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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

基本信息

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

项目摘要

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.

本文对反应扩散系统中的斑图动力学、Hele-Shaw盒中的粘性指进现象、蒸发过程中水所占区域的动力学行为等典型动力学界面现象进行了数值模拟，得到了以下结果：1）发展了反应扩散系统中的TCD（Threshold Competition Dynamics）方法，使我们能够实现R^n（n=1，2，3.）中自由边界的动力学行为。该方法的思想是基于“奇异极限法”的理论。2）晶体生长的数学模型是考虑对流效应的反应扩散方程的形式，并给出了有趣的数学结果。3）在粘性指进现象中，研究了Hele-Shaw池中气泡上升的浮力驱动路径不稳定性。作为一个有趣的现象，出现了一个类似彗星的尾迹。4）建立了基于晶体均匀化方法的多尺度有限元方法，用于预测金属板料成形过程中的界面动力学行为。5）研究了蒸发过程中的重复支撑分裂和连接特性，其中支撑指的是水所占据的区域。建立了这一过程的数值方法，并明确地得到了这种性质出现的初始分布的形状。