Numerical solution of Boundary Layer Equations based on optimization: The Ostrach and Blasius models

Abstract

The numerical solutions for the Blasius equation and for the Ostrach system where investigated. A combination of optimization procedure and Shooting Method where systematized in order to produce a powerful method for solving nonlinear systems of differential equations, namely Initial Value Problem Approximation by Sequential Parameter Optimization (IVASO). Using the IVASO method, it was shown to be possible and easy to obtain an accurate solution for the Blasius equation. It was also demonstrated that the Ostrach system can be solved by IVASO. Thissystem has a large sensibility to initial conditions, and that its solution for near zero (η≈0) is strongly correlated with its solution far from the origin (η≫0), and consequently, an accurate solution for the boundary layer demands a highly accurate solution of the initial values problem, this is similar to the butterfly effect usually studied in chaotic systems.