非結構化增量修正多重網絡法的概括性研究

Generalization of the Unstructured Additive Correction Multigrid Method

黃耀新(Yao-Hsin Hwang)

《技術學刊》 28卷2期 (2013/06) Pp. 97-108

摘要

本篇論文將擴展目前增量修正多重網格法的處理方式，其中著重在計算變數的修正方向與方程式的結合方式。根據這樣的概念，推導出兩個有別於傳統的增量修正法：最小誤差與正交增量修正法。前者可以在給定變數修正方向的條件下，得到對應方程式最小誤差的結合權重值；相反地，後者可以在已知方程式的結合權重值，獲得與變數平面互為垂直的修正方向。另外，本文又提出根據格點相鄰幾何基礎的連結式Gauss-Seidel法。在實例驗證結果中可知，正交增量修正法可以在流場Reynolds 數較小時得到較快速的收歛結果，而使用最小誤差增量修正法即使在極高的Reynolds數時，仍可獲得收歛結果；至於連結式Gauss-Seidel法在非結構化格點計算中則可以有效地增加求解效率。

關鍵字

增量修正多重網格 ； 方程式的結合權重 ； 最小誤差增量修正 ； 正交修正法

並列摘要

The present study aims at generalizing the additive correction multigrid method. Based on its underlying perceptions, one can derive two useful alternatives: minimum-error and orthogonal additive corrections. The former determines the weighting factors for equation agglomeration with a given solution correction direction; the latter yields a solution correction direction normal to the solution hyper-plane provided that the weighting factors have been specified. Furthermore, a linked Gauss- Seidel scheme complying with solution information propagation is suggested to improve convergence effectiveness. From numerical experiments, it is found that the multigrid strategy with orthogonal additive correction yields a more efficient solution procedure in the cases of lower Reynolds number flows. On the other hand, that with minimum-error additive correction still provides a convergent solution for higher Reynolds number flows. Meanwhile, the solution convergent rate is effectively increased by the linked Gauss-Seidel scheme, especially in problems formulated with unstructured grids.

並列關鍵字

additive correction multigrid ； equation agglomeration weighting ； least squared error correction ； orthogonal correction