A second-order asymptotic-preserving and positivity-preserving exponential Runge-Kutta method for a class of stiff kinetic equations
Date/Time:26 Dec 2019 16:00
Venue: S17 #05-11 SR5
Speaker: Hu Jingwei, Purdue University
A second-order asymptotic-preserving and positivity-preserving exponential Runge-Kutta method for a class of stiff kinetic equations
We introduce a second-order time discretization method for stiff kinetic equations. The method is asymptotic-preserving (AP) — can capture the Euler limit without numerically resolving the small Knudsen number; and positivity-preserving — can preserve the non- negativity of the solution which is a probability density function for arbitrary Knudsen numbers. The method is based on a new formulation of the exponential Runge-Kutta method and can be applied to a large class of stiff kinetic equations including the BGK/ES-BGK equation (relaxation type), the Fokker-Planck equation (diffusion type), and even the full Boltzmann equation (nonlinear integral type).
Furthermore, we show that when coupled with suitable spatial discretizations the fully discrete scheme satisfies an entropy-decay property. Various numerical results are provided to demonstrate the theoretical properties of the method. This is joint work with Ruiwen Shu (University of Maryland).
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