A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations
John Loverich 1*, Ammar Hakim 1, Uri Shumlak 21 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  and existing numerical solutions to the GEM challenge magnetic reconnection problem . 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.
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