Numerical Analysis Seminar

Date: November 13, 2020

Time: 11:00AM - 12:00PM

Location: ZOOM

Speaker: Ruiwen Shu, University of Maryland

Title: Positivity-preserving asymptotic-preserving second order schemes for stiff kinetic equations

Abstract: Kinetic equations like the Boltzmann and the BGK equations naturally have multiscale features because of the possibly small Knudsen number, which makes them numerically challenging. To solve them efficiently without resolving the small Knudsen number, one usually needs to treat the stiff collision term more or less implicitly, to achieve the asymptotic-preserving (AP) property. Also, it is desired to preserve the positivity of the particle density function. However, a well-known result by Gottlieb-Shu-Tadmor 01' is that there is no strong-stability-preserving (SSP) implicit scheme of order higher than one. To overcome this order barrier, we developed new schemes for stiff kinetic equations based on the frameworks of implicit-explicit Runge-Kutta (IMEX-RK) and exponential Runge-Kutta. These schemes preserve the positivity and asymptotics, as well as achieve second order accuracy in both the kinetic and the fluid regimes.