Development of a Core-Spreading Vortex Method with No-Slip Boundary Condition
Date Issued
2007
Date
2007
Author(s)
Su, Huan-Syun
DOI
zh-TW
Abstract
Based on the core-spreading vortex method developed by Leonard and the blobs-splitting-and-merging scheme developed by Huang, this thesis develops a new numerical method for two-dimensional viscous incompressible flows with solid boundaries. The no-penetration boundary condition is satisfied by placing a vortex sheet along the boundary, which strength must be adapted to cancel the slip velocity on the boundary induced by all the other flow components. The strength of the vortex sheet is computed in the present work by the constant panel method. To simulate the diffusion of the vortex sheet into the flow field as time goes on, Koumoutsakos’ analytical solution is employed, in which an effective vorticity flux is derived and used for solving the vorticity diffusion equation. The solution is then discretized into blobs (called “ -blobs”) in the vicinity of the boundary.
Moreover, to prevent the vorticity from entering into the body, the concept of “residual vorticity” is introduced in the sense that partial circulation of the vortex sheet is remained at the boundary without being diffused into the flow field. Blobs very close to the wall are thus unnecessary. Moreover, blobs may move too close to the boundary because of advection errors or other numerical errors. It may cause serious fluctuations in evaluating the strength of the vortex sheet. In order to reduce the fluctuations, these near-wall blobs (NWB) are also manipulated in use of the concept of “residual vorticity”. Finally, we apply the so-developed solver to a simulation of the flow past an impulsively started circular cylinder at different Reynolds numbers. The simulation results are compared with previous experimental as well as numerical data. The validity and the accuracy of this newly developed Navier-Stokes solver are confirmed.
Subjects
渦漩方法
無滑移邊界條件
面積擴散
殘留渦度
Vortex method
No-slip boundary condition
Core spreading
residual vorticity
Type
thesis
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