Control and optimization problems in fluid mechanics

流体力学中的控制与优化问题

• 批准号: 298430-2009
• 负责人: Protas, Bartosz
• 金额: $ 1.17万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503749
• 关键词: Control; optimization; problems; fluid; mechanics

The proposed research will address a range of topics that bridge the theoretical and computational fluid mechanics with the modern theory of control and optimization. Our goal is to develop and validate a suite of advanced computational methods for a number of fundamental problems in this field. The theoretical foundations established by this project will provide the basis for more applied investigations to be pursued in the future. In one part of the proposed effort we will revisit vortex-based models for inviscid and incompressible flows characterized by continuous vorticity distributions, such as vortex patches and vortex sheets. These models are relevant for understanding the mechanisms of hydrodynamic propulsion important, for instance, for fish-like locomotion. Our research will add new value to these classical models by providing a suite of tools for solution of control and optimization problems formulated based on such models. In another part of the proposed effort we will extend the methods of control and optimization to flow phenomena involving multiphysics effects and featuring interfaces and contact lines. Such flows are ubiquitous as models in a number of important industrial applications. Mathematically, all of these phenomena are described as 'free-boundary problems' in which the shape of the domain must be determined as a part of the solution. This fact has far-reaching consequences for the mathematical formulation of inverse problems for such systems. As a result, one is required to develop special approaches combining classical methods of applied mathematics with a number of novel techniques. In addition, in this investigation we will also seek to make contributions to some outstanding problems in classical hydrodynamics concerning flows past obstacles. The funding provided by this grant will allow Dr. Protas to train several graduate students in interdisciplinary research rooted in applied mathematics and involving also elements of scientific computing, physics and engineering science.

拟议的研究将介绍一系列主题，这些主题以现代的控制和优化理论启动理论和计算流体力学。我们的目标是开发和验证一套高级计算方法，以解决该领域的许多基本问题。该项目建立的理论基础将为将来进行更多应用调查提供基础。在拟议的工作的一部分中，我们将重新访问基于涡旋的模型，以进行无粘性和不可压缩的流动，其特征是连续涡度分布，例如涡旋补丁和涡流表。这些模型与理解流体动力推进的机制有关，例如，对于鱼类的运动很重要。我们的研究将通过提供一套基于此类模型制定的控制和优化问题的工具来为这些经典模型增加新价值。在拟议的工作的另一部分中，我们将将控制和优化方法扩展到涉及多物理效应的流现象，并具有界面和接触线。在许多重要的工业应用中，这种流程无处不在。从数学上讲，所有这些现象都被描述为“自由边界问题”，其中必须确定域的形状作为解决方案的一部分。这一事实对此类系统的逆问题的数学表述产生了深远的影响。结果，需要开发一种将经典数学的经典方法与许多新型技术相结合的特殊方法。此外，在这项调查中，我们还将寻求为有关流过过去障碍的经典流体动力学方面的一些杰出问题做出贡献。该赠款提供的资金将使Protas博士能够培训几位研究生的跨学科研究，这些研究植根于应用数学，还涉及科学计算，物理和工程科学的元素。