Sharp interface limits for diffuse interface models for two-phase flows of viscous incompressible fluids

粘性不可压缩流体两相流扩散界面模型的尖锐界面限制

• 批准号: 135025629
• 负责人: Professor Dr. Helmut Abels
• 金额: --
• 依托单位: Lehrstuhl für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/135025629?language=en
• 关键词: Sharp; interface; limits; diffuse; models

We seek a rigorous understanding of sharp interface limits of so-called diffuse interface models for the flow of two viscous fluids like oil and water. In diffuse interface models a partial mixing of the macroscopically immiscible fluids on a small length scale \vareepsilon > 0 and diffusion of the mass particles are taken into account. These models are capable of describing such two-phase flows beyond the occurrence of topological singularities of the interface due to collision or droplet formation. Both for theoretical and numerical purposes a deeper understanding of the limit \vareepsilon rightarrow 0 in dependence of the scaling of the mobility m_{vareepsilon} is of interest. Here the mobility is the inverse of the Peclet number and controls the strength of the diffusion. In particular, we want to understand the influence of the scaling of the mobility coefficient m_{vareepsilon} as \vareepsilon rightarrow 0 on the limit system and on the convergence rates rigorously. This way we want to clarify numerical observations and formal derivations in the literature and obtain new insights.

我们寻求一个严格的理解，所谓的扩散界面模型的两个粘性流体，如油和水的流动的尖锐的界面限制。在扩散界面模型中，考虑了在小长度尺度上宏观上不混溶的流体的部分混合和质量颗粒的扩散。这些模型能够描述这种两相流超出发生的拓扑奇点的接口，由于碰撞或液滴形成。从理论和数值两方面考虑，我们都有兴趣深入了解迁移率m_{varecom}与极限\varecom rightarrow 0之间的关系。这里的迁移率是Peclet数的倒数，并控制扩散的强度。特别地，我们希望严格地理解迁移率系数m_{vareq}的缩放为\vareq rightarrow 0对极限系统和收敛速度的影响。通过这种方式，我们希望澄清文献中的数值观测和形式推导，并获得新的见解。