The Frontier of Numerical Analysis for Dynamics of Interfaces and Developments in Sciences and Engineering

界面动力学数值分析前沿及科学与工程发展

• 批准号: 16340029
• 负责人: TOMOEDA Kenji
• 金额: $ 10.26万
• 依托单位: Osaka Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340029/
• 关键词: free boundary; TCD method; singular limit method; multi-fluid flows; crystal growth; viscous fingering; multi-scale FEM; support splitting phenomena; Hele-Shawセル; リーゼガング現象; ヘリカル燃焼波; ギブス・トムソン効果; 燃焼パルス解; 二流体問題; 渦の相互作用; カーボンナノチューブ; レーリー・ベナール方; free boundary; TCD method; singular limit method; multi-fluid flows; crystal growth; viscous fingering; multi-scale FEM; support splitting phenomena; Hele-Shawセル; リーゼガング現象; ヘリカル燃焼波; ギブス・トムソン効果; 燃焼パルス解; 二流体問題; 渦の相互作用; カーボンナノチューブ; レーリー・ベナール方

We were concerned with the following numerical methods to the phenomena appearing in the repre-sentative dynamical interfaces :i) Pattern dynamics in the reaction-diffusion system,ii) Viscous fingering phenomena in Hele-Shaw Cell,iii) Dynamical behavior of the region occupied by the water in the process of evaporation.We obtained several results :1) The TCD (Threshold Competition Dynamics) method is developed for the numerical computation in reaction-diffusion system, and enables us to realize the dynamical behavior of free boundary in R^n (n=1, 2, 3.). The idea of this method is based on the theory of "Singular limit method".2) The mathematical model for the crystal growth is considered in the, form of the reaction-diffusion equation with the effect of a convection, and gives us interesting mathematical results.3) In viscous fingering phenomena, the buoyancy-driven path instabilities of bubble rising in Hele-Shaw Cell are examined. As an interesting phenomenon there appears a wake which is similar to a comet. However, such a wake is not realized in numerical method yet.4) Multi-scale FEM based on crystallographic homogenization method is developed to predict the dynamics of interfaces in the formability of sheet metal.5) The repeated support splitting and connecting property in the process of evaporation is investigated, where the the support means the region occupied by the water. The numerical methods for this process are established and the shape of the initial distribution for which such a property appear is explicitly obtained.

我们关注以下在代替式动态界面中出现的现象的数值方法：i）反应扩散系统中的模式动态，ii）Hele-Shaw细胞中的粘性指法现象，iii）在蒸发过程中由水占据的区域的动力学行为。我们获得了几个结果。系统，使我们能够实现r^n中自由边界的动态行为（n = 1，2，3。）。该方法的概念基于“单数极限方法”的理论。2）晶体生长的数学模型以对流的影响为反应扩散方程的形式，并给予了我们有趣的数学结果。33）在粘性指法现象中，浮标驱动的驱动式路径在Hele-Shaw Cell中的泡泡式路径升高。作为一个有趣的现象，似乎唤醒与彗星相似。然而，在数值方法中尚未实现这种唤醒。4）基于晶体均质均质化方法的多尺度FEM开发出来预测碎片金属可成形性的界面动力学。5）5）在研究蒸发过程中的重复支撑和连接属性，在研究的地方意味着在水上占据了支持的区域。建立了此过程的数值方法，并明确获得了该特性出现的初始分布的形状。