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Thursday, October 25

Asymptotic-Preserving Schemes for Boltzmann Equation
and Relative Problems with Stiff Sources

Shi Jin, Shanghai Jiao Tong University, and the University of Wisconsin, Madison
Computer Science and Mathematics Division Seminar
10:00 AM — 11:00 AM, Research Office Building (5700), Room L-202
Contact: Clayton Webster (, 865.574.3649


Dr. Shi Jin will propose a general framework to design asymptotic preserving schemes for the Boltzmann 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. Dr. Jin will 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 naturally 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. Dr. Jin will show how this idea can be applied to other collision operators; such as the Landau-Fokker-Planck operator, Ullenbeck-Urling model, and in the kinetic-fluid model of disperse multiphase flows.