二維水理、污染傳輸及沉滓運移模式之研發與應用

Abstract

本研究之主要目的乃在發展一水深平均二維水理、污染傳輸及沉滓運移數值模式，座標系統採用正交曲線座標，水理控制方程採用連續及動量方程式求解。為使水理與污染傳輸的理論趨於完整，模式在發展過程中不忽略延散剪應力項及環流傳輸項，並於此兩項中植入彎道二次流的效應。藉由比較分析考慮與不考慮二次流效應的模式，進行彎道模擬水理模式及污染傳輸模式之適用性分析，以提供與模式使用者選用合適模式之參考。沉滓類別同時包含凝聚性沉滓與非凝聚性沉滓，沉滓傳輸型態則採用河床載及懸浮載分開計算的方式，並將水力篩選及甲護功能納入模式中。在數值處理上，水理部分採用雙階分割操作趨近法，將水理控制方程分割成延散步驟和傳播步驟二個步驟求解，其中傳播步驟將包含底床剪應力項與壓力項。在數值差分上採用隱式法，使模式可採用較大之演算間距。污染傳輸控制方程較為單純，可利用ADI法求解。沉滓運移部分採用結合演算法(同時求解所有的沉滓運移控制方程式)，利用Newton- Raphson疊代聯立求解。為驗證模式的合理性與正確性，分別採用具有量測數據的試驗案例，進行模式功能展示與模式正確性的的驗證工作。最後，將此模式應用於現場案例之探討分析，包含景美溪案例及阿公店水庫案例。

The purpose of this study is to develop a 2D depth-averaged model for water, contaminant, and sediment movements in open channel. The orthogonal curvilinear coordinate system is adopted. The continuity and momentum equations are used as the flow governing equations. To complete the mathematical requirement, the secondary-current effect is embedded in the dispersion stress term of the flow momentum equations and the circulatory transport term of the contaminant transport equation for the curved-channel simulation. The suitability of 2D depth-averaged model for flow and contaminant transport simulation in a bend can be determined by comparing the results from models with and without considering the secondary-current effect. The suitability analyses can provide a guideline for model users to select the proper kind of model to simulate the flow and contaminant transport problems in a bend. The sediment transport sub-model contains the following characteristics: the model has the capability of simulating the cohesive and noncohesive sediment transport; the suspended load and bed load can be treated separately; hydraulic sorting and armoring are included in this model. As for the numerical solution procedure, the split-operator approach is used to solve the flow equations. Based on the decomposition of the momentum equations, the split-operator procedure involves two steps in which the pressure and bed friction terms are included in the second step, propagation step. Implicit discretized methods are adopted to relax the time step restriction allowing large time steps. The contaminant transport equation is solved by the ADI method. The direct coupling, i.e. simultaneous solution of the sediment equations, and Newton-Raphson methods are used to solve the sediment governing equations. Studies on the cases with measured data have been demonstrated to show the capability and accuracy of the model. Finally, the model is applied to field cases including the Ching-Mei Creek and the Ah Gong Diann Reservoir.