Mathematical and computational modeling of fluid-structure-control interactions with multidisciplinary applications in science and engineering

流体-结构-控制相互作用的数学和计算建模与科学和工程中的多学科应用

• 批准号: 0610026
• 负责人: Padmanabhan Seshaiyer
• 金额: $ 20.05万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2008-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0610026&HistoricalAwards=false
• 关键词: Mathematical; computational; modeling; fluid; structure

The efficient solution of modeling the complex nonlinear interaction of a fluid with a structure has remained a challenging problem in computational mathematics. Such applications often involve complex dynamic interactions of multiple physical processes which present a significant challenge, both in representing the multiphysics involved and in handling the resulting coupled behavior. If the desire to control and design the system is added to the picture, then the complexity increases even further. The focus of the proposed research will therefore be to sytematically develop non-conforming finite element methods tuned to high performance computing applied to several computatationally challenging multidisciplinary applications involving fluid-strucuture-control interaction. The thrust will be to mathematically and computationally investigate the stability, convergence and control of a variety of non-conforming finite element techniques and use this information to develop an efficient and general solution methodology for fluid-structure-control applications. More specifically, the proposed research will explore the robustness of this methodology by investigating (a) computational stability and convergence of fully-coupled algorithms; (b) computational stability and convergence for iterative coupling and; (c) theoretical and computational investigation for shape, boundary and distributed control applications. The performance of the compuational algorithms developed as a part of this research will be applied to two realistic fluid-structure applications: (a) Blood flow in a parent-artery-aneurysm multistructure and (b) Computational aeroelasticity of micro-air-vehicles. The proposed research aims to develop optimal computational algorithms for fluid-stucture-control interaction problems arising in science and engineering applications. The proposed work is highly multidisciplinary and the algorithms developed as a part of this research can be quickly adopted to a wide range of engineering and medical applications. For instance, this research may be used to better understand the rupture of aneurysms which are responsible for significant morbidity and mortality in the country. This work may also be used to develop enhanced and efficient design of micro air vehicles with flexible aircraft wings, that may be used for a variety of missions such as reconnaissance and surveillance, targeting, tagging, bio-chemical sensing and many more. Integrated with the research component is also an educational plan that will encourage interdisciplinary research, that will involve the pedagogical implications of the proposed research in curriculum development and that will contribute to the scientific development of graduate students, undergraduate students, high school students and teachers. More specifically, the proposed research will be used to develop learning modules that will be used to train students and teachers on the efficient use of compuatational mathematics to solve multidisciplinary problems in science and engineering. The research will also greatly encourage women and underrepresented minorities to pursue careers in computational mathematics, especially in interdisciplinary areas that bridge the biological, mathematical, and compuational sciences.

在计算数学中，对流体与结构的复杂非线性相互作用进行建模的有效解决方案仍然是一个具有挑战性的问题。这种应用通常涉及多个物理过程的复杂动态相互作用，这些过程在表示所涉及的多物理和处理所得的耦合行为方面都带来了重大挑战。如果将控制和设计系统的愿望添加到图片中，那么复杂性就会进一步增加。因此，拟议的研究的重点将是在秘密上开发不合格的有限元方法，该方法调整了用于高性能计算的高性能计算，该方法应用于几种涉及流体 - 检测到控制相互作用的计算挑战性的多学科应用。该推力将是在数学上和计算上研究各种不合格的有限元技术的稳定性，收敛性和控制，并使用此信息为流体结构控制应用开发有效且一般的解决方案方法。更具体地说，拟议的研究将通过研究（a）（a）完全耦合算法的计算稳定性和收敛性来探讨该方法的鲁棒性。 （b）迭代耦合的计算稳定性和收敛性和； （c）形状，边界和分布式控制应用的理论和计算研究。作为这项研究的一部分开发的组合算法的性能将应用于两个逼真的流体结构应用：（a）亲本 - 动脉瘤多结构中的血流，以及（b）微动物的计算空气弹性。拟议的研究旨在开发最佳的计算算法，以用于在科学和工程应用中引起的流体结构控制问题。拟议的工作是高度多学科的，作为这项研究的一部分，开发的算法可以快速地用于广泛的工程和医疗应用。例如，这项研究可以用来更好地理解负责该国大量发病率和死亡率的动脉瘤的破裂。这项工作还可以用来开发具有灵活的飞机机翼的微型航空车辆的增强，有效的设计，这些车辆可用于各种任务，例如侦察和监视，靶向，标记，标签，生物化学感应等。与研究组成部分集成的也是一项教育计划，它将鼓励跨学科研究，这将涉及拟议的课程发展研究的教学意义，这将有助于研究生，本科生，高中生和老师的科学发展。 更具体地说，拟议的研究将用于开发学习模块，该模块将用于培训学生和教师有效利用合成数学来解决科学和工程中的多学科问题。这项研究还将极大地鼓励妇女和代表性不足的少数民族从事计算数学的职业，尤其是在弥合生物学，数学和合成科学的跨学科领域。