Geodesic
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 mehanika, no. 66 (2020), pp. 132-142

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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.
Keywords: Navier-Stokes equations, iterative method, thin plate, integral equations.
Mots-clés : viscous fluid 
@article{VTGU_2020_66_a10,
     author = {M. A. Sumbatyan and Ya. A. Berdnik and A. A. Bondarchuk},
     title = {An iterative method for the {Navier-Stokes} equations in the problem of a viscous incompressible fluid flow around a thin plate},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {132--142},
     publisher = {mathdoc},
     number = {66},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2020_66_a10/}
}
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M. A. Sumbatyan; Ya. A. Berdnik; A. A. Bondarchuk. 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 mehanika, no. 66 (2020), pp. 132-142. http://geodesic.mathdoc.fr/item/VTGU_2020_66_a10/