Applied/GPS

GPS Applied Mathematics Seminar

The GPS (Graduate Participation Seminar) is a weekly seminar by and for graduate students. If you're interested in presenting a topic or your own research, contact the organizers, Qin Li and Sarah Tumasz.

All seminars are on Mondays from 2:25pm to 3:15pm in B211 Van Vleck.

Fall 2011

date	speaker	title
Sept 19	Qin Li	AP scheme for multispecies Boltzmann equation
Sept 26	Sarah Tumasz	An Introduction to Topological Mixing
Oct 3	Zhennan Zhou	Perturbation Theory and Molecular Dynamics
Oct 10	Li Wang	A class of well balanced scheme for hyperbolic system with source term
Oct 17	E. Alec Johnson	Boundary Integral Positivity Limiters
Oct 24	Bokai Yan	TBA
Oct 31
Nov 7	David Seal	TBA
Nov 14
Nov 21
Nov 28
Dec 5
Dec 12

Abstracts

Monday, Sept 19: Qin Li

AP scheme for multispecies Boltzmann equation

It is well-known that the Euler equation and the Navier–Stokes equation are 1st and 2nd order asymptotic limit of the Boltzmann equation when the Knudsen number goes to zero. Numerically the solution to the Boltzmann equation should converge to the Euler limit too. However, when the Knudsen number is small, one has to resolve the mesh to avoid instability, which causes tremendous computational cost. Asymptotic preserving scheme is a type of schemes that only uses coarse mesh but preserves the asymptotic limits of the Boltzmann equation in a discrete setting when Knudsen number vanishes. I'm going to present an AP scheme -- the BGK penalization method to solve the multispecies Boltzmann equation. New difficulties for this multispecies system come from: 1. the accurate definition of BGK term, 2. the different time scaling needed for different species to achieve the equilibrium.

Monday, Sept 26: Sarah Tumasz

An Introduction to Topological Mixing

What does topology have to do with mixing fluids? I will give an introduction to topological mixing from the bottom up. The talk will include a description of the basic theory, and demonstration of how to apply the techniques to a specific system. No prior knowledge of topology is needed!

Monday, Oct 3: Zhennan Zhou

Perturbation Theory and Molecular Dynamics

I would like to give a brief introduction to quantum molecular dynamics  with the method of adiabatic perturbation theory.In the framework of Quantum Mechanics, the dynamics of a molecule is governed by the (time-dependent) Schr\"odinger equation, involving nuclei and electrons coupled through electromagnetic interactions. In recent years, Born-Oppenheimer approximation with many applications in mathematics, physics and chemistry, turns out to be a very successful approximation scheme, which is a prototypical example of adiabatic decoupling, and plays a fundamental role in the understanding of complex molecular systems.

Monday, Oct 10: Li Wang

A class of well balanced scheme for hyperbolic system with source term

In many physical problems one encounters source terms that are balanced by internal forces, and this kind of problem can be described by a hyperbolic system with source term. In comparison with the homogeneous system, a significant difference is that this system encounters non-constant stationary sloutions. So people want to preserve the steay state solutions, or some discrete versions at least, with enough accuracy. This is the so called well balanced scheme. I will give some basic idea of the scheme through a typical example, the Saint-Venant system for shallow water flows with nonuniform bottom. This talk is based on the paper [E.Audusse, etc SIAM J. Sci. Comput. 2004].