Email this article Decay of Unstable Strong Discontinuities in the Case of a Convex-Flux Scalar Conservation Law Approximated by the CABARET Scheme
- Authors: Zyuzina N.A.1,2, Ostapenko V.V.1,2
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Affiliations:
- Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences
- Novosibirsk State University
- Issue: Vol 58, No 6 (2018)
- Pages: 950-966
- Section: Article
- URL: https://journals.rcsi.science/0965-5425/article/view/179664
- DOI: https://doi.org/10.1134/S0965542518060155
- ID: 179664
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Abstract
Monotonicity conditions for the CABARET scheme approximating a quasilinear scalar conservation law with a convex flux are obtained. It is shown that the monotonicity of the CABARET scheme for Courant numbers \(r \in (0.5,1]\) does not ensure the complete decay of unstable strong discontinuities. For the CABARET scheme, a difference analogue of an entropy inequality is derived and a method is proposed ensuring the complete decay of unstable strong discontinuities in the difference solution for any Courant number at which the CABARET scheme is stable. Test computations illustrating these properties of the CABARET scheme are presented.
About the authors
N. A. Zyuzina
Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences; Novosibirsk State University
Author for correspondence.
Email: nzyuzina1992@gmail.com
Russian Federation, Novosibirsk, 630090; Novosibirsk, 630090
V. V. Ostapenko
Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences; Novosibirsk State University
Author for correspondence.
Email: ostapenko_vv@ngs.ru
Russian Federation, Novosibirsk, 630090; Novosibirsk, 630090
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