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

9502766 勒弗洛克 这项工作得到了美国国家科学基金会的支持 教师早期 职业发展奖。 研究部分将重点关注 上 非线性双曲守恒律的研究;这些定律 是必不可少的 连续体中大量问题的描述 机械师， 从流体动力学到材料科学（例如，多相 流动，传播 接口）。 该计划将有两个主要目标：（1） 提供新 熵不连续非线性稳定性研究 解决方案及 激波捕捉器的设计与非线性分析 数值方法 （2）有助于更好地理解几个 应用题 物理学中承认非标准冲击波。 教育 这一部分将包括在 研究生水平， 向科学界传播研究成果， 包括 工业实验室，指导学生的工作， 强调 与工程师和研究人员的合作活动， 物理 以理工科为重 美国国家科学基金会强烈鼓励 早期 发展学术教师作为教育工作者和 研究人员 的 教师早期职业发展（CAREER）计划是一个 基金会- 一项广泛的计划，为青少年提供支持 学院内部 在整体职业发展的背景下。 它结合了 单个 计划支持高质量的研究和教育， 最广泛意义 以及那些传统上 在科学领域代表性不足 与工程学 该计划增强并强调了 重要性 基金会致力于发展全面、均衡的 学术 包括研究和教育的职业。

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.