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Entropy stable numerical schemes for two-fluid MHD equations

by H. Kumar and S. Mishra

(Report number 2011-22)

Abstract
Two-fluid ideal magnetohydrodynamics (MHD) equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of their non-linear nature and the presence of stiff source terms, especially for high charge to mass ratios. In this article, we design entropy stable finite difference schemes for the two-fluid equations by combining entropy conservative fluxes and suitable numerical diffusion operators. Furthermore, to overcome the time step restrictions imposed by the stiff source terms, we devise time-stepping routines based on implicit-explicit (IMEX)-Runge Kutta (RK) schemes. The special structure of the two-fluid MHD equations is exploited by us to design IMEX schemes in which only local (in each cell) linear equations need to be solved at each time step. Benchmark numerical experiments are presented to illustrate the robustness and accuracy of these schemes.

Keywords: Convection-dffusion problem, discrete differential forms, discrete Lie derivative, semi-Lagrangian methods

@Techreport{KM11_98,
  author = {H. Kumar and S. Mishra},
  title = {Entropy stable numerical schemes for two-fluid MHD equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-22},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-22.pdf },
  year = {2011}
}

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