Difference between revisions of "Applied/GPS"
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It is very 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 a well known 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 equilibrium. | It is very 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 a well known 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 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! |
Revision as of 17:05, 24 September 2011
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 | TBA |
Oct 10 | Li Wang | TBA |
Oct 17 | E. Alec Johnson | TBA |
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 very 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 a well known 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 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!