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Second Order, Unconditionally Stable, Linear Ensemble Algorithms for the Magnetohydrodynamics Equations

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Abstract

We propose two unconditionally stable, linear ensemble algorithms with pre-computable shared coefficient matrices across different realizations for the magnetohydrodynamics equations. The viscous terms are treated by a standard perturbative discretization. The nonlinear terms are discretized fully explicitly within the framework of the generalized positive auxiliary variable approach (GPAV). Artificial viscosity stabilization that modifies the kinetic energy is introduced to improve accuracy of the GPAV ensemble methods. Numerical results are presented to demonstrate the accuracy and robustness of the ensemble algorithms.

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Acknowledgements

J. Carter was partially supported by the US National Science Foundation grant DMS-1720001 and DMS-1912715. D. Han was supported by the US National Science Foundation Grant DMS-1912715. N. Jiang was partially supported by the US National Science Foundation Grants DMS-1720001 and DMS-2120413. The authors thank Dr. Suchuan Dong for helpful discussions.

Funding

US National Science Foundation grant DMS-1720001, DMS-1912715, DMS-2120413.

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  1. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, 65409, USA

    John Carter & Daozhi Han

  2. Department of Mathematics, University of Florida, Gainesville, FL, USA

    Nan Jiang

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Correspondence to Daozhi Han.

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Carter, J., Han, D. & Jiang, N. Second Order, Unconditionally Stable, Linear Ensemble Algorithms for the Magnetohydrodynamics Equations. J Sci Comput 94, 41 (2023). https://doi.org/10.1007/s10915-022-02091-4

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