AN ITERATIVE METHOD FOR THE NAVIER-STOKES EQUATIONS IN THE PROBLEM OF A VISCOUS INCOMPRESSIBLE FLUID FLOW AROUND A THIN PLATE

Abstract

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.