2000 Fiscal Year Final Research Report Summary
Mathematical analysis of flows directly associated with environmental problems.
| Project/Area Number |
10640100
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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 | Ibaraki University |
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Principal Investigator |
ONISHI Kazuei Ibaraki Univ., Faculty of Sci., Prof., 理学部, 教授 (20078554)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIMA Shohiti Ibaraki University., Faculty of Sci., Assoc. Prof., 理学部, 助教授 (00209082)
HASEGAWA Hiroshi Ibaraki Univ., Faculty of Sci., Assoc. Prof., 理学部, 助教授 (70282283)
SAKATA Fumihiko Ibaraki Univ., Faculty of Sci., Prof., 理学部, 教授 (50013438)
NAKAMURA Gen Gunma Univ., Fac.Engng., Prof., 工学部, 教授 (50118535)
SHIROTA Kenji Ibaraki University., Faculty of Sci., Assis. Prof., 理学部, 助手 (90302322)
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| Project Period (FY) |
1998 – 2000
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| Keywords | Water environment / Atmospheric environment / Navier-Stokes equations / Shallow water equations / Finite element method / Finite analytical method / κ-εmodel / Dirichlet-Neumann alternating method |
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| Research Abstract |
The purpose of the research project is to investigate mathematical problems in the flow analysis closely connected with the problems of environmental pollution. The research aimes at the development of computer simulation techniques for the protection of the environment in the aquious and atmospheric fields. For the objectives, we obtain the following results :
1. The finite element method is used for numerical solution of flow equations in order to cope with the complex geometry of the flow domian in question. The governing equations are discretized by using the fractional step scheme for incompressible viscous fluid flow and using the Taylor-Galerkin's method for the flow in shallow waters.
2. Boundary conditions are discussed from the view points of the domain decomposition method and the inverse problems. When relatively small areas are considered for numerical simulation of environmental flow problems, artificial boundaries need to be introduced in the formulation, on which some for
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ms of fictitious boundary values should be prescribed. The values to be prescribed on the artificial boundaries play the crucial role for the success of the simulation. However the boundary values are not known a priori, in fact they constitute unknowns of the problem itself. We found from our numerical experiment on the flow simulation around airfoils that appropriate boundary values can be obtained by the Dirichlet-Neumann alternating method after quite a few times of iteration.
3. Laminar flow model turns out to be insufficient for the numerical simulation of flows in the environmental study. We extended our analysis to turbulent models. We concluded that the κ-ε model is the most suitable from the stand points of practical use ; (1) the model is easy-to-use, and (2) data requisite for the implementation of the model are easily accessible. For flows at high Reynolds numbers or order 10^5 in turbulent regime, the finite analytical method was applied for the numerical simulation. The simulation showed good agreement with the corresponding results in physical experiment. Less
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