Discontinuous Galerkin algorithms for fully kinetic plasmas
Abstract
Here, we present a new algorithm for the discretization of the non-relativistic Vlasov–Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a high order accurate solution for the plasma's distribution function. Time stepping for the distribution function is done explicitly with a third order strong-stability preserving Runge–Kutta method. Since the Vlasov equation in the Vlasov–Maxwell system is a high dimensional transport equation, up to six dimensions plus time, we take special care to note various features we have implemented to reduce the cost while maintaining the integrity of the solution, including the use of a reduced high-order basis set. A series of benchmarks, from simple wave and shock calculations, to a five dimensional turbulence simulation, are presented to verify the efficacy of our set of numerical methods, as well as demonstrate the power of the implemented features.
- Authors:
-
[1];
[2];
- Univ. of Maryland, College Park, MD (United States)
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Univ. of Maryland, College Park, MD (United States); Princeton Univ., Princeton, NJ (United States)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1414922
- Alternate Identifier(s):
- OSTI ID: 1549501
- Grant/Contract Number:
- AGS-1622306; FG02-93ER54197; AC02-09CH11466; FA9550-15-1-0193; ACI-1548562
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 353; Journal Issue: C; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Discontinuous Galerkin; Vlasov–Maxwell
Citation Formats
Juno, J., Hakim, A., TenBarge, J., Shi, E., and Dorland, W. Discontinuous Galerkin algorithms for fully kinetic plasmas. United States: N. p., 2017.
Web. doi:10.1016/j.jcp.2017.10.009.
Juno, J., Hakim, A., TenBarge, J., Shi, E., & Dorland, W. Discontinuous Galerkin algorithms for fully kinetic plasmas. United States. https://doi.org/10.1016/j.jcp.2017.10.009
Juno, J., Hakim, A., TenBarge, J., Shi, E., and Dorland, W. Tue .
"Discontinuous Galerkin algorithms for fully kinetic plasmas". United States. https://doi.org/10.1016/j.jcp.2017.10.009. https://www.osti.gov/servlets/purl/1414922.
@article{osti_1414922,
title = {Discontinuous Galerkin algorithms for fully kinetic plasmas},
author = {Juno, J. and Hakim, A. and TenBarge, J. and Shi, E. and Dorland, W.},
abstractNote = {Here, we present a new algorithm for the discretization of the non-relativistic Vlasov–Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a high order accurate solution for the plasma's distribution function. Time stepping for the distribution function is done explicitly with a third order strong-stability preserving Runge–Kutta method. Since the Vlasov equation in the Vlasov–Maxwell system is a high dimensional transport equation, up to six dimensions plus time, we take special care to note various features we have implemented to reduce the cost while maintaining the integrity of the solution, including the use of a reduced high-order basis set. A series of benchmarks, from simple wave and shock calculations, to a five dimensional turbulence simulation, are presented to verify the efficacy of our set of numerical methods, as well as demonstrate the power of the implemented features.},
doi = {10.1016/j.jcp.2017.10.009},
journal = {Journal of Computational Physics},
number = C,
volume = 353,
place = {United States},
year = {2017},
month = {10}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 67 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria
journal, January 1982
- Frieman, E. A.
- Physics of Fluids, Vol. 25, Issue 3
Foundations of nonlinear gyrokinetic theory
journal, April 2007
- Brizard, A. J.; Hahm, T. S.
- Reviews of Modern Physics, Vol. 79, Issue 2
On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods
journal, January 2016
- Camporeale, E.; Delzanno, G. L.; Bergen, B. K.
- Computer Physics Communications, Vol. 198
Pegasus: A new hybrid-kinetic particle-in-cell code for astrophysical plasma dynamics
journal, February 2014
- Kunz, Matthew W.; Stone, James M.; Bai, Xue-Ning
- Journal of Computational Physics, Vol. 259
A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma
journal, July 2007
- Valentini, F.; Trávníček, P.; Califano, F.
- Journal of Computational Physics, Vol. 225, Issue 1
Numerical study of ion-cyclotron resonant interaction via hybrid-Vlasov simulations
journal, May 2010
- Valentini, Francesco; Iazzolino, Antonio; Veltri, Pierluigi
- Physics of Plasmas, Vol. 17, Issue 5
Inhomogeneous kinetic effects related to intermittent magnetic discontinuities
journal, December 2012
- Greco, A.; Valentini, F.; Servidio, S.
- Physical Review E, Vol. 86, Issue 6
Vlasov Simulations of Multi-Ion Plasma Turbulence in the Solar wind
journal, December 2012
- Perrone, D.; Valentini, F.; Servidio, S.
- The Astrophysical Journal, Vol. 762, Issue 2
Differential kinetic dynamics and heating of ions in the turbulent solar wind
journal, December 2016
- Valentini, F.; Perrone, D.; Stabile, S.
- New Journal of Physics, Vol. 18, Issue 12
Wave dispersion in the hybrid-Vlasov model: Verification of Vlasiator
journal, November 2013
- Kempf, Yann; Pokhotelov, Dimitry; von Alfthan, Sebastian
- Physics of Plasmas, Vol. 20, Issue 11
Ion distributions upstream and downstream of the Earth's bow shock: first results from Vlasiator
journal, January 2013
- Pokhotelov, D.; von Alfthan, S.; Kempf, Y.
- Annales Geophysicae, Vol. 31, Issue 12
A high resolution wave propagation scheme for ideal Two-Fluid plasma equations
journal, November 2006
- Hakim, A.; Loverich, J.; Shumlak, U.
- Journal of Computational Physics, Vol. 219, Issue 1
Extended MHD Modelling with the Ten-Moment Equations
journal, July 2007
- Hakim, Ammar H.
- Journal of Fusion Energy, Vol. 27, Issue 1-2
The island coalescence problem: Scaling of reconnection in extended fluid models including higher-order moments
journal, November 2015
- Ng, Jonathan; Huang, Yi-Min; Hakim, Ammar
- Physics of Plasmas, Vol. 22, Issue 11
A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse
journal, February 2015
- Shi, E. L.; Hakim, A. H.; Hammett, G. W.
- Physics of Plasmas, Vol. 22, Issue 2
Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection
journal, January 2015
- Wang, Liang; Hakim, Ammar H.; Bhattacharjee, A.
- Physics of Plasmas, Vol. 22, Issue 1
Continuum kinetic and multi-fluid simulations of classical sheaths
journal, February 2017
- Cagas, P.; Hakim, A.; Juno, J.
- Physics of Plasmas, Vol. 24, Issue 2
The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V
journal, April 1998
- Cockburn, Bernardo; Shu, Chi-Wang
- Journal of Computational Physics, Vol. 141, Issue 2
A brief survey of the discontinuous Galerkin method for the Boltzmann-Poisson equations
journal, April 2011
- Cheng, Yingda; Gamba, Irene M.; Majorana, Armando
- SeMA Journal, Vol. 54, Issue 1
Energy-conserving discontinuous Galerkin methods for the Vlasov–Ampère system
journal, January 2014
- Cheng, Yingda; Christlieb, Andrew J.; Zhong, Xinghui
- Journal of Computational Physics, Vol. 256
Discontinuous Galerkin Methods for the Vlasov--Maxwell Equations
journal, January 2014
- Cheng, Yingda; Gamba, Irene M.; Li, Fengyan
- SIAM Journal on Numerical Analysis, Vol. 52, Issue 2
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
A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
journal, May 1954
- Bhatnagar, P. L.; Gross, E. P.; Krook, M.
- Physical Review, Vol. 94, Issue 3
The Statistical Mechanical Theory of Transport Processes II. Transport in Gases
journal, January 1947
- Kirkwood, John G.
- The Journal of Chemical Physics, Vol. 15, Issue 1
Plasma Oscillations with Diffusion in Velocity Space
journal, December 1958
- Lenard, A.; Bernstein, Ira B.
- Physical Review, Vol. 112, Issue 5
Model Fokker—Planck Equations: Part 2. The equation for a multicomponent plasma
journal, August 1967
- Dougherty, J. P.; Watson, S. R.
- Journal of Plasma Physics, Vol. 1, Issue 3
The Serendipity Family of Finite Elements
journal, March 2011
- Arnold, Douglas N.; Awanou, Gerard
- Foundations of Computational Mathematics, Vol. 11, Issue 3
Development of a Godunov method for Maxwell's equations with Adaptive Mesh Refinement
journal, November 2015
- Barbas, Alfonso; Velarde, Pedro
- Journal of Computational Physics, Vol. 300
Von Neumann stability analysis of globally divergence-free RKDG schemes for the induction equation using multidimensional Riemann solvers
journal, May 2017
- Balsara, Dinshaw S.; Käppeli, Roger
- Journal of Computational Physics, Vol. 336
A subluminal relativistic magnetohydrodynamics scheme with ADER-WENO predictor and multidimensional Riemann solver-based corrector
journal, May 2016
- Balsara, Dinshaw S.; Kim, Jinho
- Journal of Computational Physics, Vol. 312
Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
journal, May 1966
- Kane Yee,
- IEEE Transactions on Antennas and Propagation, Vol. 14, Issue 3
Formation and Structure of Electrostatic Collisionless Shocks
journal, December 1970
- Forslund, D. W.; Shonk, C. R.
- Physical Review Letters, Vol. 25, Issue 25
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
journal, April 1988
- Brio, M.; Wu, C. C.
- Journal of Computational Physics, Vol. 75, Issue 2
Small-scale structure of two-dimensional magnetohydrodynamic turbulence
journal, January 1979
- Orszag, Steven A.; Tang, Cha-Mei
- Journal of Fluid Mechanics, Vol. 90, Issue 1
Kinetic dissipation and anisotropic heating in a turbulent collisionless plasma
journal, March 2009
- Parashar, T. N.; Shay, M. A.; Cassak, P. A.
- Physics of Plasmas, Vol. 16, Issue 3
Diagnosing collisionless energy transfer using field–particle correlations: Vlasov–Poisson plasmas
journal, January 2017
- Howes, Gregory G.; Klein, Kristopher G.; Li, Tak Chu
- Journal of Plasma Physics, Vol. 83, Issue 1
Divergence Correction Techniques for Maxwell Solvers Based on a Hyperbolic Model
journal, July 2000
- Munz, C. -D.; Omnes, P.; Schneider, R.
- Journal of Computational Physics, Vol. 161, Issue 2
A three-dimensional finite-volume solver for the Maxwell equations with divergence cleaning on unstructured meshes
journal, July 2000
- Munz, C. -D.; Ommes, P.; Schneider, R.
- Computer Physics Communications, Vol. 130, Issue 1-2
A Finite-Volume Method for the Maxwell Equations in the Time Domain
journal, January 2000
- Munz, C. D.; Schneider, R.; Voss, U.
- SIAM Journal on Scientific Computing, Vol. 22, Issue 2
Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics
journal, December 2001
- Balsara, Dinshaw S.
- Journal of Computational Physics, Vol. 174, Issue 2
Second‐Order–accurate Schemes for Magnetohydrodynamics with Divergence‐free Reconstruction
journal, March 2004
- Balsara, Dinshaw S.
- The Astrophysical Journal Supplement Series, Vol. 151, Issue 1
Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics
journal, August 2009
- Balsara, Dinshaw S.
- Journal of Computational Physics, Vol. 228, Issue 14
Implicit–Explicit Runge–Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
journal, October 2005
- Pareschi, Lorenzo; Russo, Giovanni
- Journal of Scientific Computing, Vol. 25, Issue 1
AstroGK: Astrophysical gyrokinetics code
journal, December 2010
- Numata, Ryusuke; Howes, Gregory G.; Tatsuno, Tomoya
- Journal of Computational Physics, Vol. 229, Issue 24
Electron temperature gradient driven turbulence
journal, May 2000
- Jenko, F.; Dorland, W.; Kotschenreuther, M.
- Physics of Plasmas, Vol. 7, Issue 5
Kinetic solvers with adaptive mesh in phase space
journal, December 2013
- Arslanbekov, Robert R.; Kolobov, Vladimir I.; Frolova, Anna A.
- Physical Review E, Vol. 88, Issue 6
Adaptive kinetic-fluid solvers for heterogeneous computing architectures
journal, December 2015
- Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir
- Journal of Computational Physics, Vol. 303
Works referencing / citing this record:
ViDA: a Vlasov–DArwin solver for plasma physics at electron scales
journal, October 2019
- Pezzi, Oreste; Cozzani, Giulia; Califano, Francesco
- Journal of Plasma Physics, Vol. 85, Issue 5
An Extended MHD Study of the 16 October 2015 MMS Diffusion Region Crossing
journal, November 2019
- TenBarge, J. M.; Ng, J.; Juno, J.
- Journal of Geophysical Research: Space Physics, Vol. 124, Issue 11
Drift Instabilities in Thin Current Sheets Using a Two‐Fluid Model With Pressure Tensor Effects
journal, May 2019
- Ng, Jonathan; Hakim, Ammar; Juno, J.
- Journal of Geophysical Research: Space Physics, Vol. 124, Issue 5
Turbulent electromagnetic fields at sub-proton scales: Two-fluid and full-kinetic plasma simulations
journal, January 2019
- González, C. A.; Parashar, T. N.; Gomez, D.
- Physics of Plasmas, Vol. 26, Issue 1
Temperature-dependent Saturation of Weibel-type Instabilities in Counter-streaming Plasmas
journal, February 2019
- Skoutnev, V.; Hakim, A.; Juno, J.
- The Astrophysical Journal, Vol. 872, Issue 2
Low Mach-number collisionless electrostatic shocks and associated ion acceleration
journal, January 2018
- Pusztai, I.; TenBarge, J. M.; Csapó, A. N.
- Plasma Physics and Controlled Fusion, Vol. 60, Issue 3
Role of electron inertia and electron/ion finite Larmor radius effects in low-beta, magneto-Rayleigh-Taylor instability
journal, September 2018
- Srinivasan, B.; Hakim, A.
- Physics of Plasmas, Vol. 25, Issue 9
Nonlinear saturation of the Weibel instability
journal, November 2017
- Cagas, P.; Hakim, A.; Scales, W.
- Physics of Plasmas, Vol. 24, Issue 11
On the Importance of Spatial and Velocity Resolution in the Hybrid-Vlasov Modeling of Collisionless Shocks
journal, May 2018
- Pfau-Kempf, Yann; Battarbee, Markus; Ganse, Urs
- Frontiers in Physics, Vol. 6
A survey of fluid and kinetic instabilities relevant to space and laboratory plasmas
journal, February 2019
- Srinivasan, Bhuvana; Cagas, Petr; Masti, Robert
- Radiation Effects and Defects in Solids, Vol. 174, Issue 1-2
Open-boundary spectral and flux-balance Vlasov simulation
journal, December 2019
- Klimas, Alexander J.; Viñas, Adolfo F.
- Journal of Plasma Physics, Vol. 85, Issue 6
Low Mach-number collisionless electrostatic shocks and associated ion acceleration
text, January 2017
- Pusztai, Istvan; TenBarge, Jason M.; Csapó, Aletta N.
- arXiv
Turbulent electromagnetic fields at sub-proton scales: two-fluid and full-kinetic plasma simulations
text, January 2018
- González, C. A.; Parashar, T.; Gomez, D.
- arXiv
Effect of a weak ion collisionality on the dynamics of kinetic electrostatic shocks
text, January 2018
- Sundström, Andréas; Juno, James; TenBarge, Jason M.
- arXiv
An extended MHD study of the 16 October 2015 MMS diffusion region crossing
text, January 2019
- TenBarge, J. M.; Ng, J.; Juno, J.
- arXiv
Drift instabilities in thin current sheets using a two-fluid model with pressure tensor effects
text, January 2019
- Ng, J.; Hakim, A.; Juno, J.
- arXiv
Electromagnetic full-$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods
text, January 2019
- Mandell, N. R.; Hakim, A.; Hammett, G. W.
- arXiv