本研究利用Marker-and-Cell (MAC)，配合非均勻網格，以速度、壓力為主要變數，使用顯性有限差分直接求解Navier-Stokes方程組，建立三維不可壓縮黏滯層流數值模式。其中對流項採用上風權重差分法，黏滯項則使用中央差分，最後利用壓力差值修正速度及壓力修正量。為驗證模式之正確性及探討實際應用的可行性，文中針對不可壓縮黏滯層流流經方柱流場進行三維數值模擬，主要探討尾流形成區之流場形態、方柱受力情形及底部邊界影響；模擬結果發現底床邊界對此不穩定流場造成極大影響，當邊界層與方柱尾流漩渦群交互影響，造成流場向上發展之趨勢，並使得尾流漩渦群產生扭曲之三維運動情形；且流體在流經障礙物時於障礙物底部前產生馬蹄形漩渦(Horseshoe vortex)，其旋轉中心即為流體流動之奇異點(A three-dimensional singular point)，此一漩渦可能告成障礙物底部掏蝕之現象。In this study we have established a numerical simulation of three-dimensional viscous flow. The explicit time dependent finite-difference method which based on the Marker-and-Cell technique and nonuniform mesh to solve the Navier-Stokes equations. We employed the methods of weighted-upwind difference for convective terms and central difference for viscous terms. The pressure correction method was used to obtain the velocities and pressure which satisfied the divergence-free constrained. The numerical study of incompressible viscous laminar fluid flow past a square cylinder is presented. The vortex shedding and the drag force of the square cylinder are discussed particularly. The computed result shows the wall effect and vortex shedding interaction and produces complicated three-dimensional flow pattern, the streaklines and cross-flow velocity fields demonstrate the development of this motion. The velocity profiles indicated the boundary layer and vortex street developments. According to this study we have found the center of the horseshoe vortex is a three-dimensional singular point and it may produce erosion in the bottom of the hydraulic structures.
