We come across the term 'numerical diffusion' (ref. contributions by S.V. Patankar and B.P. Leonard). We perhaps experience it (problem specific) especially when using lower order upwind scheme for the convection term. Is there any way to estimate the quantity of 'numerical diffusion' - localised or in the domain?

This analysis technique is detailed by C. W. Hirt, "Heuristic Stability Theory for Finite-Difference Equations," J. Comp. Physics, v. 8, p. 119 (1968).

One way is to consider inviscid subsonic flow in which there should be no entropy production. Whatever entropy is generated is purely due to numerical dissipation.

In the textbook on Numerical Methods (such as Tannehill et al 1997) you can find the expression for the numerical diffusion due to the upwind first order discretization of the convective (first derivative) terms. It has the form: u*h/2

u-velocity, h-grid spacing

To see how large is your artificial diffusion, send a vortex in the still fluid. Integrate the vorticity over the domain for each time step. There is an analytical experssion for the decay of vorticity. See how the numerical integration correspond to analytical function.