Augmented methods for Navier Stokes equations involving free boundary and moving interface and applications

涉及自由边界和移动界面的纳维斯托克斯方程的增强方法及应用

• 批准号: 0911434
• 负责人: Zhilin Li
• 金额: $ 36.88万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2015-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0911434&HistoricalAwards=false
• 关键词: Augmented; methods; Navier; Stokes; equations

This proposal concerns the development and analysis of new numerical methods for Navier-Stokes equations involving discontinuities,free boundaries, moving interfaces, and problems on irregular domains. The new methods will be applied to several important applications inmulti-phase flows, fluid structure interactions with interfaces, fluids, or solids. In the proposal, augmented immersed interface methods are proposedto tackle those difficulty problems. The new methods are based on sharp interface models (no smearing), second order and implicit discretization. The new methods are proposed to be implemented to simulate several important applications such as the moving contact line problem using one and two phase flow models; non-extensible interfaces in incompressible flows, open-ended interfaces, and moving interfaces with masses. The projects described in the proposal have wide applications in mathematical biology, material science, aerodynamic and mechanical engineering. The non-extensible interfaces have been used to model the motion of red blood cells in the life science. Efficient numerical simulations will have positive impact on early detection of illness related to the red-blood cells. The movingcontact line problem has direct applications in the material science. Efficient numerical simulations using computers may avoid expensive experiments. Thisis true for other projects in the proposal as well. This proposal will also have positive effect on education by attracting under and graduate students to conduct research in this area. Some components of theprojects will be designed as undergraduate projects. Furthermore, the research results can lead to a computer software package that would be useful to thecomputational science involving free boundary and moving interface, and problems defined on complicated domain.

这一建议涉及发展和分析涉及不连续、自由边界、运动界面和不规则区域上的问题的Navier-Stokes方程的新的数值方法。新方法将应用于多相流、流体结构与界面、流体或固体的相互作用等几个重要的应用领域。在该方案中，提出了增强沉浸式界面方法来解决这些困难问题。新方法是基于尖锐界面模型(无拖尾)、二阶和隐式离散。这些新方法被用来模拟几个重要的应用，如使用单相流和两相流模型的移动接触线问题、不可压缩流动中的不可伸缩界面、开放界面和有质量的移动界面。提案中描述的项目在数学生物学、材料科学、空气动力学和机械工程中有广泛的应用。不可扩展界面在生命科学中已被用来模拟红细胞的运动。有效的数值模拟将对及早发现与红细胞有关的疾病产生积极影响。运动接触线问题在材料科学中有着直接的应用。使用计算机进行高效的数值模拟可以避免昂贵的实验。提案中的其他项目也是如此。这项建议还将通过吸引本科生和研究生在这一领域进行研究，对教育产生积极影响。这些项目的一些组成部分将被设计为本科项目。此外，这些研究结果还可以为涉及自由边界和运动界面的计算科学以及定义在复杂区域上的问题提供一个有用的计算机软件包。