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Development of new solution methods in fluid dynamics based on first integrals of Navier-Stokes equations

基于纳维-斯托克斯方程一阶积分的流体动力学新求解方法的开发

基本信息

批准号：
216035594
负责人：
Professor Dr. Markus Scholle
金额：
--
依托单位：
Institut für angewandte Forschung (iaf)
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2018-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/216035594?language=en
关键词：
Development new solution methods fluid

项目摘要

Computational fluid dynamics (CFD) has emerged as an essential investigative tool in nearly every field of technology. Despite a well-developed mathematical theory and available commercial software codes the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved. In contrast to the first project which was mainly related to the development of the general theory and its testing by applying the solving procedure to flows of prototypic character, this second part of the project is more focused on selected applications of current scientific relevance, especially on such problems where the use of the first integral of the equations of motion instead of the original Navier-Stokes equations appears to be beneficial. These are in particular: (i) various 2D flow problems with free surface, since a complex formulation of the field equations and a Dirichlet/Neumann formulation of the dynamic boundary condition are available here and (ii) 3D coating flows over cones and half-spheres, using lubrication approximation for reduction of complexity of the problem.Apart from the above, (iii) the formulation of turbulent flows within the framework of the first integral is a general topic requiring a thorough investigation, motivated by the particular importance of turbulent flows in general.

计算流体动力学（CFD）已经成为几乎每个技术领域必不可少的研究工具。尽管有发达的数学理论和可用的商业软件代码，但运动控制方程的解的计算仍然具有挑战性，特别是由于所涉及的非线性。第一个项目主要涉及一般理论的发展及其通过将求解过程应用于原型特征流的测试，与此相反，该项目的第二部分更侧重于当前科学相关性的选择应用，特别是在使用运动方程的第一个积分而不是原始的Navier-Stokes方程似乎有益的问题上。特别是：(i)具有自由表面的各种二维流动问题，因为这里有复杂的场方程公式和动态边界条件的狄利克雷/诺伊曼公式；（ii）在锥体和半球体上的三维涂层流动，使用润滑近似来降低问题的复杂性。除此之外，（iii）在第一个积分的框架内紊流的公式是一个需要深入研究的一般主题，这是由于紊流在一般情况下的特殊重要性。