Using extensive numerical simulation of the Navier–Stokes equations, we study the transition from the Darcy’s law for slow flow of fluids through a disordered porous medium to the nonlinear flow regime in which the effect of inertia cannot be neglected. The porous medium is represented by twodimensional slices of a threedimensional image of a sandstone. We study the problem over wide ranges of porosity and the Reynolds number, as well as two types of boundary conditions, and compute essential features of fluid flow, namely, the strength of the vorticity, the effective permeability of the pore space, the frictional drag, and the relationship between the macroscopic pressure gradient
It has been recently established in David and Mayboroda (Approximation of green functions and domains with uniformly rectifiable boundaries of all dimensions.
 Award ID(s):
 1839077
 NSFPAR ID:
 10369381
 Publisher / Repository:
 Springer Science + Business Media
 Date Published:
 Journal Name:
 Mathematische Annalen
 Volume:
 385
 Issue:
 34
 ISSN:
 00255831
 Page Range / eLocation ID:
 p. 17971821
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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