| Project/Area Number |
17K17585
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
Computational science
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| Research Institution | Kyoto University (2018-2020)
Tohoku University (2017) |
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Principal Investigator |
Imoto Yusuke 京都大学, 高等研究院, 特定助教 (60793982)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 偏微分方程式の数値解析 / 数値流体力学 / 粒子法 / 数値解析 / 安定性 / 収束性 / 非圧縮性Navier-Stokes方程式 / 誤差評価 / 数値計算手法 / 最小二乗法 |
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| Outline of Final Research Achievements |
We have established the truncation error estimates of approximate differential operators and error estimates of the particle method for heat and Poisson equations based on mathematical analysis such as functional analysis, partial differential equation analysis, and discrete geometry. Besides, the stability analysis of particle methods for incompressible flow problems has been obtained. From these mathematical results, we have developed improved methods that can reduce the stability conditions and have presented their mathematical interpretations. Moreover, in collaboration with engineers, we have applied the improved methods to practical problems such as vertical-jet flow and sediment flow experiments, and have shown the proposed method can obtain highly accurate and stable results rather than conventional methods.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は粒子法の数学解析の先駆的な研究であり、本研究の成果により、差分法や有限要素法のような代表的な偏微分方程式の数値解析手法と同様に数学的側面からの研究の発展が期待できる。また、粒子法の数学的理解が深まることで、粒子法のパラメータの設定方法の明確化による高汎化、あるいは粒子法の精度面の改良による高信頼化などが期待できる。その結果、粒子法による流体シミュレーションに基づく高信頼なハザードマップの作成や、防波堤の設計といった防災研究への貢献も期待できる。
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