2000 Fiscal Year Final Research Report Summary
Generalization of a Spectral Finite Difference Scheme
| Project/Area Number |
11640102
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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, 大学院・理工学研究科, 教授 (90092577)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Spectral Method / Finite Difference Method / Numerical Analysis / Natural Convection |
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| Research Abstract |
In the current spectral finite difference scheme, dependent variables are assumed to be expressed in a complete spectral expansion (in one spatial component) such as Fourier expansion, which leads to a system of simultaneous partial differential equations in space normal to the direction (s) of expansion and in time. As a result, no error is introduced in decomposing the original partial differential equations in spatial components, so that the scheme possesses better resolution in space and high computation speed in nature at least for natural convection/forced convection/non-Newtonian fluid flow in a simply-connected region or over a doubly-connected region expressed in terms of a simple analytic function. Under the current project, proposed is introduction of a unified functional which maps the boundary to a circle in case of a two-dimensional simply-connected region. For several complex configuration, e.g. a. rectangular equilateral triangle cavity, a rectangular cavity, and a polygon cavity, a concrete mapping analytic function is obtained. For several cases mapping is expressed in terms of Jacobian elliptic functions. As a result, current schemes are found to be effective to get a steady-state solution at least under laminar natural convection for various combinations of parameters such as a Grashof number, a Prandtl number, and an elastic number (for a viscoelastic fluid).
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