Nonlinear corrections to Darcy's law at low Reynolds numbers

By M. Firdaouss, Jean-Luc Guermond, P. Quéré. 1997

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Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data (2019, background): “It has been shown both theoretically [74] and experimentally [75, 76] that the constitutive relation undergoes”
Continuous dependence and decay for the Forchheimer equations (2003, background): “1) are given by Firdaouss et al. (1997), Giorgi (1997) and Whitaker (1996) (see also Nield & Bejan 1999).”
On the non-linear behavior of a laminar single-phase flow through two and three-dimensional porous media (2004, result): “[21] showed that these experiments are qualitatively in accordance with the cubic law.”
Navier–Stokes/Forchheimer models for filtration through porous media (2013, background): “Detailed discussions about their physical interpretation can be found in [23,43].”
Existence of global attractors for the three‐dimensional Brinkman–Forchheimer equation (2008, methodology): “Actually, to obtain the H2( )-energy equation, we need to take the inner product of Equation (1) with 2u in L2( ).”