臺灣博碩士論文加值系統

本論文運用 relaxation factor 和 Richardson extrapolation 的
數值計算方法，來加速以 second order upwind 的有限差分數值方法計
算的循環流場。首先使用 relaxation factor 加速收歛，使最大相對誤
差值達到 0.5 以內後停止， 然後，藉由測試連續疊代的 10 個最大誤差
值，判斷滿足於規律遞減的條件後，接下來改為使用這 10 次連續疊代的
函數值所構成的數列，求得之 Richardson extrapolation 數列收歛之極
值，再將此預測之極限值作為猜測值代回差分方程式疊代，直到最大相對
誤差值小於 0.00001為止。結果顯示，對於 driven cavity flow 問題，
當雷諾數 Re= 100, 400,1000, 2000 以及 5000，計算的疊代次數，確
實要比只使用 upwind 差分方法的疊代次數減少許多，相對於原疊代次
數所減少之百分比依次為 39.82%, 55.19%, 47.07%, 44.21%以及
40.74%。

This study is to apply extrapolation methods speeding up
the convergenceof the second order upwind numerical computation
for the recirculating flow.First, the convergence of numerical
computation for maximum relative error isattained under 0.5 by
using the relaxation method. Then it is followed
bysuccessively using a 10-point extrapolation of the
Richardson extrapolationto forecast a convergent limit for
the values of consequential iterationswhenever all the ten
consequent maximum errors are decreasing monotonously.Finally,
this limit is considered as a next initial guess to continue
theiterating procedure until the maximum relative error is less
than 0.00001. Asa result, for Reynolds number at values of
100, 400, 1000, 2000 and 5000 inthe driven cavity flow,the
number of iterations by using the relaxation factorand
Richardson extrapolation methods can be saved up to the
percentages of39.82%, 55.19%, 47.07%, 44.21% and 40.74%
respectively than those by usingthe upwind differencing scheme
only.