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Cabaret Difference Scheme with Improved Dispersion Properties

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Abstract

A difference scheme for the transfer problem, constructed as a linear combination of the Cabaret scheme and the central difference scheme, is proposed. The stability and dispersion properties of the scheme are studied. It is shown that the constructed scheme has the best dispersion properties for high-frequency harmonics at small Courant numbers compared with the known Cabaret scheme for the transport equation. A comparison is made of the errors of this scheme and the two-parameter third-order difference accuracy scheme based on the numerical experiments on the previously used test problem sets. It is shown that in the normal grid space L1 the developed scheme has smaller errors and also uses a more compact template (in calculating the inode the node values i – 1, i, and i + 1 are used), and the transition to the next time layer is carried out for a smaller number of arithmetic operations.

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Funding

The study was financially supported by the Russian Science Foundation (grant no. 17-11-01286).

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Authors and Affiliations

  1. Don State Technical University, 344002, Rostov-on-Don, Russia

    A. I. Sukhinov & A. E. Chistyakov

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  1. A. I. Sukhinov
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  2. A. E. Chistyakov
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Correspondence to A. I. Sukhinov or A. E. Chistyakov.

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Sukhinov, A.I., Chistyakov, A.E. Cabaret Difference Scheme with Improved Dispersion Properties. Math Models Comput Simul 11, 867–876 (2019). https://doi.org/10.1134/S207004821906019X

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  • DOI: https://doi.org/10.1134/S207004821906019X

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