Non-singular vortex methods employing anisotropic elements with piece-wise constant vorticity distributions have Resolution of boundary layer flows at moderate or high Reynolds numbers with the vortex blob method requires a great many iso-been used by Teng [2] for elliptical elements and by Huyer tropic elements. In this paper, an approximate method for determiet al. [3] for rectangular elements. Bernard [4] recently nation of the induced velocity from highly anisotropic vorticity blobs presented a method for boundary layer flows in which the is presented, and issues related to use of anisotropic elements in velocity field is obtained by integrating over anisotropic calculations with vortex blob algorithms for high Reynolds number rectangular vorticity tiles in which the vorticity varies near-wall flows are examined. The method presented here can be used to determine the induced velocity from smooth blob functions within each tile but is discontinuous at the tile edges. While of arbitrary form, provided that the vorticity length scale associated non-singular, but discontinuous, vorticity representations with the blob is much less in one direction than in orthogonal considerably lessen the noise problems experienced with directions. The ratio of these length scales is called the blob aspect singular representations, the contribution to velocity at a ratio, , and is used as a small parameter to construct an asymptotic point due to nearby elements is still inaccurately estimated approximation to the induced velocity field. This method is applied in the present paper to derive induced velocity expressions for with these methods because the vorticity tiles in some anisotropic Gaussian blob functions in both two and three dimenplaces overlap and in other places separate to leave gaps sions. It is argued, using test calculations for a Blasius boundary between tiles.
layer, that although direct calculation of the induced velocity re-Several recent vortex blob methods (e.g., Knio and Ghoquires about an order of magnitude more CPU time for anisotropic
niem [5], Winckelmans and Leonard [6], Koumoutsakos
Gaussian elements than for isotropic elements, this difference is more than made up for by a reduction of several orders of magnitude et al. [7]) avoid problems with singular and discontinuous in the number of elements needed to resolve boundary layer flows vorticity fields by using a representation consisting of a at moderate to high Reynolds numbers. It is also found that the set of smooth, overlapping vorticity ''blobs,'' a popular standard vortex blob representation leads to errors in the calculation example being the Gaussian distribution. In order for a of wall slip velocity and wall shear stress due to smoothing of the vortex blob representation to be useful, it must be possible discontinuity between the real and image vorticity fields at the wall, but that these errors can be avoided by placing doublet-type ele-to determine the velocity induced by the vorticity element ments along the wall.