Metriplectic integrators for the Landau collision operator

Michael Kraus, Eero Hirvijoki

2017 · Physics of Plasmas · vol. 24 · no. 10 · AIP Publishing · 10.1063/1.4998610

Abstract

We present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonic behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.

@article{Kraus_2017,
 title={Metriplectic integrators for the Landau collision operator},
 volume={24},
 ISSN={1089-7674},
 url={http://dx.doi.org/10.1063/1.4998610},
 DOI={10.1063/1.4998610},
 number={10},
 journal={Physics of Plasmas},
 publisher={AIP Publishing},
 author={Kraus, Michael and Hirvijoki, Eero},
 year={2017},
 month=oct }