An iterative method for the navier-stokes equations in the problem of a viscous incompressible fluid flow around a thin plate | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2020. № 66. DOI: 10.17223/19988621/66/11

An iterative method for the navier-stokes equations in the problem of a viscous incompressible fluid flow around a thin plate

In this paper, the problem on a viscous fluid flow around a thin plate is considered using the exact Navier-Stokes equations. An iterative method is proposed for small velocity perturbations with respect to main flow velocities. At each iterative step, an integral equation is solved for a function of the viscous friction over the plate. The collocation method is used at each iteration step to reduce an integral equation to a system of linear algebraic equations, and the shooting method based on the classical fourth-order Runge-Kutta technique is applied. The solution obtained at each iteration step is compared with the Harrison-Filon solution at low Reynolds numbers, with the classical Blasius solution, and with the results computed using the direct numerical finite-volume method in the ANSYS CFX software for moderate and high Reynolds numbers. The proposed iterative method converges in a few steps. Its accuracy is rather high for small and large Reynolds number, while the error can reach 15% for moderate values.

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Keywords

уравнения Навье - Стокса, итерационный метод, вязкая жидкость, тонкая пластинка, интегральные уравнения, Navier-Stokes equations, iterative method, viscous fluid, thin plate, integral equations

Authors

Name	Organization	E-mail
Sumbatyan Mezhlum A.	Institute of Mathematics, Mechanics and Computer Science named after I.I. Vorovich	sumbat@math.rsu.ru
Berdnik Yanina A.	Southern Federal University	yaninaberdnik@mail.ru
Bondarchuk Aleksey A.	Southern Federal University	melchior@list.ru

Всего: 3

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