Distinguished Lect. in Appl. and Comp. Analysis: Prof. Shi Jin (UW Madison and Shanghai Jiao Tong), 'Asymptotic-preserving schemes for Boltzmann eqn.'

Event Date: 

Tuesday, April 2, 2013 -
3:30pm to 4:30pm

Event Location: 

  • 6635 South Hall

Event Contact: 

Carlos Garcia-Cervera

Email: cgarcia@math.ucsb.edu

Phone: 8055638873

We propose a general framework to design asymptotic preserving schemes for the Boltzmann kinetic kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free or relaxation time. We propose to penalize the nonlinear collision term by a BGK-type relaxation term, which can be solved explicitly even if discretized implicitly in time. Moreover, the BGK-type relaxation operator helps to drive the density distribution toward the local Maxwellian, thus natually imposes an asymptotic-preserving scheme in the Euler limit. The scheme so designed does not need any nonlinear iterative solver or the use of Wild Sum. It is uniformly stable in terms of the (possibly small) Knudsen number, and can capture the macroscopic fluid dynamic (Euler) limit even if the small scale determined by the Knudsen number is not numerically resolved. We will show how this idea can be applie to other collision opearators, such as the Landau-Fokker-Planck operator, Ullenbeck-Urling model, and in the kinetic-fluid model of disperse multiphase flows.