Numerical Methods for Two-Fluid Dispersive Fast MHD Phenomena
Bhuvana Srinivasan 1*, Ammar Hakim 2, Uri Shumlak 11 Aerospace and Energetics Research Program, University of Washington, Seattle, WA 98195, USA.
2 Tech-X Corporation, 5621 Arapahoe Avenue Suite A, Boulder, CO 80303, USA.
Received 23 September 2009; Accepted (in revised version) 2 September 2010
Available online 30 March 2011
The finite volume wave propagation method and the finite element Runge-Kutta discontinuous Galerkin (RKDG) method are studied for applications to balance laws describing plasma fluids. The plasma fluid equations explored are dispersive and not dissipative. The physical dispersion introduced through the source terms leads to the wide variety of plasma waves. The dispersive nature of the plasma fluid equations explored separates the work in this paper from previous publications. The linearized Euler equations with dispersive source terms are used as a model equation system to compare the wave propagation and RKDG methods. The numerical methods are then studied for applications of the full two-fluid plasma equations. The two-fluid equations describe the self-consistent evolution of electron and ion fluids in the presence of electromagnetic fields. It is found that the wave propagation method, when run at a CFL number of 1, is more accurate for equation systems that do not have disparate characteristic speeds. However, if the oscillation frequency is large compared to the frequency of information propagation, source splitting in the wave propagation method may cause phase errors. The Runge-Kutta discontinuous Galerkin method provides more accurate results for problems near steady-state as well as problems with disparate characteristic speeds when using higher spatial orders.AMS subject classifications: 35Q35, 35Q61, 65L60, 65M08, 82D10
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Key words: Two-fluid plasma model, 5 moment, discontinuous Galerkin, high-resolution wave propagation, dispersive source terms, hyperbolic conservation laws, dispersive Euler, soliton, Z-pinch.
Email: firstname.lastname@example.org (B. Srinivasan), email@example.com (A. Hakim), firstname.lastname@example.org (U. Shumlak)