  We consider sewing machinery between finite difference and analytical
solutions defined at different scale: far away and near source of the
perturbation of the flow. One of the essences of the approach is that coarse
problem and boundary value problem in the proxy of the source model two
different flows. We are proposing method to glue solution via total fluxes,
which is predefined on coarse grid. It is important to mention that the coarse
solution "does not see" boundary.
  From industrial point of view our report provide mathematical tool for
analytical interpretation of simulated data for fluid flow around a well in a
porous medium. It can be considered as a mathematical "shirt" on famous
Peaceman well-block radius formula for linear (Darcy) radial flow but can be
applied in much more general scenario.
  As an important case, we consider nonlinear Forchheimer flow. In the article
we rigorously obtained well-block radius, explicitly depending on
$\beta-$Forchheimer factor and total rate of the flow on the well, and provide
generalization of the Dake Formula and evaluation of the $D-$factor.
