New explicit solution of the Blasius equation in the boundary layer around the hull of a ship by approximation of derivatives

Naval hydrodynamics fundamentally depends on a detailed understanding of the boundary layers forming around a ship’s hull, which generate resistance to advancement. Accurately modeling these layers is critical for calculating hydrodynamic resistance and estimating the propulsion power needed to achieve the desired speed specified by the shipowner. Traditionally, the velocity distribution within the boundary layer is described by the Blasius equation, a nonlinear third-order differential equation commonly solved using the Runge-Kutta numerical method, renowned for its accuracy. This study proposes a novel direct and explicit approach to solving the Blasius equation around a ship’s hull, leveraging a derivative approximation technique implemented with MATLAB to obtain numerical results. By employing sufficiently small step sizes, the method produces highly accurate results that can serve as a benchmark for evaluating the precision of other numerical techniques applied in ship design. The proposed derivative approximation method provides a simple yet robust tool for solving complex differential equations, demonstrating its potential as an effective alternative for tackling problems similar to the Blasius equation in naval engineering applications.

کلیدواژه ها:

Naval hydrodynamics ، Boundary layers ، Resistance to advancement ، The Blasius equation ، The Runge-Kutta method ، Approximation of derivatives