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Numerical Analysis of an Artificial Compression Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers

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Abstract

Magnetohydrodynamics (MHD) is the study of the interaction of electrically conducting fluids in the presence of magnetic fields. MHD applications require substantially more efficient numerical methods than currently exist. In this paper, we construct two decoupled methods based on the artificial compression method (uncoupling the pressure and velocity) and partitioned method (uncoupling the velocity and electric potential) for magnetohydrodynamics flows at low magnetic Reynolds numbers. The methods we study allow us at each time step to solve linear problems, uncoupled by physical processes, per time step, which can greatly improve the computational efficiency. This paper gives the stability and error analysis, presents a brief analysis of the non-physical acoustic waves generated, and provides computational tests to support the theory.

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Authors and Affiliations

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

    Yao Rong

  2. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    William Layton & Haiyun Zhao

Authors
  1. Yao Rong
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  2. William Layton
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  3. Haiyun Zhao
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Corresponding author

Correspondence to Yao Rong.

Additional information

Yao Rong was supported by NSFC (Grants 11171269 and 11571274) and China Scholarship Council (Grant 201606280154). William Layton and Haiyun Zhao supported by NSF Grants DMS 1522267 and CBET 160910.

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Rong, Y., Layton, W. & Zhao, H. Numerical Analysis of an Artificial Compression Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers. J Sci Comput 76, 1458–1483 (2018). https://doi.org/10.1007/s10915-018-0670-5

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  • DOI: https://doi.org/10.1007/s10915-018-0670-5

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