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High-Order Low-Dissipation Targeted ENO Schemes for Ideal Magnetohydrodynamics

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Abstract

The recently proposed targeted ENO (TENO) schemes (Fu et al. J Comput Phys 305:333–359, 2016) are demonstrated to feature the controllable low numerical dissipation and sharp shock-capturing property in compressible gas dynamic simulations. However, the application of low-dissipation TENO schemes to ideal magnetohydrodynamics (MHD) is not straightforward. The complex interaction between fluid mechanics and electromagnetism induces extra numerical challenges, including simultaneously preserving the ENO-property, maintaining good numerical robustness and low dissipation as well as controlling divergence errors. In this paper, based on an unstaggered constrained transport framework to control the divergence error, we extend a set of high-order low-dissipation TENO schemes ranging from 5-point to 8-point stencils to solving the ideal MHD equations. A unique set of built-in parameters for each TENO scheme is determined. Different from the TENO schemes in Fu et al.  (2016), a modified scale-separation formula is developed. The new formula can achieve stronger scale separation, and it is simpler and more efficient than the previous version as the computation cost of high-order global smoothness measure \({\tau _K}\) is avoided. The performances of tailored schemes are systematically studied by several benchmark simulations. Numerical experiments demonstrate that the TENO schemes in the constrained transport framework are promising to simulate more complex MHD flows.

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Notes

  1. Computing time is measured based on the same desktop workstation and CentOS Linux system.

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Acknowledgements

The first author is funded by U.S. Air Force Office of Scientific Research (AFOSR) (Grant No. 1194592-1-TAAHO). The second author is supported by the Eliza Ricketts Postdoctoral Fellowship.

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Authors and Affiliations

  1. Center for Turbulence Research, Stanford University, Stanford, CA, 94305, USA

    Lin Fu

  2. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Qi Tang

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Correspondence to Lin Fu.

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Fu, L., Tang, Q. High-Order Low-Dissipation Targeted ENO Schemes for Ideal Magnetohydrodynamics. J Sci Comput 80, 692–716 (2019). https://doi.org/10.1007/s10915-019-00941-2

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