Splitting scheme for gyro-kinetic equations with Semi-Lagrangian and Arakawa substeps

TL;DR

This paper introduces a new algorithm for gyro-kinetic equations that combines Semi-Lagrangian and Arakawa schemes to improve conservation properties by decomposing the system into fast and slow components.

Contribution

The paper presents a novel splitting scheme that integrates Semi-Lagrangian and Arakawa methods for gyro-kinetic equations, enhancing conservation of physical constants.

Findings

Successful combination of SL and AKW methods for different subsystems

Improved conservation of physical constants compared to previous schemes

Effective decomposition of the problem into fast and slow dynamics

Abstract

The gyro-kinetic model is an approximation of the Vlasov-Maxwell system in a strongly magnetized magnetic field. We propose a new algorithm for solving it combining the Semi-Lagrangian (SL) method and the Arakawa (AKW) scheme with a time-integrator. Both methods are successfully used in practice for different kinds of applications, in our case, we combine them by first decomposing the problem into a fast (parallel) and a slow (perpendicular) dynamical system. The SL approach and the AKW scheme will be used to solve respectively the fast and the slow subsystems. Compared to the scheme in [1], where the entire model is solved using only the SL method, our goal is to replace the method used in the slow subsystem by the AKW scheme, in order to improve the conservation of the physical constants.