Hi,

I would like to have an idea about formulas for calculating the residual over a domain with uniform grid to fix the convergence criteria.

Usually I use (Finite difference scheme):

res = sqrt((Un+1-Un)^2/N) where N is the number of nodes.

Is it correct???

Usually, when you have an equation as d(u)/dt + L(u) = S

where L(u) is the spatial operator and S is the source, you tend to represent (L(u)-S) as the residual.

For a steady state, this (averaged over all nodes) needs to be zero and hence the convergence criteria. There are many different methods.

For finite volume, it should be the average and not the integral quantity for a stringent condition. (For smaller cells near the physical boundary, this tends to be higher)