High-Order Numerical Analysis of Two-Dimensional Square Driven Cavity Flow Using Vorticity Transport Equation.

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  • 渦度輸送方程式を用いた二次元正方キャビティ内流れの高精度解析
  • ウズド ユソウ ホウテイシキ オ モチイタ 2ジゲン セイホウ キャビティナイ

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Abstract

In this work, the two-dimensional square driven cavity flow problem is solved by the finite difference method with a uniform mesh. The 3 rd-order upwind scheme and the 5 th-order upwind scheme are applied to the convective term in the vorticity transport equation. It is necessary that the approximation of the convective term is treated carefully. First, therefore, the accuracy of the convective velocity is considered. As a result, it is clarified that accuracy of convective velocity is important in the numerical flow analysis in which vorticity and stream function are unknown quantities. Next, comparison of the 3 rd-order scheme and the 5 th-order scheme is carried out. Finally, by adopting of the highest-order calculation condition, more accurate results than Ghia's data for high Reynolds numbers are obtained. The steady solution can be obtained for Reynolds numbers as high as 25000.

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