| Project/Area Number |
15K05002
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kyushu University |
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Principal Investigator |
TAGAMI Daisuke 九州大学, マス・フォア・インダストリ研究所, 准教授 (40315122)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 粒子法 / 特性曲線法 / 流れ問題 / 誤差評価 / 一般化粒子法 / 移流拡散方程式 / 安定性 / 正則条件 / 補間作用素 / 近似微分作用素 / Poisson方程式 / 熱方程式 / 打ち切り誤差評価 |
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| Outline of Final Research Achievements |
Mathematical analysis of a characteristic generalized particle method for flow problems is considered. The particle methods approximate material derivative with the Lagrange coordinate, and move the particles by following flow fields. However, in general, the particle motion cause particle distributions unevenness and numerical schemes instability.
In this research, to overcome this difficulty, a semi-implicit characteristic method has been introduced into an approximation of the material derivative. By introducing the characteristic method, we can distribute particles at every time steps satisfying the regularity condition without following the motion of particles.
Moreover, when we are required to refer physical values at the previous time step, we just evaluate interpolants of physical values at the previous time step. Then, energy inequalities and error estimates of the semi-implicit characteristic genelarized particle method for convection-diffusion problems are established.
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| Academic Significance and Societal Importance of the Research Achievements |
粒子法はその特徴から, 対象となる流体領域が時間経過に伴い変化する移動境界問題の取扱いが容易なため, 近年, 産業における製品設計や, 防災シミュレーションなどの場面で盛んに用いられている数値計算手法の一つである. しかしながら, 有限差分法や有限要素法などの数値計算手法と比較すると, その数学的観点からの基盤理論の整備がなされているとは言い難い. そこで本研究課題の成果により, 粒子法を用いた数値計算結果に対する信頼性や計算手法の効率性を高めることができれば, 粒子法を適用する例えば津波遡上数値計算を基にしたより良い避難経路策定に繋がる可能性がある, などの社会的意義が将来的に期待できる.
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