Multiscale formulation of two-phase flow at the pore scale

Direct numerical simulation (DNS) of multiphase flow yields the highest fidelity predictions of pore-scale fluid dynamics in porous media. The drawback of DNS is its high computational cost. We develop a pore-level multiscale method (PLMM) that accelerates DNS by producing successively improved approximations to the immiscible two-phase Navier-Stokes equations. PLMM starts with a binary image of the porous medium and decomposes the void space into subdomains that coincide with physical pores. For each subdomain, single-phase basis functions are constructed once. Correction functions are then computed only for subdomains containing a fluid-fluid interface. Basis and correction functions are coupled through a global problem, which yields an accurate velocity field used to propagate interfaces. By treating two-phase dynamics as local perturbations to single-phase flow, PLMM adaptively localizes computations to the displacement front. Prediction errors are additionally estimated and controlled with an iterative strategy. PLMM is parallelizable and allows for different meshes, models, and physics in each subdomain.