Spectral Adaptivity for a High-Performance Kinetic Solver*

Flow systems with kinetic physics are high-dimensional, requiring efficient numerical methods to simulate a broad range of scales. A relevant treatment of the particle distribution function expands the velocity space in terms of Asymmetrically Weighted Hermite (AWH) bases, which completely describe the continuum limit in just a few low-order terms at each spatial point. While this method enables large-scale simulations of flows containing both near-continuum and kinetic regions, the efficiency of these low-order expansions must be balanced with the need for higher-order terms describing the kinetic physics of interest. We address this challenge with a novel spectral adaptivity scheme implemented for our high-performance kinetic model, MASS-APP.

 

In the context of the Vlasov-Maxwell equations, we develop an adaptivity scheme that identifies the regions where higher-order expansions are needed to resolve the distribution function to a prescribed error estimate. While our variable-length AWH expansion allows for considerable computational savings, changes in local macroscopic velocity and temperature reduce our efficiency for near-Maxwellian problems. By additionally scaling the bases to capture the local velocity and temperature, we can capture the dynamics with fewer bases. We test our method via simulations of Landau damping and large-scale plasma turbulence. Time permitting, we apply our method to a kinetic study of the Rayleigh-Taylor instability via a collisional Boltzmann equation.