2005 Fiscal Year Final Research Report Summary
Numerical Conformal Mappings by the Charge Simulation Method and Their Applications to Fluid Mechanics
| Project/Area Number |
15340033
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ehime University |
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Principal Investigator |
AMANO Kaname Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (80113512)
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| Co-Investigator(Kenkyū-buntansha) |
OKANO Dai Ehime University, Faculty of Engineering, Ressearch Assistant, 工学部, 助手 (90294785)
TSUCHIYA Takuya Ehime University, Faculty of Science, Professor, 理学部, 教授 (00163832)
OGATA Hidenori The Univetsity of Electro-Communications, Faculty of Electro-Communications, Associate Professor, 電気通信学部, 助教授 (50242037)
SUGIHARA Masaaki The University of Tokyo, Graduate School of Information Science and Technology, Professor, 情報理工学系研究科, 教授 (80154483)
YOTSUTANI Shoji Ryukoku University, Department of Science and Engineering, 理工学部, 教授 (60128361)
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| Project Period (FY) |
2003 – 2005
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| Keywords | charge simulation method / Laplace's equation / fundamental solution / numerical conformal mapping / multiply connected domain / potential flow / numerical analysis / complex analysis |
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| Research Abstract |
The numerical conformal mapping has been an important subject in computational and applied mathematics. Our major concern is to develop new methods of numerical conformal mappings by the charge simulation method (or the fundamental solution method) and apply them to potential flow problems.
1.We constructed approximate mapping functions of the conformal mapping w= f(z) of an unbounded multiply connected domains D onto the unbounded canonical slit domains of Nehari (Mc-Graw Hill, 1952) under the condition f(v) = ∞, where v is a finite point given in the problem domain. They were applied to the problem of potential flows past obstacles caused by a dipole source, a pair of positive and negative vortexes or a pair of point source and sink.
2.We constructed by the charge simulation method approximate mapping functions of the conformal mapping of bounded multiply connected domains onto all the unbounded and bounded canonical slit domains of Nehari.
3.We proposed a new technique to apply the charge simulation method to a nonlinear compressible fluid flow problem. We also proposed a fundamental solution method for viscous flow problems with obstacles in a periodic array, which gives an approximate solution by a linear combination of periodic fundamental solutions.
4.We proved the convergence of the approximate mapping function obtained by the charge simulation method.
Many other interesting results were obtained in relation to methods of numerical computation and thier application to fluid mechanics.
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[Journal Article] Bi-directional method for numerical conformal mappings of multiply connected domains by the charge simulation method,2005
Author(s)
Okano, D., Terazono, M., Amano, K., Ogata, H.
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Journal Title
Theoretical and Applied Mechanics, Proceedings of the 54th Japan National Congress on Theoretical and Applied Mechanics (Hokusensha, Tokyo) Vol.54
Pages: 357-363
Description
「研究成果報告書概要(欧文)」より
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[Journal Article] A numerical conformal mapping onto the radial slit domain by the charge simulation method2004
Author(s)
Amano, K., Okano, D., Tamai, M., Shimada, H., Ogata, H.
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Journal Title
Proceedings of The Third International Conference on Information (Edited by L.Li, K.-K.Yen) (International Information Institute)
Pages: 384-387
Description
「研究成果報告書概要(欧文)」より
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[Journal Article] Numerical conformal mapping by the charge simulation method and their application to potential flow problems (in Japanese)2004
Author(s)
Amano, K., Tamai, M., Okano, D., Ogata, H., Sugihara, M.
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Journal Title
IPSJ Journal Vol.45, No.5
Pages: 1322-1325
Description
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[Journal Article] Numerical conformal mappings of bounded multiply-connected domains by the charge simulation method,2003
Author(s)
Okano, D., Ogata, H., Amano, K., Sugihara, M.
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Journal Title
Journal of Computational and Applied Mathematics, Proceedings of The Sixth Japan-China Joint Seminar on Numerical Mathematics, Tsukuba, Japan Vol.159, No.〜1
Pages: 109-117
Description
「研究成果報告書概要(欧文)」より
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[Journal Article] A charge simulation method for spatially periodic problems,2003
Author(s)
Ogata, H., Okano, D., Amano, K., Sugihara, M.
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Journal Title
Progress in Analysis, Proceedings of the 3rd International ISAAC Congress (Edited by H.G.W.Begehr, R.P.Gilbert, M.W.Wong) (World Scientific, New Jersey) Vol.2
Pages: 1459-1468
Description
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