| Project/Area Number |
15340033
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Ehime University |
|---|
Principal Investigator |
AMANO Kaname Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (80113512)
|
|---|
| 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)
|
|---|
| Project Period (FY) |
2003 – 2005
|
| Project Status |
Completed (Fiscal Year 2005)
|
| Budget Amount *help |
¥7,900,000 (Direct Cost: ¥7,900,000)
Fiscal Year 2005: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2004: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2003: ¥3,000,000 (Direct Cost: ¥3,000,000)
|
|---|
| Keywords | charge simulation method / Laplace's equation / fundamental solution / numerical conformal mapping / multiply connected domain / potential flow / numerical analysis / complex analysis |
|---|
| 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.
|
