Numerical analysis to support splitting and merging phenomena in interfacial dynamics

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540171
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyoto University (2014); Osaka Institute of Technology (2011-2013)
• Principal Investigator: TOMOEDA Kenji 京都大学, 情報学研究科, 研究員 (60033916)
• Co-Investigator(Renkei-kenkyūsha): IMAI Hitoshi 同志社大学, 理工学部, 教授 (80203298) ; KURAMA Hiroyuki 大阪工業大学, 工学部, 准教授 (90298802)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 自由境界サポートの分離・併合 / 界面ダイナミクス / 自由境界 / 差分法

Outline of Final Research Achievements

Numerical experiments suggest interesting properties in the several fields. Among such properties, there are support splitting and merging phenomena in the behaviour of non-stationary seepage. The model equation in one dimensional space is written in the form of the initial-boundary value problem with the effect of a non-linear filtration.
In this study, such phenomena are realized by use of finite difference schemes, and are justified from numerical and analytical points of view. Thus we obtained following results: (1) Our difference scheme has the property of the stability and the convergence; (2) The solution of the initial-boundary value problem converges to the stationary solution when the boundary conditions are constant; (3) Repeated support splitting and merging phenomena appears when the period of the boundary conditions is sufficiently long; (4) We are able to show some example such that the support splitting phenomena never appears when the period is sufficiently short.

Free Research Field

偏微分方程式に対する数値解析