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An Efficient Low-Dissipation High-Order TENO Scheme for MHD Flows

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Abstract

In this paper, an efficient low-dissipation high-order TENO scheme is proposed for ideal MHD flows. For high computational efficiency, a troubled-cell indicator based on the ENO-like stencil selection strategy in TENO schemes is introduced to isolate the discontinuities from smooth regions. While the high-order linear scheme is adopted for the smooth regions, a low-dissipation TENO scheme is applied for capturing discontinuities detected by the troubled-cell indicator. The case-independent parameters are given based on spectral analysis. Both the governing equations of the ideal MHD and the Hamilton–Jacobi type constrained transport equation for divergence-free condition can be solved by the newly proposed scheme. Since most computational regions are resolved by the linear scheme without expensive characteristic decomposition, flux splitting and nonlinear weight calculation, the proposed scheme is highly efficient. A set of benchmark cases has been simulated to demonstrate the performance of the proposed scheme. Numerical results reveal that remarkable speedup is achieved by the present scheme while the oscillation-free property and the high-order accuracy are preserved.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

Lin Fu acknowledges the generous startup fund from The Hong Kong University of Science and Technology (No. R9280) and the fund from Shenzhen Municipal Central Government Guides Local Science and Technology Development Special Funds Funded Projects (No. 2021Szvup138).

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  1. Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Lin Fu

  2. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Lin Fu

  3. Shenzhen Research Institute, The Hong Kong University of Science and Technology, Shenzhen, China

    Lin Fu

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Fu, L. An Efficient Low-Dissipation High-Order TENO Scheme for MHD Flows. J Sci Comput 90, 55 (2022). https://doi.org/10.1007/s10915-021-01722-6

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