Advanced Modeling, Numerical Studies and Analysis of Fluid-Structure Interaction Problems

流固耦合问题的高级建模、数值研究和分析

• 批准号: 1418806
• 负责人: Pengtao Sun
• 金额: $ 13.22万
• 依托单位: University of Nevada Las Vegas
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1418806&HistoricalAwards=false
• 关键词: Advanced; Modeling; Numerical; Studies; Analysis

The purpose of this project is to develop advanced modeling and novel numerical techniques in order to effectively perform stable, precise, and state of the art simulations for a type of dynamic fluid-structure interaction (FSI) problem with a possibly large rotational and deformable elastic structure. Coupled fluid-structure problems, which are characterized by the interaction of fluid forces and structural deformations/rotations, play prominent roles in many scientific and engineering fields such as aerodynamics, bio-engineering and hydrodynamics. Yet, a comprehensive study of such problems remains a challenge due to their strongly nonlinear coupling and multidisciplinary nature, so a correct mathematical model equation to precisely demonstrate the basic characteristics of FSI becomes more important. For most FSI problems, analytical solutions to the model equations are impossible to obtain, whereas laboratory experiments are also limited in scope; thus to investigate the fundamental physics involved in the complex interaction between fluids and solids, mathematical modeling and numerical simulations become more necessary and promising. Because of the complexity of the underlying mathematical model of FSI problems, current solution techniques are still far from being satisfactory, and therefore more efficient and robust numerical techniques are urgently needed.While there is still a long way before such multiphysics FSI problems can be completely solved in an efficient and precise manner, this proposal will be devoted to the development of advanced modeling and novel numerical techniques for the following three methods: Arbitrary Lagrangian-Eulerian (ALE) method, fictitious domain method, and full Eulerian-phase field method. These methods still possess the problems of well-posedness, stability and/or convergence analysis, as well as a number of critical numerical difficulties caused by the mismatched grid on the interface, nonlinear coupling, and discontinuous/degenerate coefficients. The goal of this project is to address these difficulties, develop and analyze proper discretization schemes, robust iterative methods, and high performance computing techniques to solve the discretized system of FSI model in the sense of stable, fast and accurate convergence. The advanced and novel modeling and numerical techniques to be developed include: (1). A newly developed FSI model for a rotational and deformable elastic structure that is immersed in fluid, and its efficient numerical method with an ALE approach and method of characteristics (MOC). (2). A new fictitious domain method for FSI problem with incompressible fluid and compressible structure, and its well-posedness analysis. (3). A new stable implicit scheme for a full Eulerian FSI model with phase field formulation to deal with the degenerate structural momentum equation in Eulerian description. Newly developed numerical techniques will be immediately implemented to enrich our in-house codes and to validate our FSI model with the obtained numerical solutions. It is hoped that the effective numerical techniques developed in this proposed project will result in one to two orders of magnitude of improvement over current existing FSI solvers. Industrial applications are natural outcomes of this research because of its extensive applications in industry, and the close ties of my collaborators with engineers in the fields of hydrodynamics and bio-engineering.

本项目的目的是开发先进的建模和新的数值技术，以便有效地对一类可能具有大型旋转和可变形弹性结构的动态流固耦合(FSI)问题进行稳定、精确和最先进的模拟。以流体力和结构变形/转动相互作用为特征的流固耦合问题，在空气动力学、生物工程和流体力学等许多科学和工程领域具有重要意义。然而，由于这些问题的强非线性耦合和多学科性质，全面研究这些问题仍然是一个挑战，因此正确的数学模型方程变得更加重要，以准确地反映FSI的基本特性。对于大多数FSI问题，模型方程的解析解是不可能获得的，而实验室实验的范围也是有限的；因此，为了研究流体与固体之间复杂相互作用所涉及的基本物理，数学建模和数值模拟变得更加必要和有前途。由于FSI问题的基本数学模型的复杂性，目前的求解技术仍远远不能令人满意，因此迫切需要更高效、更健壮的数值技术。尽管要以高效和精确的方式完全解决此类多物理FSI问题仍有很长的路要走，但本提案将致力于发展先进的建模和新的数值技术，用于以下三种方法：任意拉格朗日-欧拉(ALE)方法、虚拟区域方法和全欧拉相场方法。这些方法仍然存在适定性、稳定性和/或收敛分析的问题，以及由于界面上的网格不匹配、非线性耦合和不连续/退化系数而造成的一些关键的数值困难。本项目的目标是解决这些困难，开发和分析合适的离散化方案、稳健的迭代方法和高性能计算技术来求解稳定、快速和准确收敛的FSI模型的离散化系统。有待开发的先进和新颖的建模和数值技术包括：(1)。提出了一种新的流体中旋转可变形弹性结构的FSI模型及其采用ALE方法和特征线法(MOC)的高效数值方法。(2)。具有不可压缩流体和可压缩结构的FSI问题的一种新的虚域方法及其适定性分析。(3)。针对欧拉描述中的简并结构动量方程，提出了一种新的稳定的隐式全欧拉FSI模型的相场格式。新开发的数值技术将立即实施，以丰富我们的内部代码，并用所获得的数值解来验证我们的FSI模型。希望在这个拟议的项目中开发的有效的数值技术将导致比现有的FSI解算器改进一到两个数量级。工业应用是这项研究的自然结果，因为它在工业中的广泛应用，以及我的合作者与流体力学和生物工程领域的工程师的密切联系。