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首页> 外文期刊>Journal of Computational Physics >A METHOD FOR DETERMINING THE VELOCITY INDUCED BY HIGHLY ANISOTROPIC VORTICITY BLOBS
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A METHOD FOR DETERMINING THE VELOCITY INDUCED BY HIGHLY ANISOTROPIC VORTICITY BLOBS

机译：一种确定高各向异性涡泡引起的速度的方法

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摘要

Resolution of boundary layer flows at moderate or high Reynolds numbers with the vortex blob method requires a great many isotropic elements. in this paper, an approximate method for determination of the induced velocity from highly anisotropic vorticity blobs is presented, and issues related to use of anisotropic elements in calculations with vortex blob algorithms for high Reynolds number near-wall flows are examined. The method presented here can be used to determine the induced velocity from smooth blob functions of arbitrary form, provided that the vorticity length scale associated with the blob is much less in one direction than in orthogonal directions. The ratio of these length scales is called the blob aspect ratio, epsilon, and is used as a small parameter to construct an asymptotic approximation to the induced velocity field. This method is applied in the present paper to derive induced velocity expressions for anisotropic Gaussian blob functions in both two and three dimensions. It is argued, using test calculations for a Blasius boundary layer, that although direct calculation of the induced velocity requires about an order of magnitude more CPU time for anisotropic Gaussian elements than for isotropic elements, this difference is more than made up for by a reduction of several orders of magnitude in the number of elements needed to resolve boundary layer flows at moderate to high Reynolds numbers, it is also found that the standard vortex blob representation leads to errors in the calculation of wall slip velocity and wall shear stress due to smoothing of the discontinuity between the real and image vorticity fields at the wall, but that these errors can be avoided by placing doublet-type elements along the wall. (C) 1996 Academic Press. Inc. [References: 18]
机译：用涡流斑点法分辨中等或高雷诺数下的边界层流需要大量各向同性元素。本文提出了一种从高各向异性涡旋斑点中确定感应速度的近似方法，并探讨了在高雷诺数近壁流涡旋斑点算法计算中使用各向异性元素的相关问题。如果与斑点相关的涡度长度尺度在一个方向上比在正交方向上小得多，则此处介绍的方法可用于从任意形式的平滑斑点函数确定感应速度。这些长度比例的比率称为斑点长宽比epsilon，它用作一个小参数来构造对感应速度场的渐近近似。本文将这种方法应用于二维和三维各向异性高斯Blob函数的感应速度表达式。通过对Blasius边界层的测试计算，尽管各向异性高斯元素的感应速度比各向同性元素的直接计算大约需要多一个数量级，但争论的是，尽管这种差异要通过减小来弥补在解析中等到高雷诺数的边界层流所需的元素数量的几个数量级时，还发现标准涡流斑点表示会由于平滑而导致计算壁滑速度和壁切应力时出现错误壁上实涡和图像涡场之间的不连续性，但可以通过在壁上放置双峰型元素来避免这些误差。 （C）1996年学术出版社。 Inc. [参考：18]

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