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On the Accuracy of a MUSCL-Type Scheme when Calculating Discontinuous Solutions

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Abstract

The accuracy of the central difference Nessyahu-Tadmor (NT) scheme is studied when calculating shock waves propagating at a variable velocity. It is shown that this scheme (in the construction of which the second-order MUSCL reconstruction of flows is used) has approximately the first order of both local convergence in the regions of influence of shock waves and integral convergence in intervals, one of the boundaries of which is in the region of influence of the shock wave. As a result, in these areas, the local accuracy of the NT scheme is significantly reduced. Test calculations are presented that demonstrate these properties of the NT scheme.

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Funding

This study was supported by the Russian Science Foundation (grant no. 16-11-10033).

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    O. A. Kovyrkina & V. V. Ostapenko

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  1. O. A. Kovyrkina
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  2. V. V. Ostapenko
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Correspondence to O. A. Kovyrkina or V. V. Ostapenko.

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Kovyrkina, O.A., Ostapenko, V.V. On the Accuracy of a MUSCL-Type Scheme when Calculating Discontinuous Solutions. Math Models Comput Simul 13, 810–819 (2021). https://doi.org/10.1134/S2070048221050136

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