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Numerical Methods for Two-Fluid Dispersive Fast MHD Phenomena

Published online by Cambridge University Press:  20 August 2015

Bhuvana Srinivasan ,
Ammar Hakim  and
Uri Shumlak
Bhuvana Srinivasan*
Affiliation:
Aerospace and Energetics Research Program, University of Washington, Seattle, WA 98195, USA
Ammar Hakim*
Affiliation:
Tech-X Corporation, 5621 Arapahoe Avenue Suite A, Boulder, CO 80303, USA
Uri Shumlak*
Affiliation:
Aerospace and Energetics Research Program, University of Washington, Seattle, WA 98195, USA
*
Corresponding author.Email:srinbhu@u.washington.edu
Email:ammar@txcorp.com
Email:shumlak@u.washington.edu
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Abstract

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 providesmore accurate results for problems near steady-state aswell as problems with disparate characteristic speeds when using higher spatial orders.

Keywords

35Q3535Q6165L6065M0882D10Two-fluid plasma model5 momentdiscontinuous Galerkinhigh-resolution wave propagationdispersive source termshyperbolic conservation lawsdispersive EulersolitonZ-pinch
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 1 , July 2011 , pp. 183 - 215
Copyright
Copyright © Global Science Press Limited 2011

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