Mathematics and Computer Science Speaker Series
California State University, Stanislaus
 
Date: Friday, April 4, 2008
Time:
4:00 - 5:00 p.m
Room:
P100

Speaker: Jeff Miller

Title:
A New Tool in the Fight Against Unwanted Oscillation (for
Hyperbolic Systems of Conservation Laws)

Abstract:
We’ll discuss a new numerical approach to approximating
solutions of hyperbolic systems of conservation laws. In order to do
this, we must first answer the question “what are hyperbolic systems of
conservation laws.” I give a brief overview starting from basic and
generalizing to increasingly complicated, presenting a physical example
at each stage. We discuss a major difficulty in solving such problems
numerically … the introduction of “shocks” (discontinuities) in the
solution function which causes unwanted oscillation in the numerical
solution. I finish by introducing a new approach shown to suppress such
oscillation: the inclusion of limiter functions.

The goal here is certainly not to attempt a thorough discussion of this
area of mathematics. Rather, I hope to briefly describe a new tool
useful in finding numerical solutions to this type of problem. I also
direct much of this talk to students in an attempt to say “here’s where
the material for course XYZ shows up in practice,” “here’s how you might
approach research questions of your own,” or “here’s the kind of work
you might be doing someday.”