[MITSardine]

Numerical simulation is a well explored field, we know how to do all sorts of things, the issues lie rather in the tooling and robustness of it all put together (from geometry to numerical results) than in conceptual barriers. Finite Differences have existed since the 1700's! What hadn't for the longest time, is the computational power to crunch billions of operations per simulation.

A nice thing about numerical simulation from first principles, is it innately supports arbitrary speed/precision, that's in fact the backbone of the mathematical analysis for why it works.

In some cases, as is the case for CFD, we're actually mathematically screwed because you just have to resolve the small scales to get the macro dynamics. So the standard remains a kind of hack, which is to introduce additional equations (turbulence models) that steer the dynamics in place of the small (unresolved) scales. We know how to do better though (DNS), but it costs an arm and a leg (like years to milenia on a super computer).