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Investigation of Difference Schemes for Two-Dimensional Navier–Stokes Equations by Using Computer Algebra Algorithms

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Abstract

A class of consistent difference schemes for incompressible Navier–Stokes equations in physical variables and their differential approximations are considered using an algorithm for Gröbner basis construction. Results of investigating the first differential approximations of these schemes, which are obtained by using the authors' programs implemented in the SymPy computer algebra system, are presented. For the difference schemes under consideration, the quadratic dependence of the error for large Reynolds numbers and the inversely proportional dependence for creeping currents are analyzed.

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Funding

This work was supported by the Russian Science Foundation, project no. 20-11-20257.

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Authors and Affiliations

  1. Chernyshevsky Saratov National Research State University, ul. Astrakhanskaya 83, 410012, Saratov, Russia

    Yu. A. Blinkov

  2. Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, 117198, Moscow, Russia

    Yu. A. Blinkov

  3. Joint Institute for Nuclear Research, ul. Zholio-Kyuri 6, 141980, Dubna, Moscow oblast, Russia

    Yu. A. Blinkov

  4. Gagarin State Technical University of Saratov, ul. Politekhnicheskaya 77, 410054, Saratov, Russia

    A. Yu. Rebrina

Authors
  1. Yu. A. Blinkov
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  2. A. Yu. Rebrina
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Correspondence to Yu. A. Blinkov or A. Yu. Rebrina.

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Translated by Yu. Kornienko

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Blinkov, Y.A., Rebrina, A.Y. Investigation of Difference Schemes for Two-Dimensional Navier–Stokes Equations by Using Computer Algebra Algorithms. Program Comput Soft 49, 26–31 (2023). https://doi.org/10.1134/S0361768823010024

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  • DOI: https://doi.org/10.1134/S0361768823010024