Understanding the Navier-Stokes equations

Greetings, fluid mechanics enthusiast! Welcome to the course “Understanding the Navier-Stokes equations”. My name is Leonardo, or Leo for short, I am a civil engineer with master in fluid dynamics with over 6 years of experience in computational fluid dynamics (CFD).

On this course, you will learn the physical and mathematical principles of the famous Navier-Stokes equations, one of the equations that changed the world! You'll learn how to derive them, understand the meaning of each term and how to apply these equations to solve fluid dynamics problems.

First, we will derive the Navier-Stokes from the Newton’s Second Law, by analyzing the forces acting on a fluid and how a particle of fluid is accelerated.

In the second section of the course, you will learn more about the many forms and notations used in textbooks and scientific articles to express the Navier-Stokes equations, such as the famous Einstein Notation or Summation Convention.

On the third part of the course, we will cover in more detail the stress term in the Navier-Stokes equations and the behavior of tensor variables.

Boundary conditions will be covered on the fourth part of the course. We will talk about how they appear in the context of fluid dynamics problems and how to recognize them.

On the fifth and final section, which is a more practical one, we will obtain exact solutions of the Navier-Stokes equations by solving boundary and initial value problems.

Understanding and solving the Navier-Stokes requires a lot of knowledge from other fields, so by taking this course you must have basic knowledge from calculus, mechanics, linear algebra and differential equations. However, if you are somewhat rusty in those subjects, do not be frightened! We will review the main topics from these areas if necessary.

The notes used in each class are available for download in the course page.

Did not like the course? Was it too hard? Too easy? Well, do not worry! You have 30 days to obtain your money back. Once bought, you have lifetime access to the course.

I hope I got you interested in understanding the Navier-Stokes equations with me. See you in the first class!