Commun. Comput. Phys., 9 (2011), pp. 240-268.

A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations

John Loverich 1*, Ammar Hakim 1, Uri Shumlak 2

1 Tech-X Corporation, 5621 Arapahoe Avenue Suite A, Boulder CO, 80303, USA.
2 University of Washington, Aerospace and Energetics Research Program, Seattle, WA 98195-2250, USA.

Received 25 May 2009; Accepted (in revised version) 21 June 2010
Available online 27 August 2010


A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the two-fluid electromagnetic shock [1] and existing numerical solutions to the GEM challenge magnetic reconnection problem [2]. The algorithm can be generalized to arbitrary geometries and three dimensions. An approach to maintaining small gauge errors based on error propagation is suggested.

AMS subject classifications: 35Q35, 35Q61, 65L60

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Key words: Plasma, two-fluid, 5 moment, discontinuous Galerkin, electrostatic shock, electromagnetic shock, magnetic reconnection.

*Corresponding author.
Email: (J. Loverich), (A. Hakim), (U. Shumlak)

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