Back to Departmental Colloquium: Spring 2011
Departmental Colloquium
Date: Thursday, Mar 31, 2011
Time: 4:15PM
Location: JWB 335
Smadar Karni
University of Michigan
Title |
Numerical Approximation of Shock Waves in Non-Conservative Hyperbolic Systems |
Abstract |
Non-conservative hyperbolic systems arise in a wide range of applications, which makes their theoretical study and numerical approximation very important. The mathematical theory of weak solutions has been generalized to the nonconservative setup using the notion of vanishing viscosity and viscous path. The difficulty lies in the fact that shock relations depend not only on the immediate states ahead/ behind the shock, but also on the viscous path that connects them. While advances have been made on the theoretical front, those advances have been slow to translate into successful numerical methods. In this talk, we shed light on some of the difficulties involved by considering the so-called path-conservative numerical scheme applied to an illuminating example from gas dynamics, where the choice of linear path happens to give the correct jump conditions. This is joint work with Remi Abgrall, University of Bordeaux, France |
Mathematical Biology
Computational Mathematics