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Shifting the Boundary Conditions to the Middle Surface in the Numerical Solution of Neumann Boundary Value Problems Using Integral Equations

In: Integral Methods in Science and Engineering, Volume 2

Author

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  • A. V. Setukha

    (Lomonosov Moscow State University)

Abstract

The 3-D Neumann boundary value problem for the Laplace equation exterior to a body of small thickness is considered. An approach is proposed to solve the problem in which the boundary conditions are transferred to a middle surface of the body. As a result, a new boundary value problem on the screen (the middle of the body surface) is solved. The initial shape of the body is taken into account using the corresponding boundary conditions. The resulting boundary value problem on the screen is reduced to a system of boundary integral equations with singular and hypersingular integrals. These integral equations are solved numerically using the methods of piecewise constant approximations and collocation. On the basis of the developed approach a new version of the panel method for solving the problem of the flow past a wing is built using the wing replacement with the middle surface.

Suggested Citation

  • A. V. Setukha, 2017. "Shifting the Boundary Conditions to the Middle Surface in the Numerical Solution of Neumann Boundary Value Problems Using Integral Equations," Springer Books, in: Christian Constanda & Matteo Dalla Riva & Pier Domenico Lamberti & Paolo Musolino (ed.), Integral Methods in Science and Engineering, Volume 2, chapter 0, pages 233-243, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-59387-6_23
    DOI: 10.1007/978-3-319-59387-6_23
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