On the non-linear behavior of a laminar single-phase flow through two and three-dimensional porous media

By M. Fourar, G. Radilla, R. Lenormand, C. Moyne. 2004

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Comparison of Quadratic and Power Law for Nonlinear Flow through Porous Media (2008, background): “In addition to the two empirical laws, a cubic law (see Fourar et al. 2004) has been also applied for describing the onset of the non-linear behaviour.”
Effects of image resolution and numerical resolution on computed permeability of consolidated packing using LB and FEM pore-scale simulations (2013, background): “Some notable studies have considered relatively simple 2D geometries, or simple configurations of spherical particles in 3D [45,46].”
Determination of Forchheimer equation coefficients a and b (2007, methodology): “Anyway, all three inertia-related mechanisms cited above by Skjetne and Auriault (1999), Panfilov et al. (2003) and Fourar et al. (2004) are related to the formation of boundary layer separation and recirculation eddies; thus, the basic statements of the present study persist: 1.”
Modeling Turbulent Flows in Porous Media (2020, background): “…valid for sufficiently high Rep) for predicting the Kolmogorov length and velocity scales as power-law functions of Rep. Two-dimensional (2D) flows are not addressed in this review because of the substantial differences in the characteristics of 2D and 3D flows (Fourar et al. 2004, Spalart 2015).”