CAREER: Spatiotemporal Chaos in Fluid Convection: New Physical Insights from Numerics

职业：流体对流中的时空混沌：来自数值的新物理见解

• 批准号: 0747727
• 负责人: Mark Paul
• 金额: $ 40万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-03-15 至 2014-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0747727&HistoricalAwards=false
• 关键词: CAREER; Spatiotemporal; Chaos; Fluid; Convection

CBET-0747727PaulDespite their importance in many areas of engineering, nonequilibrium systems remain difficult to analyze, to control, to design, or to predict because of the nonlinear way that spatiotemporal patterns affect the transport of energy and matter, which in turn modifies the spatiotemporal patterns. Examples include the weather and climate, the efficiency of combustion and chemical reactions, the convection of biological organisms in the oceans, heart dynamics, crystal growth from a melt, and fluid turbulence. A particular challenge is to understand spatiotemporal chaos, a commonly observed behavior of nonequilibrium systems where properties of the system evolve aperiodically in time and space. New fundamental insights into the spatiotemporal chaos of spatially-extended nonequilibrium systems will be obtained through a detailed numerical investigation of Rayleigh-Benard convection (a thin horizontal layer of fluid heated uniformly from below). The PI has developed parallel numerical methods providing accurate simulations for the precise conditions of experiment. This research builds upon these successes to explore spatiotemporal chaos in large-aspect-ratio convective domains to make predictions that can be verified by experiment. These predictions are only possible by the recent convergence of increased computing power and improved numerical algorithms, including the continuing research progress of the PI. The research will probe the origins and basic building blocks of spatiotemporal chaos to quantify the number, size, and dynamics of the individual chaotic degrees of freedom. Numerical simulations will also shed new insight upon transport in a chaotic flow field. As examples, an exploration of the enhancement of combustion efficiency in premixed gases by complex fluid velocity fields will directly affect energy production and consumption; and an understanding of the fluid convection driven by the activity of biological organisms suspended in oceans will improve models of the climate. The education program is tightly coupled with this research to provide extensive opportunities for students at all levels to participate in state-of-the-art engineering research. The PI's pre-college outreach program is focused upon exposing a large group of students, with special emphasis on under-represented groups, to challenges facing engineering today with the goal of attracting, retaining, and eventually graduating a more diverse group of world-class engineers. The PI is working closely with the Virginia Tech Center for the Enhancement of Engineering Diversity to develop and implement programs that will reach over 400 pre-college students each year. The PI will develop, organize, and lead problem solving sessions that are guided by hands-on interactive numerical experiments. The numerical experiments will be directly related to this research and will spark the interests of young students with such subjects as the difficulty of weather prediction and the scientific meaning of the popular phrase "the Butterfly Effect." The interactive programs will be written in Java and publicly available on a computational science and engineering web site established for this purpose. The PI will mentor undergraduate students each academic year and each summer on projects related to this research. Students will be selected from the Multicultural Academic Opportunities Program (MAOP) and a NSF funded Summer Undergraduate Research Program (SURP). A new multidisciplinary graduate course will be developed entitled "Spatiotemporal Chaos." A major theme of the course will be the quantitative link between theory and experiment provided by the computations of this research. The education program will be carefully assessed and improved through a close collaboration with the Virginia Tech Engineering Education Department.

CBET-0747727PauldS，尽管它们在许多工程领域的重要性，但由于非线性时空模式会影响能量和物质的运输，因此很难分析，控制，设计或预测，无法进行控制，设计或预测。例子包括天气和气候，燃烧和化学反应的效率，海洋生物生物的对流，心脏动力学，融化的晶体生长以及流体湍流。一个特殊的挑战是了解时空混乱，这是一个通常观察到的非平衡系统的行为，该系统在时间和空间中逐渐发展。将通过对雷利 - 贝纳德对流的详细数值研究（从下面均匀地均匀加热的薄层水平层）来获得对空间扩展非平衡系统的时空混乱的新基本见解。 PI开发了平行的数值方法，为实验的精确条件提供了准确的模拟。这项研究以这些成功为基础，以探索大型比对流域中的时空混乱，以做出可以通过实验验证的预测。这些预测只有通过增加计算能力和改善的数值算法（包括PI的持续研究进度）才能实现这些预测。该研究将探讨时空混乱的起源和基本构建基块，以量化单个混乱的自由度的数量，大小和动力学。数值模拟还将对混乱流场中的运输进行新的见解。例如，通过复杂的流体速度场对预混合气体中燃烧效率提高的探索将直接影响能源生产和消耗；对悬浮在海洋中的生物生物的活性驱动的流体对流的理解将改善气候模型。 教育计划与这项研究紧密相结合，为各个层次的学生提供了广泛的机会，可以参与最先进的工程研究。 PI的前大学外展计划的重点是暴露一大批学生，特别强调代表性不足的群体，以吸引，保留和最终毕业的世界一流的目标，以挑战工程面临的挑战工程师。 PI与弗吉尼亚理工大学的中心紧密合作，以增强工程多样性，以开发和实施计划，这些计划每年将达到400多名预科学生。 PI将开发，组织和铅问题解决会议，这些会话以动手交互式数值实验为指导。数值实验将与这项研究直接相关，并将激发年轻学生的利益，例如天气预测的难度和流行短语“蝴蝶效应”的科学意义。交互式程序将以Java编写，并在为此目的建立的计算科学和工程网站上公开提供。 PI将在每个学年和每个夏天指导本科生，以了解与这项研究有关的项目。将从多元文化学术机会计划（MAOP）和NSF资助的夏季本科研究计划（SURP）中选出学生。将开发一个新的多学科研究生课程，标题为“时空混乱”。该课程的一个主要主题将是本研究计算提供的理论与实验之间的定量联系。通过与弗吉尼亚理工大学工程教育部门的密切合作，将仔细评估和改进教育计划。