A multiscale mixed finite element method applied to the simulation of two-phase flows

The multiscale hybrid mixed finite element method (MHM-H(div)), previously developed for Darcy’s problems, is extended coupled flow/pressure and transport system of two-phase flow equations on heterogeneous media under the effect gravitational segregation. It combined with an implicit solver in a sequential fully (SFI) manner. MHM-H(div) designed to cope complex geometry inherent nature phenomena. discretizations are based general domain partition formed by polyhedral subregions, where hierarchy meshes approximation spaces considered. approach applied flux/pressure kernel making use coarse scale normal fluxes between subregions (trace variable). fine-scale features inside each subregion determined resolving completely independent local Neumann boundary conditions being set trace variable, using fine flux pressure representations. These properties imply that can be interpreted as classical formulation model problem whole domain, H(div)-conforming space components over macro-partition interfaces constrained space, showing divergence compatibility space. Consequently, mass conservation observed at micro-scale elements essential property flows media, divergence-free constraint strongly enforced incompressible flows. efficient static condensation leads global solved only terms primary degrees freedom associated variable piecewise constant subregion. This procedure allows substantial reduction dominant computational costs embedded numerical model. An iterative coupling technique adopted solve shared integration point memory implementation At SFI time step, efficiency improved Quasi-Newton simple but effective nonlinear acceleration. examples show proposed scheme able challenging problems.