Srecko Bradic

Navier-Stokes equations have been around since about 1845 when the idea of friction was introduced into the (frictionless) Bernoulli equation. This described how fluids flow, including with turbulence however they remained without solution until computers were invented thanks to their complexity.

The Navier-Stokes equations assume fluids to be a continuum, although in the real world, fluids are a lot of individual molecules. However, the assumption that a fluid is a continuum actually holds up pretty well. It’s not just liquid that the N-S equations can model – they can also model gases. However, there isn’t a single known analytic solution for them – if you can find a solution or prove that there isn’t a solution, you’d be in line for a million dollars from the Clay Mathematics Institute ;o)

So, I think you will struggle to find much on N-S and F1. F1 engineers tend to use CFD (Computational Fluid Dynamics) which is actually simplified versions of N-S equations. Even with incredibly powerful computers, some solutions can take weeks before a result is found, however CFD is a fairly accurate model of the real world therefore is incredibly useful in F1.

Really and truly, it would be hard to run any form of N-S equation on a standard, personal computer therefore I guess the article has been written with the simpler Bernoulli equation which provides a good introduction to aerodynamics and models can be built that will run on a personal computer without too much difficulty.