2004 Fiscal Year Final Research Report Summary
Study on the numerical analysis and its applications to engineering processes for free surface or interface flows
| Project/Area Number |
15540113
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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 | Toyama University |
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Principal Investigator |
OHMORI Katsushi Toyama University, Faculty of Education, Professor, 教育学部, 教授 (20110231)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Norikazu Toyama University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00334706)
SAKURAGI Takuya YKK Corporation, Research and Development Center, Manager, 研究開発センター, 解析室長
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| Project Period (FY) |
2003 – 2004
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| Keywords | two-fluid flows / Navier-Stokes equations / mass conservation / Lagrange multiplier technique / flux-free finite element method / Stokes interface problems / error estimates / convergence |
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| Research Abstract |
This study has been carried out during 2003-2004 in order to develop and analyze the finite element scheme for free-surace or free interface flows and to consider its application to industrial processes.
In 2003, we have proposed the flux-free finite element method for two-fluid flows with free interface, which is based a new variational formulation including the flux-free constraint by using Lagrange multiplier technique. Then we have considered the mathematical validity of the new variational formulation of our problems, the uniqueness and existence of the stationary problem and the stability of the fractional projection scheme for Navier-Stokes equations. Furthermore we have performed many numerical experiments for dam-break problems and sloshing tank problems to demonstrate the efficiency of our method. As a result, our method shows the high quality for the mass conservation.
In 2004, we have also considered the convergence of the flux-free finite element method for two-fluid flows which is modelled by Navier-Stokes equations with discontinuous viscosity and density by using the arguments on the finite element aproximation for Stokes interface problems. In fact, we have proposed an error estimate of Strang type and have shown the convergence of the flux-free finite element method under the assumption on the smoothness of the interface and the regularity of the solution of Stokes interface problem.
However, so much remains to be considered about new finite element schemes for two-fluid flows with high ratios of the density and viscosity in the real application of our method to the mold filling simulations.
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Research Products
(13 results)
