2000 Fiscal Year Final Research Report Summary
New Numerical Methods for Flow Problems and their Numerical Simulation
| Project/Area Number |
10304007
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| Research Category |
Grant-in-Aid for Scientific Research (A).
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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 | Kyushu University |
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Principal Investigator |
TABATA Masahisa Kyushu Univ.Faculty of Mathematics Professor, 大学院・数理学研究院, 教授 (30093272)
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| Co-Investigator(Kenkyū-buntansha) |
KAWARADA Hideo Chiba Univ.Faculty of Engineering Professor, 工学部, 教授 (90010793)
KANAYAMA Hiroshi Kyushu Univ.Faculty of Engineering Professor, 大学院・工学学研究院, 教授 (90294884)
USHIJIMA Teruo Univ.of Electro-Communications Professor, 電気通信学部, 教授 (10012410)
NAKAO Mitsuhiro Kyushu Univ.Faculty of Mathematics Professor, 大学院・数理学研究院, 教授 (10136418)
TOMOEDA Kenji Osaka Inst.of Technology Faculty of Engineering Professor, 工学部, 教授 (60033916)
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| Project Period (FY) |
1998 – 2000
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| Keywords | finite element method / domain decomposition / validated computation / error analysis / external domain problems / mantle convection / moving boundary problem / drag and lift |
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| Research Abstract |
(1) We have developed a numerical method for computing accurately drag and lift exerted by the fluid to a body immersed in the flow field. Transforming those values to equivalent integrals in the domain, we have succeeded in establishing error estimates. We have obtained accurate drag coefficients of a sphere by this method. The restults have been extended to evolutional problems and best possible error estimates have been obtained.
(2) The system of Rayleigh-Benard equations with infinite Prandtl number is a mathematical model describing heat convection phenomena in slow flows such as the Earth's mantle convection.We have developed a finite element scheme for this system, established error estimates, made an effective parallel code for three-dimensional computation, and performed numerical simulation for the Earth's mantle convection.
(3) We have developed mathematical theory and computation algorithms to find exact solutions of partial differential equations from numerical computation results. Those methods have been applied to the stationary Stokes equations, the Navier-Stokes equations, stationary bifurcation solution of heat convection problems.
(4) We have applied Dirichlet-Neumann mapping to exterior problems and developed combined numerical methods with a charge simulation method for the harmonic equation and with a domain decomposition method for the Helmholtz equation.
(5) We have constructed a mathematical model to analyze effect to ecological system caused by coastal oil pollution and performed the numerical simulation and the visualization. The obtained results are in good agreement with physical experimental results.
(6) The interface of porous media flow takes various behavior depending on the initial state. Using finite difference method we have given a sufficient condition for the separation of the support of the solution and upper and lower estimates of the waiting time for the initial interface to keep invariant.
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