Wietse Boon - Ensuring local mass conservation in reduced order models for Darcy flow systems

Constructing fast solution schemes often involves deciding which errors are acceptable and which approximations can be made for the sake of computational efficiency. Herein, we consider a mixed formulation of Darcy flow in porous media and take the perspective that the physical law of mass conservation is significantly more important than the constitutive relationship, i.e. Darcy's law. From this point of view, we propose an inexact solution technique that nevertheless guarantees local mass conservation. The method is based on first solving the mass balance equation and then computing a solenoidal correction using the curl of a potential field. We extend the method to flows in fractured porous media and present numerical experiments that indicate the efficiency of the scheme.