In the field of fluid dynamics, the Navier-Stokes equations are considered to be the governing equations for fluid flow. They are a mess to deal with directly. However, by ignoring the effects of viscosity and density changes (compressibility), the equations reduce down to a much more tractable form known as Laplace's equation, which has applications in more than just fluid dynamics. When used in fluid dynamics, the resulting flow is referred to as potential flow.

Directly trying to solve the Navier-Stokes equations is the realm of high end computing and PhD level research. By contrast, potential flow problems are commonly assigned as undergraduate homework. Only a minimum amount of computing power is needed. There's even enough power in a little microcontroller, like the ones found on a Matrix Portal, Feathers, and other microcontroller boards.

In this guide, we'll use a Matrix Portal to create a flow field visualizer based on potential flow. We'll cover a couple of different approaches. The goal here isn't to teach aerodynamics though. We'll provide some details, but this is more of a just-for-fun project that can create some fun and interesting animations.

Hardware

If you have an AdaBox 016, then you have everything you need for this project. Otherwise, the parts are available a la carte:

Or as a kit: