Numerical Fluid Mechanics with MATLAB and Python

Understanding how fluids behave is essential for aerospace, automotive, and environmental engineering, but solving these complex equations requires powerful numerical techniques. This written guide introduces you to the core mathematical principles and computational algorithms used to simulate fluid flow. You will transition from basic calculus to understanding and implementing numerical solvers. By reading through structured explanations and code examples, you will learn how to discretize equations, analyze stability, and model real-world fluid dynamics. What you'll learn: - Understand foundational fluid dynamics equations, including the Navier-Stokes equations and boundary layer theory. - Apply finite difference and finite volume methods to discretize partial differential equations. - Analyze numerical errors, stability, and convergence using Fourier decomposition. - Implement time-marching methods and solver algorithms in MATLAB and modern Python. - Explore advanced techniques such as spectral methods and finite element approximations. - Configure grid generation and boundary conditions for complex geometric simulations. The course begins with essential mathematical definitions and error analysis before guiding you through linear systems, spatial discretization schemes, and modern solver implementations. This text-based program is designed for engineering students, researchers, and software developers new to computational fluid dynamics, requiring only basic physics and linear algebra. Start reading today to build your computational engineering skillset from the ground up.