Conservative discontinuous Galerkin scheme of a gyro-averaged Dougherty collision operator

Francisquez, M.; Bernard, T. N.; Mandell, N. R.; Hammett, G. W.; Hakim, A.

doi:10.1088/1741-4326/aba0c9

Conservative discontinuous Galerkin scheme of a gyro-averaged Dougherty collision operator

Journal Article · Mon Aug 10 00:00:00 EDT 2020 · Nuclear Fusion

DOI:https://doi.org/10.1088/1741-4326/aba0c9· OSTI ID:1659475

^[1]; Bernard, T. N. ^[2]; Mandell, N. R. ^[3]; Hammett, G. W. ^[4]; Hakim, A. ^[4]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center
General Atomics, San Diego, CA (United States)
Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Here, a conservative discontinuous Galerkin scheme for a non-linear Dougherty collision operator in full-f long-wavelength gyrokinetics is presented. Analytically this model operator has the advective-diffusive form of Fokker-Planck operators, it has a non-decreasing entropy functional, and conserves particles, momentum and energy. Discretely these conservative properties are maintained exactly as well, independent of numerical resolution. In this work the phase space discretization is performed using a novel version of the discontinuous Galerkin scheme, carefully constructed using concepts of weak equality and recovery. Discrete time advancement is carried out with an explicit time-stepping algorithm, whose stability limits we explore. The formulation and implementation within the long-wavelength gyrokinetic solver of Gkeyll are validated with relaxation tests, collisional Landau-damping benchmarks and the study of 5D gyrokinetic turbulence on helical, open field lines.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); US Air Force Office of Scientific Research (AFOSR)

Grant/Contract Number:: FG02-95ER54309; FG02-04ER54742; FC02-08ER54966; FG02-97ER25308; AC02-09CH11466

OSTI ID:: 1659475

Alternate ID(s):: OSTI ID: 1647507
OSTI ID: 23018814

Journal Information:: Nuclear Fusion, Journal Name: Nuclear Fusion Journal Issue: 9 Vol. 60; ISSN 0029-5515

Publisher:: IOP ScienceCopyright Statement

Country of Publication:: United States

Language:: English

References (43)

FPPAC: A two-dimensional multispecies nonlinear fokker-planck package McCoy, M. G.; Mirin, A. A.; Killeen, J. Computer Physics Communications, Vol. 35 https://doi.org/10.1016/s0010-4655(84)82876-3	journal	January 1984
Improved linearized model collision operator for the highly collisional regime Sugama, Hideo; Matsuoka, Seikichi; Satake, Shinsuke arXiv https://doi.org/10.48550/arxiv.1906.07427	text	January 2019
Electromagnetic full-$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods Mandell, N. R.; Hakim, A.; Hammett, G. W. arXiv https://doi.org/10.48550/arxiv.1908.05653	text	January 2019
Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Planck Collision Operator: Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Planck Collision Operator Dorf, M. A.; Cohen, R. H.; Dorr, M. Contributions to Plasma Physics, Vol. 54, Issue 4-6 https://doi.org/10.1002/ctpp.201410023	journal	June 2014
Numerical Methods for Fluid Dynamics Durran, Dale R. Texts in Applied Mathematics https://doi.org/10.1007/978-1-4419-6412-0	book	January 2010
The Serendipity Family of Finite Elements Arnold, Douglas N.; Awanou, Gerard Foundations of Computational Mathematics, Vol. 11, Issue 3 https://doi.org/10.1007/s10208-011-9087-3	journal	March 2011
FPPAC: A two-dimensional multispecies nonlinear Fokker-Planck package McCoy, M. G.; Mirin, A. A.; Killeen, J. Computer Physics Communications, Vol. 24, Issue 1 https://doi.org/10.1016/0010-4655(81)90105-3	journal	September 1981
A numerical instability in an ADI algorithm for gyrokinetics Belli, E. A.; Hammett, G. W. Computer Physics Communications, Vol. 172, Issue 2 https://doi.org/10.1016/j.cpc.2005.06.007	journal	November 2005
A multi-species collisional operator for full-F global gyrokinetics codes: Numerical aspects and verification with the GYSELA code Donnel, P.; Garbet, X.; Sarazin, Y. Computer Physics Communications, Vol. 234 https://doi.org/10.1016/j.cpc.2018.08.008	journal	January 2019
A stabilized Runge–Kutta–Legendre method for explicit super-time-stepping of parabolic and mixed equations Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D. Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.08.021	journal	January 2014
A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma Hager, Robert; Yoon, E. S.; Ku, S. Journal of Computational Physics, Vol. 315 https://doi.org/10.1016/j.jcp.2016.03.064	journal	June 2016
The effect of weak collisions on ion-acoustic wave instabilities in a current-carrying plasma Ong, R. S. B.; Yu, M. Y. Journal of Plasma Physics, Vol. 3, Issue 3 https://doi.org/10.1017/S0022377800004505	journal	September 1969
Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T. Journal of Plasma Physics, Vol. 83, Issue 3 https://doi.org/10.1017/S002237781700037X	journal	May 2017
A solvable model of Vlasov-kinetic plasma turbulence in Fourier–Hermite phase space Adkins, T.; Schekochihin, A. A. Journal of Plasma Physics, Vol. 84, Issue 1 https://doi.org/10.1017/S0022377818000089	journal	January 2018
Nonlinear gyrokinetic Coulomb collision operator Jorge, R.; Frei, B. J.; Ricci, P. Journal of Plasma Physics, Vol. 85, Issue 6 https://doi.org/10.1017/S0022377819000734	journal	November 2019
Electromagnetic full- gyrokinetics in the tokamak edge with discontinuous Galerkin methods Mandell, N. R.; Hakim, A.; Hammett, G. W. Journal of Plasma Physics, Vol. 86, Issue 1 https://doi.org/10.1017/S0022377820000070	journal	February 2020
Conservative discontinuous Galerkin schemes for nonlinear Dougherty–Fokker–Planck collision operators Hakim, Ammar; Francisquez, Manaure; Juno, James Journal of Plasma Physics, Vol. 86, Issue 4 https://doi.org/10.1017/S0022377820000586	journal	July 2020
Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems Cockburn, Bernardo; Shu, Chi-Wang Journal of Scientific Computing, Vol. 16, Issue 3, p. 173-261 https://doi.org/10.1023/A:1012873910884	journal	September 2001
Collisional Damping of Ion Waves in a Plasma Bhadra, Dilip; Varma, Ram K. Physics of Fluids, Vol. 7, Issue 7 https://doi.org/10.1063/1.1711334	journal	January 1964
Model Fokker-Planck Equation for a Plasma and Its Solution Dougherty, J. P. Physics of Fluids, Vol. 7, Issue 11 https://doi.org/10.1063/1.2746779	journal	January 1964
Collisional damping of plasma waves on a pure electron plasma column Anderson, M. W.; O’Neil, T. M. Physics of Plasmas, Vol. 14, Issue 11 https://doi.org/10.1063/1.2807220	journal	November 2007
Linearized model Fokker–Planck collision operators for gyrokinetic simulations. I. Theory Abel, I. G.; Barnes, M.; Cowley, S. C. Physics of Plasmas, Vol. 15, Issue 12 https://doi.org/10.1063/1.3046067	journal	December 2008
Three-dimensional fluid simulations of a simple magnetized toroidal plasma Ricci, Paolo; Rogers, B. N. Physics of Plasmas, Vol. 16, Issue 9 https://doi.org/10.1063/1.3230119	journal	September 2009
Linearized model collision operators for multiple ion species plasmas and gyrokinetic entropy balance equations Sugama, H.; Watanabe, T. -H.; Nunami, M. Physics of Plasmas, Vol. 16, Issue 11 https://doi.org/10.1063/1.3257907	journal	November 2009
A multi-species collisional operator for full-F gyrokinetics Estève, D.; Garbet, X.; Sarazin, Y. Physics of Plasmas, Vol. 22, Issue 12 https://doi.org/10.1063/1.4937373	journal	December 2015
Full- f gyrokinetic simulation of turbulence in a helical open-field-line plasma Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T. Physics of Plasmas, Vol. 26, Issue 1 https://doi.org/10.1063/1.5074179	journal	January 2019
Gyrokinetic continuum simulations of plasma turbulence in the Texas Helimak Bernard, T. N.; Shi, E. L.; Gentle, K. W. Physics of Plasmas, Vol. 26, Issue 4 https://doi.org/10.1063/1.5085457	journal	April 2019
First implementation of gyrokinetic exact linearized Landau collision operator and comparison with models Pan, Qingjiang; Ernst, Darin R.; Crandall, Paul Physics of Plasmas, Vol. 27, Issue 4 https://doi.org/10.1063/1.5143374	journal	April 2020
Frequency and damping of ion acoustic waves Ono, M.; Kulsrud, R. M. Physics of Fluids, Vol. 18, Issue 10 https://doi.org/10.1063/1.861016	journal	January 1975
Linearized gyro-kinetic equation with collisions Catto, P. J.; Tsang, K. T. Physics of Fluids, Vol. 20, Issue 3 https://doi.org/10.1063/1.861902	journal	January 1977
Effect of ion collisionality on ion-acoustic waves Randall, C. J. Physics of Fluids, Vol. 25, Issue 12 https://doi.org/10.1063/1.863963	journal	January 1982
Gyrokinetic field theory Sugama, H. Physics of Plasmas, Vol. 7, Issue 2 https://doi.org/10.1063/1.873832	journal	February 2000
Study of ion turbulent transport and profile formations using global gyrokinetic full- f Vlasov simulation Idomura, Y.; Urano, H.; Aiba, N. Nuclear Fusion, Vol. 49, Issue 6 https://doi.org/10.1088/0029-5515/49/6/065029	journal	May 2009
Limitations of gyrokinetics on transport time scales Parra, Felix I.; Catto, Peter J. Plasma Physics and Controlled Fusion, Vol. 50, Issue 6 https://doi.org/10.1088/0741-3335/50/6/065014	journal	April 2008
Alternate form of model like particle collision operator Catto, Peter J.; Ernst, Darin R. Plasma Physics and Controlled Fusion, Vol. 51, Issue 6 https://doi.org/10.1088/0741-3335/51/6/062001	journal	May 2009
Fokker-Planck Equation for an Inverse-Square Force Rosenbluth, Marshall N.; MacDonald, William M.; Judd, David L. Physical Review, Vol. 107, Issue 1 https://doi.org/10.1103/PhysRev.107.1	journal	July 1957
Gyrokinetic Landau collision operator in conservative form Pan, Qingjiang; Ernst, Darin R. Physical Review E, Vol. 99, Issue 2 https://doi.org/10.1103/PhysRevE.99.023201	journal	February 2019
Gyrokinetic Fokker-Planck Collision Operator Li, B.; Ernst, D. R. Physical Review Letters, Vol. 106, Issue 19 https://doi.org/10.1103/PhysRevLett.106.195002	journal	May 2011
Damping of ion-acoustic waves in the presence of electron-ion collisions Epperlein, E. M.; Short, R. W.; Simon, A. Physical Review Letters, Vol. 69, Issue 12 https://doi.org/10.1103/PhysRevLett.69.1765	journal	September 1992
Kinetic Eigenmodes and Discrete Spectrum of Plasma Oscillations in a Weakly Collisional Plasma Ng, C. S.; Bhattacharjee, A.; Skiff, F. Physical Review Letters, Vol. 83, Issue 10 https://doi.org/10.1103/PhysRevLett.83.1974	journal	September 1999
Foundations of nonlinear gyrokinetic theory Brizard, A. J.; Hahm, T. S. Reviews of Modern Physics, Vol. 79, Issue 2 https://doi.org/10.1103/RevModPhys.79.421	journal	April 2007
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems Cockburn, Bernardo; Shu, Chi-Wang SIAM Journal on Numerical Analysis, Vol. 35, Issue 6 https://doi.org/10.1137/S0036142997316712	journal	December 1998
The Gyrokinetic Description of Microturbulence in Magnetized Plasmas Krommes, John A. Annual Review of Fluid Mechanics, Vol. 44, Issue 1 https://doi.org/10.1146/annurev-fluid-120710-101223	journal	January 2012

Cited By (1)

Magnetic Fluctuations in Gyrokinetic Simulations of Tokamak Scrape-Off Layer Turbulence Mandell, Noah arXiv https://doi.org/10.48550/arxiv.2103.16062	preprint	January 2021

Similar Records

Conservative discontinuous Galerkin schemes for nonlinear Dougherty–Fokker–Planck collision operators

Journal Article · Fri Jul 17 00:00:00 EDT 2020 · Journal of Plasma Physics · OSTI ID:1668773

Dataset from: Improved multispecies Dougherty collisions

Dataset · Sat Mar 12 23:00:00 EST 2022 · OSTI ID:1897995

Axisymmetric gyrokinetic simulation of ASDEX-Upgrade scrape-off layer using a conservative implicit BGK collision operator

Journal Article · Wed Nov 19 19:00:00 EST 2025 · Physics of Plasmas · OSTI ID:3006374

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Conservative discontinuous Galerkin scheme of a gyro-averaged Dougherty collision operator

Citation Formats

References (43)

Cited By (1)

Similar Records

Related Subjects