Abstract
本研究是利用完全多重網格法FMG(Full MultiGrid)及適用於非線性形式的完全近似值儲存法FAS(Full Approximation Storage)來加速不規則的二維穩態流場之數值模擬時的收斂速度。本法採用原變數形態 的系統方程配合交錯式網格(staggered grid)系統以及去耦合(decoupled)形態的SIMPLER演算法則，並以加權函數法(Weighting Function Scheme)來處理統御方程式中的一次微分對流項。而對於不規則形狀的處理，在本研究中則是採用較為直接的二維卡氏座標系統來離散整個計算的領域，對於那些領域外的格點則是予以跳過不計算。在本文中，共測試了四種不同的流場，包括兩種開放管流及兩種內部迴流。對於多重網格法與傳統的單層網格疊代法在這些流場中的收斂性，以及其他的計算參數，例如：雷諾數(Re)、網格解析度、鬆弛因子(under-relaxation factor)等，對於多重網格法的加速性能的影響，在本文中均作了相關的探討。根據這四種複雜不一的流場的測試結果顯示，對於此種不規則複雜流場的計算，本研究所使用的這一套多重網格計算法確實能夠提供一個兼具快速、準確而又穩定求解步驟。This paper presents a FMG-FAS multigrid technique toacceleratethe convergence rate of the computation of irregulartwo-dimensional incompressible flows. This method applies adecoupled algorithm, SIMPLER,to solve the Navier-Stokesequations in primitive variables on a staggered grid system.Also, in this work, the Weighting Function Scheme (WFS) isutilized to treat the convection term in the governingequations. As to the treatment of the irregular geometry, weadopt the two-dimensional Cartesian co-ordinate system indiscretizing the computational domain, while those nodesoutside this domain are skipped during calculation. Theperformance of this calculation procedure is assessed in fourlaminar irregular flows, including two open flows and twointernal recirculating flows. In addition to comparing theconvergence rates of the multigrid method and the traditionalsingle grid method in the calculation of these flows, theeffects of the Reynolds number, the grid resolutions and theunder-relaxation factors on the efficiency of the multigridmethod are also studied. This method is indicated from theseresults to offer a fast,accurate and also stable calculationprocedure for the simulation of irregular complex flows.