三次內插特性法於水利計算之評估研究

Abstract

在固定時間間隔法架構下，特性法之精度取決於內插方式。HP以及CS特性法乃是兩種分別利用赫米特三次(Hermite cubic)與cubic-spline內插之高階內插特性法。本研究藉由一維移流擴散方程式及一維明渠時間變量流方程式之計算，評估此兩種內插特性法，及其應用於空間軸與時間軸之差異性。基於實用性及準確性考量，採用HP特性法或CS特性法空間軸內插是較好的選擇。經分析結果發現，CS特性法之精度近似HP特性法，但由於CS特性法不需要額外求解空間微分方程式，所以較HP特性法簡單而有效率。

In the framework of specified time interval scheme, the accuracy of characteristics method is severe affected by the form of interpolation. The HP and CS characteristics methods are two types of high-order characteristics method that respectively apply Hermite cubic and cubic-spline interpolation. In this study, one-dimensional advection -diffusion equation and one-dimensional unsteady open channel flow computation are used to examine the high-order characteristics methods applied within space-line and time-line intervals. As far as practical applications and accuracy are concerned. The space-line HP and CS characteristics methods should be the better choices. The simulated results from the space-line CS characteristics method are similar to those of space-line HP characteristics method. Without tackling auxiliary spatial derivative equation, the space-line CS characteristics method is more simple and efficient than space-line HP characteristics method.