Computational Upscaling of Inertia Effects from Porescale to Mesoscale

We propose algorithms for computational upscaling of flow from porescale (microscale) to lab scale (mesoscale). In particular, we solve Navier-Stokes equations in complex pore geometries and average their solutions to derive properties of flow relevant at lab scale such as permeability and inertia coefficients. We discuss two variants of traditional discretizations: a simple algorithm which works well in periodic isotropic media and can be used when coarse approximations are needed, and a more complex one which is well suited for nonisotropic geometries. Convergence of solutions and averaging techniques are major concerns but these can be relaxed if only mesoscopic parameters are needed. The project is a proof-of-concept computational laboratory for porous media which delivers data needed for mesoscale simulations by performing microscale computational simulations.