Metriplectic integrators for the Landau collision operator
Abstract
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 infinitedimensional system into a finitedimensional, timecontinuous 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.
 Authors:
 MaxPlanckInstitut fur Plasmaphysik, Garching (Deutschland); Technische Univ. Munchen, Garching (Deutschland)
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Publication Date:
 Research Org.:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1411216
 Alternate Identifier(s):
 OSTI ID: 1395914
 Grant/Contract Number:
 708124; AC0209CH11466
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 10; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Kraus, Michael, and Hirvijoki, Eero. Metriplectic integrators for the Landau collision operator. United States: N. p., 2017.
Web. doi:10.1063/1.4998610.
Kraus, Michael, & Hirvijoki, Eero. Metriplectic integrators for the Landau collision operator. United States. doi:10.1063/1.4998610.
Kraus, Michael, and Hirvijoki, Eero. 2017.
"Metriplectic integrators for the Landau collision operator". United States.
doi:10.1063/1.4998610.
@article{osti_1411216,
title = {Metriplectic integrators for the Landau collision operator},
author = {Kraus, Michael and Hirvijoki, Eero},
abstractNote = {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 infinitedimensional system into a finitedimensional, timecontinuous 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.},
doi = {10.1063/1.4998610},
journal = {Physics of Plasmas},
number = 10,
volume = 24,
place = {United States},
year = 2017,
month =
}

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