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Hokkaido University Preprint Series in Mathematics >
A fast tree-code algorithm for the vortex method on a sphere
| Title: | A fast tree-code algorithm for the vortex method on a sphere |
| Authors: | SAKAJO, Takashi Browse this author |
| Keywords: | fast tree-code algorithms | | flows on sphere | | vortex method | | vortex sheet |
| Issue Date: | 23-Apr-2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 847 |
| Start Page: | 1 |
| End Page: | 19 |
| Abstract: | A fast and accurate algorithm to compute interaction between N point vortices on a sphere is proposed. It is an extension of the fast tree-code algorithm based on the Taylor expansion developed by Draghicescu for the point vortices in the plane. When we choose numerical parameters in the fast algorithm suitably, the computational cost of O(N2) is reduced to O(N(logN)4) and the approximation error decreases like O(1=N) as N ! 1, which are clearly con rmed in the present article. We also apply the fast method to a long-time evolution of two vortex sheets on the sphere. A key device is to embed the sphere into the three-dimensional space, in which we reformulate the equation of motion for the N point vortices. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69656 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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