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

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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.