Семинар «Индустриальная математика»
в лаборатории Чебышева

In our talk we will present recent non-published results on PDE aspects of the flow in porous media. This research was motivated by discussion with my teacher Evgeni Mikchalovich Landis.

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 can be considered as a mathematical "shirt" on famous Peaceman well-block radius formula for Darcy radial flow but can be applied in much more general scenario.

This is a joint project with E. Zakirov. I. Indrupskiy, D. Anikeev from Oil ang Gas Res. Inst. of Russian Academy of Science.