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A discontinuous Galerkin method for ideal two-fluid plasma equations. (English) Zbl 1364.35278
Summary: 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.

MSC:
35Q35 PDEs in connection with fluid mechanics
35Q61 Maxwell equations
76M10 Finite element methods applied to problems in fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
76W05 Magnetohydrodynamics and electrohydrodynamics
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