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Numerical analysis of a second order algorithm for simplified magnetohydrodynamic flows

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Abstract

In this paper, we construct a second order algorithm based on the spectral deferred correction method for the time-dependent magnetohydrodynamics flows at a low magnetic Reynolds number. We present a complete theoretical analysis to prove that this algorithm is unconditionally stable, consistent and second order accuracy. Finally, two numerical examples are given to illustrate the convergence and effectiveness of our algorithm.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China

    Yao Rong, Yanren Hou & Yuhong Zhang

Authors
  1. Yao Rong
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  2. Yanren Hou
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  3. Yuhong Zhang
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Corresponding author

Correspondence to Yao Rong.

Additional information

Communicated by: Silas Alben

Supported by NSFC (Grant No. 11171269 and 11571274).

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Rong, Y., Hou, Y. & Zhang, Y. Numerical analysis of a second order algorithm for simplified magnetohydrodynamic flows. Adv Comput Math 43, 823–848 (2017). https://doi.org/10.1007/s10444-016-9508-6

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  • DOI: https://doi.org/10.1007/s10444-016-9508-6

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