Why Navier-Stokes Partial Differential Equations Are Difficult To Simulate

Question

So I was reading this paper: https://www.nature.com/articles/s41534-020-00291-0.

I am a bit confused about this:

Little attention, however, has been given to quantum simulation of a classical nonlinear continuum system such as a viscous fluid even though this too is hard for classical computers. Such fluids obey the Navier–Stokes nonlinear partial differential equations, whose solution is essential ...

Why are the Navier-Stokes equations difficult to simulate? That's what the above quote is saying, right? It is just because there are a lot of variables?

Thanks

Answer 1

In some cases (that is, for very viscous fluids) the Navier-Stokes equations are relatively easy to simulate. In most real-life cases, the reason they are hard is because small but non-zero viscosity leads to chaotic behaviour on spatial scales smaller than the domain size, i.e. turbulence.