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 two-dimensional slices of a three-dimensional 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
- NSF-PAR ID:
- 10369381
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Mathematische Annalen
- Volume:
- 385
- Issue:
- 3-4
- ISSN:
- 0025-5831
- Page Range / eLocation ID:
- p. 1797-1821
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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