题  目： Asymptotic-preseving schemes for Boltzmann equation and relative problems with stiff sources

报告人：金石教授 上海交通大学

时  间：5月16日，周三，下午4:30－5:30

地  点：管理科研楼 1518

摘  要： 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 discredited 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 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.

主办单位：

0029cc金沙贵宾会

国家数学与交叉科学中心合肥分中心

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