NUMERICAL SCHEME FOR CALCULATING THE BOUNDARY LAYER WHEN MODELING BY THE METHOD OF DISCRETE VORTICES

Abstract

In this paper, a six-point finite-difference numerical scheme for calculating the Prandtl equation of a laminar boundary layer is proposed to determine the point of separation of flows with large Reynolds numbers when flowing around smooth bodies. The input data for this scheme are the results of modeling by the method of discrete vortices within the model of an ideal fluid. The velocity profile around the critical point is determined from the analytical solution. The resulting system of linear algebraic equations is solved by the run method. Because the coefficients of the system are nonlinear, the iteration method is used to find the solution. The thickness of the boundary layer is determined during the solution process. The point of separation and circulation of descending vortices is determined from the calculation of the boundary layer. Then at the point of separation the rise of several free vortices is modeled, the dynamics of which is modeled within the method of discrete vortices. The scheme was tested on the problem of the flow around the cylinder and showed good results in comparison with the experimental data and calculations of other authors.