Foundations of Computational Fluid Dynamics

Computational Fluid Dynamics (CFD) is a cornerstone of modern engineering, driving innovation in aerospace, automotive design, and environmental modeling. If you want to understand how computers simulate the behavior of liquids and gases, you need a solid grasp of the underlying mathematical and physical principles. This course guides you from fluid dynamics theory to the core algorithms used in industry-standard simulation software. You will transition from studying abstract differential equations to confidently setting up, discretizing, and analyzing numerical fluid flow simulations. Through structured written explanations and step-by-step mathematical derivations, you will build a robust framework for solving complex flow scenarios. What you will learn: - Understand the governing physical laws of fluid flow and their mathematical representation via the Navier-Stokes equations. - Classify partial differential equations to determine the correct numerical boundary conditions. - Apply finite difference and finite volume discretization techniques to convert continuous equations into solvable algebraic systems. - Analyze numerical stability, consistency, and convergence using proven mathematical frameworks. - Formulate algorithms for pressure-velocity coupling in incompressible flows. - Implement modern verification practices to ensure simulation accuracy and reduce computational errors. This course begins with foundational fluid mechanics terminology and basic mathematical classifications before advancing to discretization techniques and numerical solver algorithms. You will explore how physical boundary conditions translate into numerical constraints and how to assess the quality of your computational grids. This course is designed for engineering students, researchers, and practicing professionals who are new to CFD and want to build a strong theoretical and practical foundation without relying on specific proprietary software packages. No prior CFD experience is required, though a basic understanding of vector calculus and general physics will help you get the most out of the material. Start reading today to unlock the mathematical principles behind computational fluid simulations.