Mathematical Sciences: New Numerical Methods for Conservation Laws. Application to Non-Standard Shocks

数学科学：守恒定律的新数值方法。

• 批准号: 9502766
• 负责人: Philippe Le Floch
• 金额: $ 9.7万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9502766&HistoricalAwards=false
• 关键词: Mathematical; Sciences; New; Numerical; Methods

9502766 LeFloch This work is supported by a National Science Foundation Faculty Early Career Development Award. The research component will focus on the study of nonlinear hyperbolic conservation laws; these laws are essential to the description of a large number of problems in continuum mechanics, from fluid dynamics to material science (e.g., multiphase flows, propagation of interfaces). The plan will have two major goals: (1) to provide new insight on the nonlinear stability of entropy discontinuous solutions and on the design and nonlinear analysis of shock-capturing numerical methods and (2) to contribute to better understanding of several applied problems from physical sciences admitting non-standard shock waves. The education component will include curriculum development at the graduate level, disseminating the research into the scientific community, including industrial laboratories, and directing the work of students, emphasizing collaborative activities with engineers and researchers in the physical sciences. The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation- wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in science and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers which include both research and education.

9502766 LeFloch这项工作得到了国家科学基金会教师早期职业发展奖的支持。研究部分将集中于非线性双曲守恒定律的研究；这些定律对于描述连续介质力学中的大量问题至关重要，从流体动力学到材料科学（例如，多相流，界面传播）。该计划将有两个主要目标：(1)对熵不连续解的非线性稳定性以及激波捕获数值方法的设计和非线性分析提供新的见解；(2)有助于更好地理解物理科学中包含非标准激波的几个应用问题。教育部分将包括研究生阶段的课程发展，向科学界（包括工业实验室）传播研究成果，指导学生的工作，强调与工程师和物理科学研究人员的合作活动。美国国家科学基金会强烈鼓励教师作为教育工作者和研究人员的早期发展。教师早期职业发展（Career）计划是一个基金会范围内的计划，为初级教师的整体职业发展提供支持。它在一个项目中结合了对最广泛意义上的高质量研究和教育的支持，以及那些传统上在科学和工程领域代表性不足的人的充分参与。该计划加强并强调了基金会对包括研究和教育在内的全面，平衡的学术生涯发展的重要性。