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We numerically analyse fluid flow through porous media up to a limiting Reynolds number of mathcal{O}(10³). Due to inertial effects, such processes exhibit a gradual transition from laminar to turbulent flow for increasing magnitudes of Re. On the macroscopic scale, inertial transition implies non-linearities in the relationship between the effective macroscopic pressure gradient and the filter velocity, typically accounted for in terms of the quadratic Forchheimer equation. However, various inertia-based extensions to the linear Darcy equation have been discussed in the literature - most prominently cubic polynomials in velocity. The numerical results presented in this contribution indicate that inertial transition, as observed in the apparent permeability, hydraulic tortuosity and interfacial drag, is inherently of sigmoidal shape. Based on this observation we derive a novel filtration law which is consistent with Darcy's law at small Re, reproduces Forchheimer's law at large Re and exhibits higher order leading terms in the weak-inertia regime.