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Numerical analysis of the external slow flows of a viscous fluid using the R-function method

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Abstract

In this paper the problem of calculating the external slow flow of viscous incompressible fluid past bodies of revolution is considered. A numerical method, based on the joint use of the R-function structural method of V. L. Rvachev for building the structure of the boundary-value problem solution and the Galerkin projection method for approximating the indeterminate components of the structure, is proposed for solving the problem. The problem of slow viscous incompressible fluid flow past an ellipsoid of revolution is numerically solved using the proposed approach to test the developed method. The solution obtained is compared with the known exact solution of the problem in question. In addition, the problems of flow past two touching spheres and past two joined ellipsoids are solved.

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Authors and Affiliations

  1. Department of Applied Mathematics, Kharkiv National University of Radioelectronics, Lenina Av. 14, Kharkiv, 61166, Ukraine

    S. N. Lamtyugova & M. V. Sidorov

  2. Department of Advanced Mathematics, O. M. Beketov National University of Urban Economy in Kharkiv, Revolutsii Street 12, Kharkiv, 61002, Ukraine

    S. N. Lamtyugova

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  1. S. N. Lamtyugova
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  2. M. V. Sidorov
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Correspondence to S. N. Lamtyugova.

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Lamtyugova, S.N., Sidorov, M.V. Numerical analysis of the external slow flows of a viscous fluid using the R-function method. J Eng Math 91, 59–79 (2015). https://doi.org/10.1007/s10665-014-9746-x

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  • DOI: https://doi.org/10.1007/s10665-014-9746-x

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