Metriplectic Integrators for the Landau Collision Operator
arXiv:1707.01801 · doi: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.
24 pages. Comments welcome
References in corpus (3)
Cited by in corpus (14)
- Structure and structure-preserving algorithms for plasma physics
- A General Metriplectic Framework with Application to Dissipative Extended Magnetohydrodynamics
- Structure-preserving integrators for dissipative systems based on reversible-irreversible splitting
- Structure-preserving marker-particle discretizations of Coulomb collisions for particle-in-cell codes
- Stochastic variational principles for the collisional Vlasov-Maxwell and Vlasov-Poisson equations
- Multispecies structure-preserving particle discretization of the Landau collision operator
- Simulating Pitch Angle Scattering Using An Explicitly Solvable Energy Conserving Algorithm
- Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory
- Conservative Projection Between Finite Element and Particle Bases
- Hamiltonian structure of the gauge-free gyrokinetic Vlasov-Maxwell equations
- A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus
- Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities
- A metriplectic formulation of polarized radiative transfer
- Conservative polynomial approximations and applications to Fokker-Planck equations