2023 Fiscal Year Final Research Report
Mathematical modeling and analysis toward understanding pattern dynamics in circular expanding smoldering combustion
| Project/Area Number |
20K22307
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Multi-year Fund |
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| Review Section |
0201:Algebra, geometry, analysis, applied mathematics,and related fields
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| Research Institution | University of Miyazaki (2022-2023)
Kyoto University (2020-2021) |
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Principal Investigator |
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| Project Period (FY) |
2020-09-11 – 2024-03-31
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| Keywords | 燃焼現象 / 数理モデリング / 力学系理論 / 数値解析 / Kuramoto--Sivashinsky方程式 / 漸近解析 |
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| Outline of Final Research Achievements |
This study focuses on the phenomenon of smoldering combustion on thin solid fuels. So far, several mathematical models have been proposed, but the complexity of the equations and the high spatial dimensions have made mathematical analysis challenging. Consequently, no practical models have been constructed, and the dynamics of smoldering wavefronts have not been mathematically elucidated.
In this research, we have aimed to uncover the mathematical structure hidden behind the behavior of smoldering wavefronts as they change over time. We have successfully derived a new mathematical model, analyzed the instability of solutions with dynamical systems theory, and developed a high-speed, high-precision numerical scheme. Additionally, we fed the theoretical results from this study back into experiments, contributing to the discovery of combustion wavefronts that exhibit characteristic behaviors known as rotating waves.
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| Free Research Field |
応用数学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では，閉曲線の時間発展方程式による数理モデリングを試みた．これには，燃焼波面の挙動の本質を，空間一次元問題へと縮約するという狙いがある．これまで，閉曲線の時間発展方程式の解の性質は，数値シミュレーションを主体に調べられてきた．界面現象として燻焼を捉え，解の不安定性解析を展開し，解の形状・漸近挙動・安定性を数理モデルが有するパラメータと紐づけて解析した本研究手法は，燃焼現象のみならず，様々な界面現象の数理解析へと有用である．
また，本研究成果は，衣類の燻焼など現実的かつ応用性の高い問題に対し，燻焼速度や領域変化の定量的評価を計るための数理的基盤整備に繋がると期待している.
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