1998 Fiscal Year Final Research Report Summary
Development of Numerical Method for Mesoscopic Flow
| Project/Area Number |
09680474
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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 |
エネルギー学一般・原子力学
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| Research Institution | TOKYO INSTITUTE OF TECHNOLOGY |
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Principal Investigator |
YABE Takashi Tokyo Institute of Technology interdisciplinary Graduate School of Science & Engineering, Professor, 大学院・総合理工学研究科, 教授 (60016665)
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| Co-Investigator(Kenkyū-buntansha) |
AOKI Takayuki Tokyo Institute of Technology Nuclear Reactor Laboratory, Associate Professor, 原子炉工学研究所, 助教授 (00184036)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Mesoscale / Numerical Method / CIP Method / Boltzmann / Vlasov / Particle Methods / Six Dimensions / Landau Damping |
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| Research Abstract |
For the research of microscopic phenomena, molecular dynamics model has been proposed and for macroscopic level various kinds of hydrodynamic solvers have been investigated for a long time. In this research, we search for a numerical method to treat mesoscopic level that means the intermediate scale between and microscopic and macroscopic levels . For this purpose, we have used the CIP method which has been proposed by the author and has been proved to be accurate even with coarse grid system. In this research, we have used the Boltzmann equation which is six dimensions in phase space. Thus time evolution is merely an advection through six dimensions. Since the CIP method has been proved to be quite effective in solving advection equation, we applied this method and for simplicity we repeated one-dimensional CIP method to extend it to hyper-dimensional space.
In order to test the algorithm, we solved two and four dimensional Vlasov equation which is collisionless Boltzmann equation, and applied it to linear Landau damping and nonlinear two-stream instability coupled with electric fields.
Comparison with conventional particle codes and spline method has been done and it has been proven that particle codes need 10-100 times more memory than the CIP method for obtaining the same results. For a sufficiently accurate form of velocity distribution function required by mesoscopic calculations, particle codes needed 100 times more memory than the CIP method. Distribution functions given by spline methods become negative and have large spikes. These comparisons show the effectiveness of the CIP method in this research.
We have varied the velocity grids and found that even with velocity grids less than 10 the CIP can give quite an accurate result. Finally, six dimensional code has been constructed and run on personal computer. One Alpha-chip-based personal computer needed only 6.7 hours for the calculation of Landau damping with 16 X 16 X 16 X 8 X 8 X 8 grids.
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