為了能夠精確地處理日益複雜的流場問題，對於改善計算效率是非常必要的，一般計算實際的複雜流場問題時，皆需要使用相當多的格點數目，由於現有電腦記憶體的容量仍然有限，因此限制了所能使用之計算格點數。此外，在單層格點上執行疊代法的疊代次數隨著格點數的增加而遞增，導致計算時間相當可觀。多重格點法被認為是一種有效的加速計算法。
本研究模擬的問題為二維側邊加熱的自然對流場，使用的演算法為時間步進法，並將多重格點法應用在求解其中的解壓力方程式，測試的格點數從64x64、128x128到256x256，測試的層數為單層到四層，使用的多重格點循環有單一個與兩個V-循環，流場的瑞里數為1x108，以比較格點數多寡下不同多重格點層數以及不同數目的多重格點循環其對加速效率的影響。
由測試結果發現，使用多重格點法的加速效率會隨著格點數的增加而遞增，此外，多重格點法之層數的增加與多重格點循環的增加，都能有加速收斂、減少疊代次數和計算時間的效果，但是，多重格點法的層數與循環數應配合格點的數目做調整，過多的層數與循環數，會使多重格點法在內插運算過程中增加不少傳輸的時間。由測試結果可證實，多重格點法確為一種能提高加速效率的利器。

There is urgent need in improving computational efficiency in order to solve fluid flow problems of increasing geometrical complexities. While calculating complicated fluid flow problem, it always needs to use plenty of grid nodes. Because the memory capacity of computer is still limited, it restricts the computational number of grids that can be used. Moreover, iterations on single-grid method increase as increasing of grid nodes and take excessive computation time. Multigrid method is considered as an effective method to enhance the computational speed.
Natural convection in square cavity heated by sidewall is simulated in this study. The governing equations are solved with fractional time-step method, and multigrid method is applied to solve the poisson equation. The test grid meshes are from 64x64 to 256x256. The test levels are from one to four levels, while the multigrid V-cycles are from one to two cycles. The Rayleigh number of the fluid flow is 1x108. Influence of acceleration efficiency with different multigrid levels under different grid meshes is investigated. It also compares the influence of acceleration efficiency with different multigrid cycles under different grid meshes.
According to the present results, it is obviously found that the efficiency of speed-up by using multigrid method increase as increasing of grid nodes. With the increasing levels and cycles of the multigrid method, it can not only enhance the convergence rate but also decrease number of iterations and computation time. The levels and cycles of multigrid should make an adjustment in number of grids, otherwise it will cost more time in the interpolation procedure. The results show that multigrid method is indeed an effective method to accelerate calculation process.

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