Metriplectic integrators for the Landau collision operator

Kraus, Michael; Hirvijoki, Eero

doi:10.1063/1.4998610

Title: Metriplectic integrators for the Landau collision operator

Journal Article · Mon Oct 02 00:00:00 EDT 2017 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4998610· OSTI ID:1411216

^[1]; Hirvijoki, Eero ^[2]

Max-Planck-Institut fur Plasmaphysik, Garching (Deutschland); Technische Univ. Munchen, Garching (Deutschland)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Here, 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.

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Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: 708124; AC02-09CH11466

OSTI ID:: 1411216

Alternate ID(s):: OSTI ID: 1395914

Journal Information:: Physics of Plasmas, Vol. 24, Issue 10; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 17 works

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Structure-preserving integrators for dissipative systems based on reversible– irreversible splitting Shang, Xiaocheng; Öttinger, Hans Christian Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 476, Issue 2234 https://doi.org/10.1098/rspa.2019.0446	journal	February 2020
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