Numerical solutions of fluid flow problems are only approximate. There are many sources of error which need to be considered, which fall into 3 basic categories :
The NSE provide a good representation of basic fluid flow, so modelling errors do not often arise for simple Newtonian laminar flow. More complex problems such as combustion are often not well understood, and the models used usually have limitations which need to be understood if the results are to be meaningful.
A CFD method is stable if it does not magnify numerical errors. For an explicit CFD scheme to be stable, the Courant number
An important question regarding the solution of the NSE (and any other modelled equations
we might be interested in) is how closely our discretised solution will approach the true
solution of the original equations. If the original equations can be recovered mathematically
from the discretised equations by reducing the mesh spacing (
x 
0), then the discretised
equations are said to be consistent. If the scheme is consistent and stable, then the numerical
solution should converge to the true solution as x 0. CFD calculations should, if possible,
be run on sucessively finer meshes until the solution does not change, a condition known as
mesh independence.
The NSE express the conservation of mass and momentum (and energy), fundamental physical
principles which we would want our numerical method to match. In addition, physically
meaningful quantities are often bounded. For instance, negative energies make no physical
sense, and neither does a phase fraction 
< 1. Mathematical models of the flow may not be
able to fully model complex flows, but they should produce physically realistic results - they
should be realisable. Their numerical implementation as a set of difference equations, and their
solution, should also satisfy these requirements.