三次內插多方式法動床模式之研究

Abstract

本研究使用特性法結合賀利-普利斯曼兩點四階內插法,發展出三次內插多 方式法,同時求解水流連續方程式、動量方程式及沉滓連續方程式。此多 方式法由空間延後法、時間外延法、空間外延法及傳統特性法組成,有不 受可蘭數限制(Courant constraint)之優點。本文首先對所採用的數值方 法做敏感度分析,進而模擬Soni et al.(1980)之均勻質超載實驗數據。本 模式模擬之結果除了與時驗值比對之外,並與線性內插多方式法模式之模 擬結果比較,以探討本模式之精確度及穩定性。 The purpose of this study is to attempt to use the cubic interpolation multimode characteristics method extended by following the concept of Holly-Pressiman two- point scheme to solve the water continuity equation , momentum equation and sediment continuity equation simultaneously. The multimode scheme combining spatial reachback,temporal reachout and classical characteristics schemes into one can release Courant constraint. The stability analysis has been performed to show the merit of the cubic interpolation technique.The sensitivity analysis on some of key parameters has also been conducted.A set of experimental data from Soni et. al(1980) is simulated by the cubic interpolation multimode characteristics method and the conventional linear interpolation multimode characteristics method. Through the results comparison ,the model's accuracy and stability are investigated and discussed in details.