Abstract
在本研究中，使用有限差分法配合加權數法來模擬牛頓流體在流經一矩形 流道時所發生的現象。為了處理在波前部分的具有的曲面非正交邊界，引 入了曲線座標系統，此為一種橢圓型網格產生法來建立計算網格，將原本 具有曲率的物理邊界轉換到一正交的計算糸統，以求得更精確的計算結果 。此外，本文採用原變數法且完整保留統御方程式的傳導項和熱傳項，可 以正確的描述所發生的物理現象。在網格的使用上則採用非交錯網格法結 合壓力連結方程式，非交錯網格法可使程式化較簡單，並可以用到三維現 象的模擬；而壓力連結方程式則可讓原本不易描述的壓力項得到一條專為 壓力而解的方程式。 In this study, a finite difference method(FDM) based on the weighting functionscheme is developed to simulate the pipe flow of a Newtonian fluid.To dealwith the non-orthogonal boundary in the flow front region, a kind of elliptic grid generation method is introduced to generate the grid in the curvilinear coordinate system. A primitive variable approach is adopted in this work. The pressure linked equation in the non-orthogonal grid is solved to get the pressure variable; velocity components are obtained by solving the momentum equation in the primary flow direction as well as in the gapwise direction We believe this non-orthogonal grid approach is easier to program and can be extended to three dimensional problems directly.