstream and concentration. This could be applied to the water quality renovation of rivers.

並列關鍵字

Analytical ； Varied Cross Section ； Water Quality ； unsteady flow ； Mathematical model

參考文獻

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(22) 楊永漢，“天然渠道污染物擴散之研究”，私立大江大學水資源及環境工程研究所碩士論文，中華民國97年6月。

(6) Tingsanchali Ta. And Manandhar﹐S.K.﹐“Analytical Diffusion Model for Flood Routing”﹐Journal of Hydraulic Engineering﹐ASCE﹐Vol.111﹐HY3.Mar﹐1985﹐pp435-454.

(15) Gerald T.Orlob﹐“Mathematical Modeling of Water Quality：Stream﹐Lake﹐and Reservoirs”﹐1983.

(1) Mahmood﹐K﹒ and Yevjevich﹒V﹒﹐ed﹒﹐“Numerical Methods of Solution of the Unsteady Flow Equation”﹐Chap﹒4 Unsteady Flow in Open Channels﹐Vol﹒1 pp﹒89-182﹐1975.