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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 8, Pages 1281–1288 (Mi zvmmf10075)  

This article is cited in 1 scientific paper (total in 2 paper)

Two methods for direct numerical integration of the Prandtl equation and comparative analysis between them

A. V. Sahakyana, N. N. Shavlakadzeb

a Institute of Mechanics, National Academy of Sciences of Armenia, pr. Marshala Bagramyana 24b, Yerevan, 0019, Armenia
b A. Razmadze Mathematical Institute, Georgian Academy of Sciences

Abstract: Two methods based on quadrature formulas are proposed for the direct numerical integration of Prandtls singular integro-differential equation. In the first method, Prandtls equation is solved directly by applying the method of mechanical quadrature and the circulation along an airfoil section is determined. In the second method, Prandtls equation is rewritten for the circulation derivative, which is determined by applying mechanical quadratures, and the circulation is then reconstructed using the same quadrature formulas. Both methods are analyzed numerically and are shown to converge. Their convergence rates are nearly identical, while the second method requires much more CPU time than the first one.

Key words: finite wing theory, Prandtls singular integro-differential equation, complex wing geometry, numerical integration, method of mechanical quadrature.

DOI: https://doi.org/10.7868/S0044466914080134

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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:8, 1244–1250

Bibliographic databases:

UDC: 519.642
MSC: 76F40
Received: 23.09.2013
Revised: 21.01.2014

Citation: A. V. Sahakyan, N. N. Shavlakadze, “Two methods for direct numerical integration of the Prandtl equation and comparative analysis between them”, Zh. Vychisl. Mat. Mat. Fiz., 54:8 (2014), 1281–1288; Comput. Math. Math. Phys., 54:8 (2014), 1244–1250

Citation in format AMSBIB
\by A.~V.~Sahakyan, N.~N.~Shavlakadze
\paper Two methods for direct numerical integration of the Prandtl equation and comparative analysis between them
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2014
\vol 54
\issue 8
\pages 1281--1288
\jour Comput. Math. Math. Phys.
\yr 2014
\vol 54
\issue 8
\pages 1244--1250

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    This publication is cited in the following articles:
    1. A. V. Sahakyan, H. A. Amirjanyan, “Method of mechanical quadratures for solving singular integral equations of various types”, 5th International Conference on Topical Problems of Continuum Mechanics With a Special Session in Honor of Alexander Manzhirov's 60th Birthday, Journal of Physics Conference Series, 991, IOP Publishing Ltd, 2018, 012070  crossref  isi  scopus
    2. V. P. Radchenko, M. N. Saushkin, “Pamyati Olega Aleksandrovicha Repina”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:3 (2018), 401–406  mathnet  crossref
  •      Computational Mathematics and Mathematical Physics
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