2007 Fiscal Year Final Research Report Summary
Nonlinear Spectral Analysis in a Multiply-Connected Region
| Project/Area Number |
17540104
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Tokyo Institute of Technology |
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Principal Investigator |
MOCHIMARU Yoshihiro Tokyo Institute of Technology, Graduate School of Science and Engineering, Professor (90092577)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Spectral finite difference / Multiply-connected / Compatibility / Natural convection |
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| Research Abstract |
The spectral difference scheme is very effective to numerical analysis for nonlinear partial differential equations, such as Navier-Stokes equations. Effectiveness has been extended, using a conformal mapping with doubly-periodic functions.
Target equations are mainly partial differential equations with boundary values and/or initial values.
In this project, triply-connected two-dimensional regions or axisymmetric doubly-connected regions are treated. At the first stage, fluid is assumed to be Newtonian.
(i) Various conformal mapping function are introduced.
(ii) Various configurations are treated.
(iii) Region of infinite extension, non-isothermal boundary, and natural convection is treated.
As a result, conformal mapping using Jacobian elliptic functions is found to be very effective in multiply-connected region under a spectral finite difference scheme.
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