Mathematische Analyse von Modellen zur Bildung fluider Strukturen an Grenzflächen

界面处流体结构形成模型的数学分析

• 批准号: 5107018
• 负责人: Professor Dr. Günther Grün
• 金额: --
• 依托单位: Lehrstuhl für Angewandte Mathematik I
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 1998
• 资助国家: 德国
• 起止时间: 1997-12-31 至 2006-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5107018?language=en
• 关键词: Mathematische; Analyse; von; Modellen; zur

The goal of the project is to analyse, to evaluate, and to improve mathematical models for the dewetting of thin liquid films on homogeneous surfaces and the formation of fluid structures on inhomogeneous substrates. During the second period of the Schwerpunktprogramm, investigations on evaporation and condensation processes will be included. The proposed project consists of three main parts which can be summarized as follows:Modelling: Based on lubrication approximation, evolution equations for the height of condensing fluids on inhomogeneous surfaces shall be derived.Analysis: Methods from the calculus of variations and the theory of partial differential equations shall be used to obtain results on existence and qualitative behaviour of solutions to the corresponding evolution equations for film height h and pressure p. Besides their obvious importance for a better understanding of the asymptotic behaviour of solutions, these theoretical results are also the key ingredient to formulate fast and reliable algorithms for numerical sumulations.Numerical simulations: During the last two years, G. Grün and M. Rumpf succeded in developing and analysing a finite-element/finite-volume scheme which drastically reduces the computation time for the simulation of spreading phenomena. Based on this scheme, a general finite-element solver shall be designed to enable numerical simulations of all the phenomena mentioned above. The evaluation will be performed by comparison with experimental data; it strongly depends on an intense cooperation with experimentalists inside the Schwerpunktprogramm.

该项目的目标是分析、评估和改进均匀表面上薄膜的去湿以及非均匀基底上流体结构形成的数学模型。在 Schwerpunkt 计划的第二阶段，对蒸发和冷凝进行研究。所提出的项目由三个主要部分组成，可概括如下：建模：基于润滑近似，高度的演化方程。导出非均匀表面上的冷凝流体。 分析：采用变分法和偏微分方程理论的方法来获得膜高h和压力p的相应演化方程的解的存在性和定性行为的结果。除了对于更好地理解解的渐近行为具有明显的重要性之外，这些理论结果也是制定快速可靠的数值求和算法的关键要素。数值模拟：在过去的两年中，G. Grün 和 M. Rumpf 成功开发和分析了一种有限元/有限体积方案，该方案大大减少了扩散现象模拟的计算时间。基于该方案，应设计一个通用的有限元求解器以实现数值模拟。上述所有现象的评估将通过与实验数据的比较来进行；这在很大程度上取决于 Schwerpunkt 计划内实验人员的密切合作。