Analyzing Laminar Boundary Layer Flow: A Unified Approach Using Numerical and Data-Driven Methods

This paper introduces an innovative approach that melds numerical integration with data-driven techniques to tackle the intricate challenge of laminar boundary layer flow. The focal point is the Blasius equation, a fundamental cornerstone in fluid dynamics that characterizes the behavior of boundary layers over surfaces. Traditional analytical solutions to the Blasius equation often involve complex mathematical manipulations, motivating the utilization of numerical methods for practical solutions. In response, this research proposes a two-step strategy. First, a simplified version of the Blasius equation is derived using the Sparse Identification of Nonlinear Dynamics (SINDy), streamlining the subsequent numerical computations. Second, the odeint function from the SciPy library is employed for efficient numerical integration. The results yield comprehensive insights into boundary layer behavior, with visualizations offering intuitive representations of the velocity profiles. This approach bridges the gap between traditional analytical techniques and modern data-driven methods, presenting a promising avenue for enhancing our understanding of fluid dynamics phenomena and their real-world applications.