Analytical approximation of solutions to the Blasius problem in the boundary layer on a flat plate - V. M. Zubarev (Учёные записки Казанского университета: Серия Физико-математические науки, 2025)
In recent years, the steady-state flow of viscous fluids has attracted considerable research interest due to its broad engineering applications. This study provides new insights into the classical problem of the theory of the viscous laminar stationary boundary layer of an incompressible Newtonian fluid on a thin flat plate (Blasius problem). A finite-difference solution to the Blasius problem was obtained by the shooting method in combination with the Runge–Kutta numerical scheme of the fourth-order accuracy over a large interval for a very fine mesh. The numerical results were validated against similar known data of calculation tests. The Blasius function f(η) and its first two derivatives were approximated using the third-order B-spline. Excellent agreement with the results of known calculations was demonstrated. A new analytical correlation for the Blasius function, which approximates the results of the calculations in a wide range of the self-similar variable η, was established by the nonlinear least squares method (NLLSM). The values of the function f and its first- and second-order derivatives were compared with known data. The results align with previous solutions. The longitudinal velocity profile in the boundary layer, defined through the derivative f′ of the Blasius function, can serve as the initial velocity profile in the numerical modeling of turbulent flat and three-dimensional flows of an incompressible fluid.