For more information about this meeting, contact Yuxi Zheng.
|Title:||Modeling the von Neumann triple point paradox|
|Seminar:||CCMA PDEs and Numerical Methods Seminar Series|
|Speaker:||Allen Tesdall, New York|
|Modeling the von Neumann triple point paradox
College of Staten Island
Experimental observations of the reflection of very weak shock waves off a thin wedge show a pattern that closely resembles Mach reflection, in which the incident, reflected, and Mach shocks meet at a triple point. However, von Neumann showed in 1943 that a triple point configuration, consisting of three shocks and a contact discontinuity meeting at a point, is impossible for sufficiently weak shocks. In spite of intensive study, no resolution of this "von Neumann paradox" has been available until recently.
We present numerical solutions of two-dimensional Riemann problems for a sequence of systems of conservation laws that describe the reflection of
weak shock waves with increasing physical fidelity.
Our most recent solutions are of the full compressible Euler equations,
which are the fundamental physical equations. We develop a new numerical
scheme to solve the equations in self-similar coordinates, and we observe a surprising structure in the solution: not one, but an entire cascade of triple points with embedded centered rarefactions. We show that the centered rarefaction waves originating at each triple point resolve the paradox.
We will also describe current progress towards the goal of
analyzing the structure that we observe numerically.|
Room Reservation Information
|Date:||10 / 13 / 2008|
|Time:||03:35pm - 04:25pm|