Metriplectic integrators for the Landau collision operator

Kraus, Michael; Hirvijoki, Eero

doi:10.1063/1.4998610

Title: 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 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.

Authors:

^[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)

Publication Date:: 2017-10-02

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1411216

Alternate Identifier(s):: OSTI ID: 1395914

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

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 24; Journal Issue: 10; Journal ID: ISSN 1070-664X

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.

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                    Kraus, Michael, & Hirvijoki, Eero. Metriplectic integrators for the Landau collision operator.  United States.  https://doi.org/10.1063/1.4998610

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                    Kraus, Michael, and Hirvijoki, Eero. Mon .  
"Metriplectic integrators for the Landau collision operator".  United States.  https://doi.org/10.1063/1.4998610.  https://www.osti.gov/servlets/purl/1411216.

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@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 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.},

  doi          = {10.1063/1.4998610},

  journal      = {Physics of Plasmas},

  number       = 10,

  volume       = 24,

  place        = {United States},

  year         = {2017},

  month        = {10}

}

Copy to clipboard

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Works referencing / citing this record:

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Shang, Xiaocheng; Öttinger, Hans Christian
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Title: Metriplectic integrators for the Landau collision operator

Abstract

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Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system
journal, November 2011

Dissipative hamiltonian systems: A unifying principle
journal, February 1984

Hamiltonian description of the ideal fluid
journal, April 1998

Geometric integration using discrete gradients
journal, April 1999

Conservative discretization of the Landau collision integral
journal, March 2017

Variational formulation of macro-particle plasma simulation algorithms
journal, May 2014

Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
journal, September 2016

Study of conservation and recurrence of Runge–Kutta discontinuous Galerkin schemes for Vlasov–Poisson systems
journal, January 2013

Linear energy-preserving integrators for Poisson systems
journal, January 2011

A general theory for gauge-free lifting
journal, January 2013

A discontinuous Galerkin method for the Vlasov–Poisson system
journal, February 2012

Bracket formulation of dissipative fluid mechanics equations
journal, June 1984

On Bogoliubov's kinetic equation for a spatially homogeneous plasma
journal, July 1960

Discontinuous Galerkin Methods for the Multi-Dimensional Vlasov–Poisson Problem
journal, October 2012

Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov–Maxwell equations
journal, December 2015

Bracket formulation of dissipative time evolution equations
journal, August 1985

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov–Darwin particle-in-cell algorithm
journal, October 2014

A paradigm for joined Hamiltonian and dissipative systems
journal, January 1986

Variational formulation of particle algorithms for kinetic plasma simulations
journal, July 2013

Discontinuous Galerkin Methods for the Vlasov--Maxwell Equations
journal, January 2014

Finite Element Hodge for spline discrete differential forms. Application to the Vlasov–Poisson system
journal, May 2014

Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
journal, August 2012

Algebraic structure of the plasma quasilinear equations
journal, April 1982

Variational Formulation of Macroparticle Models for Electromagnetic Plasma Simulations
journal, June 2014

Nonlinear stability of fluid and plasma equilibria
journal, July 1985

Structure and structure-preserving algorithms for plasma physics
journal, April 2017

Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
journal, November 2015

Energy-conserving discontinuous Galerkin methods for the Vlasov–Maxwell system
journal, December 2014

Time integration and discrete Hamiltonian systems
journal, September 1996

The Hamiltonian structure of the Maxwell-Vlasov equations
journal, March 1982

Discrete gradient methods for solving ODEs numerically while preserving a first integral
journal, July 1996

An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm
text, January 2011

Discontinuous Galerkin Methods for the Vlasov-Maxwell Equations
preprint, January 2013

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm
text, January 2013

Energy-conserving Discontinuous Galerkin Methods for the Vlasov-Maxwell System
text, January 2014

Exactly Energy Conserving Semi-Implicit Particle in Cell Formulation
text, January 2016

GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
text, January 2016

On Bogoliubov's kinetic equation for a spatially homogeneous plasma
journal, July 1960

The Hamiltonian structure of the Maxwell-Vlasov equations
journal, March 1982

Nonlinear stability of fluid and plasma equilibria
journal, July 1985

Bracket formulation of dissipative fluid mechanics equations
journal, June 1984

The energy conserving particle-in-cell method
journal, August 2011

Discrete gradient methods for solving ODEs numerically while preserving a first integral
journal, July 1996

Geometric integration using discrete gradients
journal, April 1999

Energy-conserving Discontinuous Galerkin Methods for the Vlasov-Maxwell System
text, January 2014

Structure-preserving integrators for dissipative systems based on reversible– irreversible splitting
journal, February 2020

Structure-preserving integrators for dissipative systems based on reversible– irreversible splitting
text, January 2020

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities
preprint, January 2017