第七章 結論與建議
7.2 建議
本研究摒棄二維子模式決定自由液面位置之方法，希望自由液面之位 置藉由三維流場內部動量與質量平衡自動決定，在直線渠道之測試案例之觀 察發現，整理幾點建議供後續研究參考：
1. 對於自由液面流，流場內部垂向流速剖面形狀之垂向黏滯係數之分佈乃 相互影響，對非定常流況具時變性，流量、底床狀況等均為其影響因子，
無法由人工率定為之，因此藉由紊流模式之建立有其必要，對垂向流速 分佈尤為重要。
2. 對於小水深、流況劇烈之自由液面流，底床邊壁效應對流速剖面形狀之 影響甚鉅，藉由牆函數(wall function)合理估算近床邊界層流範圍流之速 速分佈改善流速剖面有其必要。
3. 本研究以卡氏座標建立模式，目前僅能測試簡單幾何之案例，若欲應用 於現場案例，則可考慮曲線座標；另外，對河川或水庫之模擬，由於底 床之不規則變化，考慮σ座標可將不規則之地形轉化為規則之計算網 格，以增加模式應用之彈性。
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附錄、修正湯瑪斯(Thomas)演算法
其中，
A3,3 f3w1+s3v2 +u3 =b3 ⇒u3 =b3 −s3v2 −f3w1
後向取代步驟
n
n z
x =
1 n n 1 n 1
n v x z
x − + − = − ⇒xn−1 = zn−1 − vn−1xn
2 n n 2 n 1 n 2 n 2
n v x w x z
x − + − − + − = − ⇒xn−2 = zn−2 − vn−2xn−1 − wn−2xn 得後向取代遞迴關係式
⎪⎩
⎪⎨
⎧
−
=
−
−
=
−
=
=
+ +
−
−
−
1
~ 2 n i , x w x v z x
x v z x
z x
2 i i 1 i i i i
n 1 n 1 n 1 n
n n
(A.8)
求解步驟整理如下：
1. 將係數矩陣 A 以係數遞迴關係式(A.6)分解為上下矩陣 LU，
2. 以前向消去遞迴關係式(A.7)得(A.4)右式向量{z}，
3. 以後向取代遞迴關係式(A.8)得方程組解{x}。