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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 5, Pages 876–880 (Mi zvmmf10577)  

This article is cited in 1 scientific paper (total in 1 paper)

Comparison of additional second-order terms in finite-difference Euler equations and regularized fluid dynamics equations

V. M. Ovsyannikovab

a Moscow State Academy of Water Transport, Moscow, Russia
b Noyabr'sk Branch, Tyumen Industrial University, Noyabr'sk, Yamalo-Nenets Autonomous Okrug, Russia

Abstract: In recent years, an area of research in computational mathematics has emerged that is associated with the numerical solution of fluid flow problems based on regularized fluid dynamics equations involving additional terms with velocity, pressure, and body force. The inclusion of these functions in the additional terms has been physically substantiated only for pressure and body force. In this paper, the continuity equation obtained geometrically by Euler is shown to involve second-order terms in time that contain Jacobians of the velocity field and are consistent with some of the additional terms in the regularized fluid dynamics equations. The same Jacobians are contained in the inhomogeneous right-hand side of the wave equation and generate waves of pressure, density, and sound. Physical interpretations of the additional terms used in the regularized fluid dynamics equations are given.

Key words: regularized fluid dynamics equations, Euler's finite-difference continuity equation, Jacobians, wave equation.

DOI: https://doi.org/10.7868/S004446691705009X

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:5, 876–880

Bibliographic databases:

UDC: 519.634
Received: 23.05.2016
Revised: 14.07.2016

Citation: V. M. Ovsyannikov, “Comparison of additional second-order terms in finite-difference Euler equations and regularized fluid dynamics equations”, Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017), 876–880; Comput. Math. Math. Phys., 57:5 (2017), 876–880

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Ovsyannikov, “Uravnenie nerazryvnosti Eilera s chlenami vysokogo poryadka malosti po vremeni techeniya”, Trudy mezhdunarodnoi konferentsii ЂKlassicheskaya i sovremennaya geometriyaї, posvyaschennoi 100-letiyu so dnya rozhdeniya professora Vyacheslava Timofeevicha Bazyleva. Moskva, 22Ц25 aprelya 2019 g. Chast 4, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 182, VINITI RAN, M., 2020, 95–100  mathnet  crossref
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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