Difference between revisions of "Applied/GPS"

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All seminars are on Mondays from 2::25pm to 3:15pm in B211 Van Vleck.
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All seminars are on Mondays from 2:25pm to 3:15pm in B211 Van Vleck.
  
 
== Fall 2011 ==
 
== Fall 2011 ==
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|Sept 19
 
|Sept 19
 
|Qin Li
 
|Qin Li
|''Boltzmann Equation''
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|''AP scheme for multispecies Boltzmann equation''
 
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|-
 
|Sept 26
 
|Sept 26
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===Monday, Sept 19: Qin Li===
 
===Monday, Sept 19: Qin Li===
''A bunch of applied stuff''
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''AP scheme for multispecies Boltzmann equation''
  
Here is an abstract.
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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.

Revision as of 15:22, 18 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 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.