A Virtual Element Method for the Two-Phase Flow of Immiscible Fluids in Porous Media

A primal C0-conforming virtual element discretization for the approximation of the bidimensional two-phase flow of immiscible fluids in porous media using general polygonal meshes is discussed. This work represents a first investigation of the potentialities of the Virtual Element Method (VEM) in solving this specific complex problem involving a time-dependent coupled system of nonlinear partial differential equations. The performance of the fully discrete scheme is thoroughly analysed testing it on general meshes considering both a regular problem and more realistic benchmark problems that are of interest for physical and engineering applications.