Your assumptions are wrong.I don't know how fluid dynamics is solved numerically but I assumed the problem is somehow discretized and equations are applied to each point based on the geometry. It doesn't seem that it would require solutions of large systems of simultaneous equations or nonlinear iteration but I'm not an aerospace engineer.
Numerical simulations require large 3D or 4D grids that are iteratively solved with each of the millions of grid elements variable’s being recalculated with the values of its neighbors from the previous iteration.
This requires very fast, high precision floating point operations, and millions of storage locations for each grid element, and for the last few calculation iterations for each element. That’s how complex sets of fluid dynamics differential equations are numerically calculated.
I’m a retired engineer who has worked with these kinds of problems. Although it might not seem that way to you, this does require a substantial amount of computational resources.
There may be simpler approximations that can work for a very limited subset of CFD, but that takes someone who fully understands CFD to extract and derive this subset, and you don’t run into this kind of person very often.