RUI: Multidimensional Conservation Laws

RUI：多维守恒定律

• 批准号: 1615266
• 负责人: Chung-min Lee
• 金额: $ 18.27万
• 依托单位: California State University-Long Beach Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-06-01 至 2022-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1615266&HistoricalAwards=false
• 关键词: RUI; Multidimensional; Conservation; Laws

Conservation laws are fundamental laws of nature that govern many phenomena observed in physics and fluid mechanics, as well as in engineering applications. The first part of this research project addresses the mathematical modeling and analysis of systems of multidimensional conservation laws that mostly relate to problems in dynamics of gases and liquids. It focuses on change of type (transonic) problems, from supersonic to subsonic, or mixed type problems with discontinuities, such as vortex waves and shock waves. The commonly known manifestation of the latter is generation of a sonic boom when an airplane exceeds the velocity of sound. This project aims at developing systematic theories to understand the solution structures of these transonic problems in multidimensional conservation laws. The second part of the project aims to investigate the feasibility of various wildfire spread models with sparse data, and develop efficient algorithms to perform simulations for the model problems. In recent years wildfires have become an all too frequent occurrence, especially in the Western United States. The research on the wildfire spread models will enable effective fire-fighting planning, and thus have a direct impact on the welfare of society. The project will take place at a large, urban, Hispanic-serving institution and involve undergraduate/master students in simulations of the proposed problems, preparing them for further work in the design, implementation, and development of the algorithms. This project addresses long standing open problems in multidimensional conservation laws, such as Mach shock reflections to resolve the von Neumann paradox, slip line discontinuity propagation to understand vortex waves, and the transonic flow to study a flow passing an airfoil. The investigator will focus on these nonlinear transonic problems to gain new physical insights, to develop novel analytical tools, and to find the correct mathematical framework in which to pose the nonlinear conservation laws and to perhaps develop efficient numerical methods. This research aims to provide more efficient and effective methods for applications, including compressible gas dynamics, thermodynamics, multi-phase flow, and porous medium flow. A part of this research will be devoted to modeling wildfire spread with reaction-advection-diffusion systems. The investigator will investigate the feasibility of various wildfire spread models with sparse data and develop efficient algorithms to solve the model problems. Results will be tested on realistic data. Some aspects of this project will be conducted in collaboration with early career researchers, and in communication with the USDA Forest Fire Lab in Riverside, CA.

守恒定律是自然的基本定律，支配着物理和流体力学以及工程应用中观察到的许多现象。该研究项目的第一部分涉及多维守恒定律系统的数学建模和分析，这些系统主要与气体和液体动力学问题相关。它侧重于类型（跨音速）问题的变化，从超音速到亚音速，或具有不连续性的混合类型问题，例如涡旋波和冲击波。后者众所周知的表现是当飞机超过音速时产生音爆。该项目旨在发展系统理论来理解多维守恒定律中这些跨音速问题的解结构。该项目的第二部分旨在研究稀疏数据下各种野火蔓延模型的可行性，并开发有效的算法来对模型问题进行模拟。近年来，野火频繁发生，尤其是在美国西部。对野火蔓延模型的研究将有助于制定有效的消防规划，从而对社会福祉产生直接影响。该项目将在一个大型的城市拉美裔服务机构进行，让本科生/硕士生模拟所提出的问题，为他们在算法的设计、实现和开发方面的进一步工作做好准备。该项目解决了多维守恒定律中长期存在的开放性问题，例如解决冯诺依曼悖论的马赫激波反射、理解涡流的滑移线不连续性传播以及研究通过机翼的流动的跨音速流。研究人员将重点研究这些非线性跨音速问题，以获得新的物理见解，开发新颖的分析工具，并找到正确的数学框架来提出非线性守恒定律，并可能开发有效的数值方法。本研究旨在为可压缩气体动力学、热力学、多相流和多孔介质流动等应用提供更高效、更有效的方法。这项研究的一部分将致力于利用反应平流扩散系统模拟野火蔓延。研究人员将研究稀疏数据的各种野火蔓延模型的可行性，并开发有效的算法来解决模型问题。结果将根据实际数据进行测试。该项目的某些方面将与早期职业研究人员合作进行，并与位于加利福尼亚州河滨市的美国农业部森林火灾实验室进行沟通。