多方式特性法應用於淤積渠道之研究

Abstract

本研究發展一多方式特性法（簡稱多方式法）結合演算數值模式，具有模 擬變量流非均勻質河道沖淤現象之能力。模式結合水流連續方程式、動量 方程式、輸砂連續方程式及河床質篩分方程式，依照特性法導出特性曲線 及其相應方程式，並採用多方式法中之顯式法、空間延後法、時間延後法 及隱式法求解，同時可得出每一時段之水深、流速、底床高層及粒徑組成 等變量。多方式法擁有不受可蘭數限制之特點，能有效地解決水面波、河 床波與粒徑篩分波之間巨大波速差異所面臨之難題。多方式法係依 Lagrange之觀點推導而成，每一待求未知量藉由本身之波傳速度，傳遞至 下一時段，再解其相應方程式而得。若模式控制方程式超過三條以上，其 波傳速度則無法以解析解求出，而必須利用數值姐解法。上游邊界條件影 響模式之模擬精度甚巨，故本研究採緩衝段法(buffer reach method)加 以解決。本文最後以Soni et al. (1980)之均勻質及顏等(1987)之非均勻 質模型式驗資料，檢討本模式在超載情況之下，底床高層及粒徑組成變化 之情形，進而探討上游邊界條件對底床高層之影響，並配合穩定性及準確 度分析，以測試模式之實用性。 The purpose of this study is to develop a numerical model based on multimode characteristics method for fully coupled simulation of water and sediment movement in mobile-bed alluvial channels with nonuniform bed materials. According to multimode characteristics method, the characteristics equations and tota- -lly differential compatible equations of the numerical model could be obtained by consolidating water continuity and momen- -tum equations, sediment continuity equation and bed material sorting equtaions. The model contains explicit scheme, spatial reachback scheme, temporl reachback scheme and implicit scheme for solving flow depth, velocity, bed elevation, and bed-mate- -rial size fraction at each time step. The multimode scheme has the advantages of releasing Courant constraint and of effectively dealing with the problem of large differences in celerities among water-surface waves, bed-mate- -rial sorting waves. The multimode scheme is based on Lagrangian concept. The unknows could be computed from one time step to another by solving the compatible equations along the corres- ponding characteristics curves. When there are more then three governing equations, the eignvalues can only be solved numeri- -cally. The concept of buffer reach was adopted in this study to improve the stabilty and accuracy in numerical simulation affected by the upstream boundary condition. The simulation results for aggradation based on experimen- -tal data of Soni et al.(1980) and Yen et al.(1987) show that the proposed model can reasonably predict the evolution of bed elevation. Through the numerical simulation, the effect of boun- -dary condition on simulation results was examined. Furthermore, an assessment of model applicability was made through the analy- -sis of models stabilty, accuracy, and sensitivity.