假頻譜元素法結合直接施力邊界沉浸法之誤差分析──以自由流經球體為例

Error Analysis of Pseudospectral Element Method Coupled with Direct-Forcing Immersed Boundary Modelling–Flow Past A Sphere

本研究利用兩種方法的結合，探討在低雷諾數的自由流下，流體流經球體後，計算球在不同雷諾數的阻力系數、尾流長度等數據，並將阻力係數的數值解與解析解和實驗結果比較誤差。而為了不讓邊界條件影響球體附近流場，在必須建構出大範圍的流場，同時又需要確保球體周圍網格的密集度情況下，本研究使用了區域分解法，建構非均勻網格，加密球體附近的流場網格，增加準確性。而最終結果驗證了，此兩種方法結合後，數值結果與實驗值的差異隨著網格數增加而大幅減少，但球體附近的網格也要夠密集才能地到更精準的數值解，因此必須使用區域分解法來提升其準確度。

"Error analysis is performed for the pseudospectral element method (PSME) incorporated with direct-forcing im-mersed boundary (DFIB) method. The benchmark case–free flow past a sphere–is simulated by the proposed PSME-DFIB model to predict drag coefficient, wake length and relevant physical quantities at a variety of Reynolds numbers. The domain decomposition approach is utilized to generate non-uniform grids for a large flow field in comparison with the size of sphere. Grids in the vicinity of the sphere are locally re-fined to preserve accuracy of solutions. In terms of numerical results, it turns out that the discrepancy between numerical prediction by the proposed model and experi-mental results decreases with increasing grid number. It means that the spectral accuracy of PSME method is still retained despite the DFIB method is employed."