這問題是研究關於一個三維power-law非牛頓流體流經非同軸的環管狀體且內管會旋轉的流動情形。因為是非牛頓流體的關係，黏滯項也成了數值計算上非線性的來源之一，使得計算的複雜度增高。且此為三維的問題，計算量比二維大的可觀。我們用Galerkin/least squares finite element的方法去做空間上離散的動作；平行演算法上是用Newton-Krylov-Schwarz演算法為基礎，因此可執行大量的數值計算。我們提供了一個可以觀察三維流體的solver，而且不只可以觀察在全展流狀態下的流體流動情形，亦可以觀察發展中流體的流動情形。經過計算得到以下的數值結果：網格的收斂度測試、二維和三維的比較、一些物理量三維的呈現、非牛頓影響的入口長度，以及平行運算的效能討論。

This work is about a numerical study of 3D flow of an inelastic power-law fluid through eccentric annuli with
inner cylinder rotation. The nonlinearity due to the shear-rate dependent viscosity and the truly 3D flow behavior makes us to solve the flow problem challenging and
parallel computing is necessary to handle such compute-intensive task. We use Galerkin/least squares finite element formulation for the spatial discretization, and the resulting large sparse nonlinear system of equations is solved by a Newton-Krylov-Schwarz algorithm that is suitable for large scale computing. In this study, we investigate the behavior of flow under different values of power law index and the Reynolds number ratios between axial and azimuthal directions within both of the developing and developed regions.
We provide some numerical results including the grid independent test, a comparison between 2D and 3D cases,
3D plots for physical quantities of flows, non-Newtonian effect on entrance length, and parallel performance
study.

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