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A Heterogeneous Multi-scale Approach to Liquid-Vapour Flow with Phase Transition

相变液汽流动的非均相多尺度方法

基本信息

批准号：
170470158
负责人：
Professor Dr. Christian Rohde
金额：
--
依托单位：
Centre de Mathématiques Appliquées (CMAP)
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2010
资助国家：
德国
起止时间：
2009-12-31 至 2015-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/170470158?language=en
关键词：
Heterogeneous Multi scale Approach Liquid

项目摘要

The description of compressible liquid-vapour flow with phase transition is characterized by completely different spatial scales in the bulk phases and in the vicinity of the phase interfaces. Most of the classical mathematical models for direct numerical simulation involve a complex coupling of scales such that even advanced numerical techniques do not suffice to give the necessary resolution for bubble dynamics on a relevant continuum-mechanical length-scale, say the centimeter range. To overcome these difficulties by scale separation we propose a class of new heterogeneous multi-scale models: the dynamics of the bulk phases on the macro-scale domain is modeled by the compressible Euler equations as a macro-scale model. For the micro-scale model we study sharp-interface (SI) as well as diffuse-interface (DI) models on full- and lower-dimensional microscale domains close to the interface. The SI-approach leads to the study of generalized Riemann problems while the DI-approach is realized by Navier- Stokes-Korteweg systems and phase field models. The basic numerical tool to solve the macro-scale model is the hp-adaptive Discontinuous-Galerkin method on unstructured grids. Compression and reconstruction of microscale information will be handled via the Ghostfluid idea. The complete numerical method will be validated by comparison with results for diffuse-interface models on the whole macro-scale domain, e.g. those which have been obtained in the Project A1 in the previous funding period. It will then be applied to typical phase transition problems involving a single bubble/droplet or a small number of bubbles/droplets. In particular we shall focus on the rise of bubbles in an evaporating vessel. Analytically we want to study the heterogeneous multi-scale model rigorously on the level of a model problem. A principal item is the continuation of our studies on sharp interface limits.

具有相变的可压缩液-汽流的描述的特点是体相和相界面附近完全不同的空间尺度。大多数直接数值模拟的经典数学模型都涉及复杂的尺度耦合，因此即使先进的数值技术也不足以在相关的连续机械长度尺度（例如厘米范围）上为气泡动力学提供必要的分辨率。为了通过尺度分离克服这些困难，我们提出了一类新的异构多尺度模型：宏观尺度域上体相的动力学通过可压缩欧拉方程作为宏观尺度模型进行建模。对于微尺度模型，我们研究了靠近界面的全维和低维微尺度域上的锐界面（SI）和扩散界面（DI）模型。 SI 方法导致了广义黎曼问题的研究，而 DI 方法则通过 Navier-Stokes-Korteweg 系统和相场模型实现。求解宏观模型的基本数值工具是非结构化网格上的 HP 自适应间断伽辽金方法。微观信息的压缩和重建将通过 Ghostfluid 理念进行处理。完整的数值方法将通过与整个宏观尺度域上的扩散界面模型的结果进行比较来验证，例如上一资助期A1项目已获得的成果。然后将其应用于涉及单个气泡/液滴或少量气泡/液滴的典型相变问题。我们将特别关注蒸发容器中气泡的上升。从分析上讲，我们希望在模型问题的层面上严格研究异构多尺度模型。一个主要项目是继续我们对尖锐界面限制的研究。