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Abstract <p>The paper considers the problems of motion of thin bodies in a viscous incompressible liquid. In the Stokes approximation, the equations of motion are linear. This assumption allows using the fundamental solutions to reduce the problem of motion of thin bodies of finite size to singular integral equations. A numerical method for solving the obtained integral equations for the three-dimensional motion of bodies int he form of a set of thin impermeable and permeable plates (not a direct boundary element method) is proposed. The solution to the problem in this method is obtained in the form of a finite series expansion according to the found basic functions. Using the fundamental solutions to the Stokes equations, the problem of three-dimensional motion of thin bodies in a viscous liquid is reduced to a system of singular integral equations. The program codes for solving the resulting system of singular integral equations are written. The program allows obtaining the velocity fields, stress components, vortex distribution, and forces and moments acting on the plates.</p>

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Numerical Study of the Motion of Thin Plates in a Viscous Fluid at Small Reynolds Numbers

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • A. V. Zvyagin,
  • A. A. Shamina,
  • A. Yu. Shamin

摘要

Abstract

The paper considers the problems of motion of thin bodies in a viscous incompressible liquid. In the Stokes approximation, the equations of motion are linear. This assumption allows using the fundamental solutions to reduce the problem of motion of thin bodies of finite size to singular integral equations. A numerical method for solving the obtained integral equations for the three-dimensional motion of bodies int he form of a set of thin impermeable and permeable plates (not a direct boundary element method) is proposed. The solution to the problem in this method is obtained in the form of a finite series expansion according to the found basic functions. Using the fundamental solutions to the Stokes equations, the problem of three-dimensional motion of thin bodies in a viscous liquid is reduced to a system of singular integral equations. The program codes for solving the resulting system of singular integral equations are written. The program allows obtaining the velocity fields, stress components, vortex distribution, and forces and moments acting on the plates.