Shi Jin : Asymptotic-preseving schemes for the Boltzmann equation and relative problems with multiple scales (Apr 20, 2015 11:55 AM)

We 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. 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 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. We 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, and can be implemented in the Monte-Carlo framework in which is time step is not limited by the possibly small mean free time.

• Category: Applied Math and Analysis
• Duration: 01:14:46
• Date:  April 20, 2015 at 11:55 AM
• Views: 106
• Tags:   seminar, Applied Math And Analysis Seminar