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Implicit-explicit Runge-Kutta methods for the two-fluid MHD equations

by H. Kumar

(Report number 2011-26)

Abstract
Two-fluid ideal magnetohydrodynamics (MHD) equations are a generalized form of the ideal MHD equations in which the electrons and ions are considered as separate species. A major difficulty in the design of efficient numerical algorithms for these equations is the presence of stiff source terms, particularly for realistic charge to mass ratio (i.e. low Larmor radius). Following [9, 10, 11], we design implicit-explicit (IMEX) Runge-Kutta (RK) time stepping schemes. The numerical flux is treated explicitly with strong stability preserving (SSP)-RK methods and the stiff source term is treated implicitly using implicit Runge-Kutta methods. The special structure of the two-fluid MHD equations enable us to split the source terms carefully and ensure that only local (in each cell) equations need to be solved at each time step. Benchmark numerical experiments are presented to illustrate the efficiency of this approach.

Keywords: Implicit Explicit Runge-Kutta Method, Two-fluid MHD, Plasma flows, Hyperbolic systems

@Techreport{K11_138,
  author = {H. Kumar},
  title = {Implicit-explicit Runge-Kutta methods for the two-fluid MHD equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-26},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-26.pdf },
  year = {2011}
}

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