A Multi-Scale Time Integration Method for Kinetic Simulations

We report progress developing a kinetic multi-scale time integration method based on equation-free projective integration [1]. Here, a fully resolved kinetic simulation is performed over a short time interval to produce a history of fluid moments. The moments are then extrapolated over a large time step and used in initializing a subsequent kinetic simulation to repeat the process. This enables long timescale simulations without the need for coupling to transport equations. A method for “lifting” fluid moments to a distribution function has been developed based on transforming a previous time step distribution function using polynomials in the velocity space variables. This method is implemented in XGCa and is demonstrated to eliminate spurious transients, which were present for previous lifting operators. When the fluid moments are extrapolated over too large of a time step however, inaccuracies may excite fast time scale modes. This imposes a constraint on the extrapolation time step size, limiting the computational gains that can be achieved. We explore advanced extrapolation methods and constraints on the fluid moments to mitigate this effect. [1] I. G. Kevrekidis et. al., Comm Math Sci, 1(4), 715, (2003).