Multiscale computation of pore-scale fluid dynamics: Single-phase flow

Direct numerical simulation (DNS) of interstitial fluid dynamics in porous media is hindered by the sheer size and complexity of the discretized equations. While reduced-complexity methods such as pore-network models (PNM) can occasionally yield satisfactory solutions at a much lower cost, they can neither estimate nor control their error. We focus on the single-phase Navier–Stokes equations and develop a computationally efficient multiscale method that produces a sequence of increasingly accurate approximations to DNS. The pore-level multiscale method (PLMM) decomposes the pore space into several subdomains and constructs a set of local basis functions on them. The bases are coupled with a global interface problem to obtain an initial approximation to DNS. The approximation is excellent because subdomains coincide with physical pores in the void space and physics-informed boundary conditions are used to construct the bases. Errors in the initial approximation can be arbitrarily reduced with an iterative strategy presented. The method is parallelizable, memory efficient, and allows for different physics, models, and meshes to be incorporated within each subdomain.