A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics

Qamar, Shamsul; Warnecke, Gerald

doi:10.1016/j.jcp.2004.11.004

Title: A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics

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Abstract

In this paper we extend the special relativistic hydrodynamic (SRHD) equations [L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Pergamon, New York, 1987] and as a limiting case the ultra-relativistic hydrodynamic equations [M. Kunik, S. Qamar, G. Warnecke, J. Comput. Phys. 187 (2003) 572-596] to the special relativistic magnetohydrodynamics (SRMHD). We derive a flux splitting method based on gas-kinetic theory in order to solve these equations in one space dimension. The scheme is based on the direct splitting of macroscopic flux functions with consideration of particle transport. At the same time, particle 'collisions' are implemented in the free transport process to reduce numerical dissipation. To achieve high-order accuracy we use a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. For the direct comparison of the numerical results, we also solve the SRMHD equations with the well-developed second-order central schemes. The 1D computations reported in this paper have comparable accuracy to the already published results. The results verify the desired accuracy, high resolution, and robustness of the kinetic flux splitting method and central schemes.

Authors:

Qamar, Shamsul ^[1]; Warnecke, Gerald ^[1]

Institute for Analysis and Numerics, Otto-von-Guericke University PSF 4120, D-39106 Magdeburg (Germany)

Publication Date:: Sun May 01 00:00:00 EDT 2005

OSTI Identifier:: 20687230

Resource Type:: Journal Article

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 205; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2004.11.004; PII: S0021-9991(04)00463-2; Copyright (c) 2004 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; CHARGED-PARTICLE TRANSPORT; COMPARATIVE EVALUATIONS; CONSERVATION LAWS; EQUATIONS; HYDRODYNAMIC MODEL; MAGNETOHYDRODYNAMICS; MATHEMATICAL SOLUTIONS; RELATIVISTIC RANGE

Citation Formats


                    Qamar, Shamsul, and Warnecke, Gerald. A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics.  United States: N. p., 2005. 
        Web.  doi:10.1016/j.jcp.2004.11.004.

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                    Qamar, Shamsul, & Warnecke, Gerald. A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics.  United States.  https://doi.org/10.1016/j.jcp.2004.11.004

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                    Qamar, Shamsul, and Warnecke, Gerald. 2005.  
        "A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics".  United States.  https://doi.org/10.1016/j.jcp.2004.11.004.

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@article{osti_20687230,

  title        = {A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics},

  author       = {Qamar, Shamsul and Warnecke, Gerald},

  abstractNote = {In this paper we extend the special relativistic hydrodynamic (SRHD) equations [L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Pergamon, New York, 1987] and as a limiting case the ultra-relativistic hydrodynamic equations [M. Kunik, S. Qamar, G. Warnecke, J. Comput. Phys. 187 (2003) 572-596] to the special relativistic magnetohydrodynamics (SRMHD). We derive a flux splitting method based on gas-kinetic theory in order to solve these equations in one space dimension. The scheme is based on the direct splitting of macroscopic flux functions with consideration of particle transport. At the same time, particle 'collisions' are implemented in the free transport process to reduce numerical dissipation. To achieve high-order accuracy we use a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. For the direct comparison of the numerical results, we also solve the SRMHD equations with the well-developed second-order central schemes. The 1D computations reported in this paper have comparable accuracy to the already published results. The results verify the desired accuracy, high resolution, and robustness of the kinetic flux splitting method and central schemes.},

  doi          = {10.1016/j.jcp.2004.11.004},

  url          = {https://www.osti.gov/biblio/20687230},
  journal      = {Journal of Computational Physics},

  issn         = {0021-9991},

  number       = 1,

  volume       = 205,

  place        = {United States},

  year         = {Sun May 01 00:00:00 EDT 2005},

  month        = {Sun May 01 00:00:00 EDT 2005}

}

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