A mixed framework for topological model reduction of coupled PDEs

Abstract

In this work, we consider a set of mixed-dimensional PDEs that are used to model e.g. microcirculation, root water uptake and the flow of fluids in a reservoir perforated with wells. To be more precise, we consider here the Poisson equation posed in two distinct domains. The two are then coupled by the use of a filtration law. We show how the mixed framework is a natural setting for this problem, as it allows the two equations to be posed using global variables. Further, the applications we consider are characterized by a scale disparity between the two domains. With this in mind, we perform a physically motivated averaging of the coupling condition. This has the advantage of allowing the solution to be approximated using non-conforming, coarse meshes.