The same thing applies to lots of fields of computation. In fluid dynamics, for instance, a direct simulation of the Navier-stokes equations is quite straightf

The same thing applies to lots of fields of computation. In fluid dynamics, for instance, a direct simulation of the Navier-stokes equations is quite straightforward and will produce the most accurate solution. All the complicated parts are layers and layers of tricks to save large amounts of compute time with (hopefully) negligable effects on the ultimate accuracy.