Discontinuous Galerkin algorithms for fully kinetic plasmas
Abstract
Here, we present a new algorithm for the discretization of the nonrelativistic 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 strongstability 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 highorder 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:

 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 Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1414922
 Alternate Identifier(s):
 OSTI ID: 1549501
 Grant/Contract Number:
 AGS1622306; FG0293ER54197; AC0209CH11466; FA95501510193; ACI1548562
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 353; Journal Issue: C; Journal ID: ISSN 00219991
 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. doi: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. doi: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 nonrelativistic 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 strongstability 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 highorder 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}
}
Web of Science
Works referencing / citing this record:
Low Machnumber 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