Seminar on Compressible Fluids

Wednesday March 16, 2011

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

4 Place Jussieu, 75258  PARIS

Jussieu campus. Building 15/16. Lecture room 309.


Abstract. We will discuss the decay property for a class of symmetric hyperbolic systems with relaxation. The Shizuta-Kawashima stability condition gives the characterization of the standard decay structure for systems with symmetric relaxation matrices. Recently, we found several interesting systems with non-symmetric relaxation which have different decay structure. In this talk, we discuss these examples and report the recent progress on the stability theory for a class of symmetric hyperbolic systems.

Abstract. We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff source term. On one hand, we determine the relevant asymptotic expansion, derive a reduced system in the limit, and discuss the role of an entropy condition to establish the diffusive nature of the reduced system. On the other hand, we propose a new numerical scheme of finite volume type, which allows us to recover the correct asymptotic regime. The associated discrete form of the diffusion system is achieved via a suitable discretization compatible with the stiff source term. Our theoretical results are illustrated with several models from continuum physics and numerical experiments demonstrating the relevance of the proposed theory and numerical strategy. (This is a joint work with C. Berthon and R. Turpault.)


Organizers: Frédéric Coquel, Edwige Godlewski, et Philippe LeFloch