2006-08-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/708214摘要：分析三維具複雜幾何外形及高度非線性渦流行為的流體力學問題往往要耗上數個月的計算時間，隨著電腦技術的進步，利用高速且具平行計算能力之電腦執行高性能、高效率之平行計算已是不可迴避的趨勢。本研究之目的在於發展一可平行地求解複雜幾何外形之實際流場問題。本研究整體架構是在三維正交卡氏座標系統上，于非交錯式網格上的配置方式，採用有限差分方法離散統御方程式，結合高階準確單調1D+2D之數值算則及IBM（Immerse Boundary Method）以有效地平行求解具複雜外形的流體力學問題。為了克服因非線性迭代所產生在大型且具複雜物理行為問題，本研究為了不易收斂性、減少電腦計算之時間與存取的浪費，將1D/2D ADI算則執行在多層次(multi-level)、多重網格(multi-grid)的三階Newton-Raphson線性化的架構上。分析之結果將與實際流場量測結果做一比較，以驗證數值平台之正確性。經由本計畫之執行，預期可達成在不可壓縮流與質量守恆條件下得以分析三維具複雜幾何外形之實際流場，以建立「具高度平行能力的流體力學數值模擬」之功能。<br> Abstract: Analysis of three-dimensional fluid dynamics problems with complex geometries and highly nonlinear vertical flow nature normally takes months of computing time. With the advent of high-speed parallel computers, it is now the state-of-art and trend of solving large-scale problems of this type. The present proposal aims to solve physically realistic fluid flow problems, with complex physics and geometry, within the parallelized framework. The current finite difference analysis is developed in the 3D Cartesian coordinate system, on which the primitive variables are stored on the non-staggered grids for avoiding coding complexity without incurring oscillatory pressures. For making use of parallel ability in shortening the computational time, we plan to match the solution alternating and well-parallelized in one direction (x, y, z-axis). At the same time, the solutions for (u, p) are solved on the yz, xz and xy planes, respectively so that large-sized problems with mesh sizes as large as 1024×1024 can be effectively solved. To cope with problems with slow convergence or even divergence in solving nonlinear Navier-Stokes equations, we plan to include the multi-level solution algorithm within the above 1D/2D parallelized ADI (Alternating Direct Implicit) framework to speed up convergence by reducing the condition number of the invoked matrix equation. In the coarse-level, we apply the multi-grid (4-grid) technique to solve the resulting two-dimensional equations so that solutions can be effectively obtained. Also, linearization can be further rigorously made be developing the higher-order (third-order) Newton-Raphson linearization method. All the above proposed model parallelized solution algorithms and linearization means will be validated by solving three-dimensional benchmark problems to demonstrate its excellent computational performances. Through this 3-year development project, we expect to solve the very large-sized industrial flow problems computationally effective on the Cartesian grids using the proposed IBM (Immerse Boundary Method) method.非線性平行計算計算流體力學黏性流