Numerical study of motion of thin plates in a viscous liquid for small Reynolds numbers

A. V. Zvyagin ; A. A. Shamina ; A. Yu. Shamin

Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2025), pp. 44-51

Résumé

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 us to use 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 in the form of a set of thin impermeable and permeable plates (not a direct boundary element method) is proposed. The solution of the problem in this method is obtained in the form of a finite series-expansion according to the found basic functions. Using fundamental solutions of 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 us to obtain velocity fields, stress components, vortex distribution and forces and moments acting on the plates.