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Title: Conservative discretization of the Landau collision integral

Abstract

Here we describe a density, momentum-, and energy-conserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finite-element implementation.

Authors:
 [1];  [2]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1379746
Alternate Identifier(s):
OSTI ID: 1373960
Grant/Contract Number:  
AC02-05CH11231; AC02-09CH11466
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 3; 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; Tensor methods; Polynomials; Galerkin methods; Plasma collisions; Conservation of momentum

Citation Formats

Hirvijoki, E., and Adams, M. F.. Conservative discretization of the Landau collision integral. United States: N. p., 2017. Web. doi:10.1063/1.4979122.
Hirvijoki, E., & Adams, M. F.. Conservative discretization of the Landau collision integral. United States. https://doi.org/10.1063/1.4979122
Hirvijoki, E., and Adams, M. F.. Tue . "Conservative discretization of the Landau collision integral". United States. https://doi.org/10.1063/1.4979122. https://www.osti.gov/servlets/purl/1379746.
@article{osti_1379746,
title = {Conservative discretization of the Landau collision integral},
author = {Hirvijoki, E. and Adams, M. F.},
abstractNote = {Here we describe a density, momentum-, and energy-conserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finite-element implementation.},
doi = {10.1063/1.4979122},
journal = {Physics of Plasmas},
number = 3,
volume = 24,
place = {United States},
year = {Tue Mar 28 00:00:00 EDT 2017},
month = {Tue Mar 28 00:00:00 EDT 2017}
}

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Cited by: 13 works
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Works referenced in this record:

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma
journal, June 2016


Development of variational guiding center algorithms for parallel calculations in experimental magnetic equilibria
journal, April 2015


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


Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
journal, September 2009

  • Geuzaine, Christophe; Remacle, Jean-François
  • International Journal for Numerical Methods in Engineering, Vol. 79, Issue 11
  • DOI: 10.1002/nme.2579

Variational integration for ideal magnetohydrodynamics with built-in advection equations
journal, October 2014

  • Zhou, Yao; Qin, Hong; Burby, J. W.
  • Physics of Plasmas, Vol. 21, Issue 10
  • DOI: 10.1063/1.4897372

Energetically consistent collisional gyrokinetics
journal, October 2015

  • Burby, J. W.; Brizard, A. J.; Qin, H.
  • Physics of Plasmas, Vol. 22, Issue 10
  • DOI: 10.1063/1.4935124

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


A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth–Fokker–Planck equation
journal, September 2015


Variational integrators for nonvariational partial differential equations
journal, August 2015


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

  • Squire, J.; Qin, H.; Tang, W. M.
  • Physics of Plasmas, Vol. 19, Issue 8
  • DOI: 10.1063/1.4742985

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

  • He, Yang; Sun, Yajuan; Qin, Hong
  • Physics of Plasmas, Vol. 23, Issue 9
  • DOI: 10.1063/1.4962573

Fokker-Planck Equation for an Inverse-Square Force
journal, July 1957

  • Rosenbluth, Marshall N.; MacDonald, William M.; Judd, David L.
  • Physical Review, Vol. 107, Issue 1
  • DOI: 10.1103/PhysRev.107.1

Works referencing / citing this record:

Metriplectic integrators for the Landau collision operator
journal, October 2017

  • Kraus, Michael; Hirvijoki, Eero
  • Physics of Plasmas, Vol. 24, Issue 10
  • DOI: 10.1063/1.4998610

Landau Collision Integral Solver with Adaptive Mesh Refinement on Emerging Architectures
text, January 2017