2000 Fiscal Year Final Research Report Summary
The research on homogenization, elasitic problems and the algorithms for numerical simulations of flows of liquids and development
| Project/Area Number |
11640098
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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 |
KAIZU Satoshi Ibaraki University, Faculty of Education, Professor, 教育学部, 教授 (80017409)
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| Co-Investigator(Kenkyū-buntansha) |
KAWASHITA Mishio Ibaraki University, College of Education, Associate Professor, 教育学部, 助教授 (80214633)
ONISHI Kazuei Ibaraki University, Faciulty of Science, Professor, 理学部, 教授 (20078554)
SOGA Hidco Ibaraki University, College of Education, Professor, 教育学部, 教授 (40125795)
FUJIMA Shoichi Ibaraki University, Faculty of Science, Associate Professor, 理学部, 助教授 (00209082)
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| Project Period (FY) |
1999 – 2000
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| Keywords | two-layers problem / the density-dependent Stokes problem / generalized boundary problems / the adjoint method / energy fecay of the Rayleigh surface waves / numeric construction of free boundaries / superosition of plane waves in the half-space / convergent finite element scheme to the Stokes equation |
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| Research Abstract |
(1) Algorithm for numeric scheme on liquids flows : First, a theorem on errors of between the exact boundaries and numeric construction of boundaries are proposed by colleague and examined by numerically. Second, convergent finite element scheme for multi-flows miscible among different liquids, are proposed and proved. The governed equations are the Navier-Stokes equation for the first topic and the Stokes equation for the second one.
(2) The Laplace equation is considered as the corresponding scalar equation to the Navier-Stokes equation, in order to treat in a unified way under the notion of the generalized boundary value probleml for elliptic partial differential equations by using the variational calculus. The approach is verified by numerical examples.
(3) Among elastic waves, the Rayleigh surface waave is researched. In particular, the propagation of the Rayleigh surface wave is interested by us, and some estimates on decay of the local energy of the Rayleigh waves are obtained in many types of regions.
(4) Generally in the total space, it is well known that waves are represented as superposition of plane waves. In this research, it is showd that, in the half-space region, a concrete form of superposition to elastic waves are obtained. This expression is expected to be applied to the construction of the Fourier transformation in the half-space.
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