Physical splitting of nonlinear effects in high-velocity stable flow through porous media

For a high-velocity stable flow through a periodic corrugated channel representing an element of porous medium, we suggest splitting the overall nonlinear macroscopic effects into two kinds of different physical origin: a pure inertia effect produced by the convective term of Navier-Stokes equations and an inertia-viscous cross effect representing a variation of the viscous dissipation due to a streamline deformation by inertia forces. We will show that the inertia-viscous cross effects may be revealed by simulating a periodic flow, whilst the pure inertia effects are produced by the microscale flow nonperiodicity. We will reveal the individual flow law for each nonlinear component and analyze the relative role of both components numerically by using the finite element method applied to the Navier-Stokes equations. Both the pure inertia and the inertia-viscous cross effects are revealed to be exponential prior to quadratic or cubic ones. The influence of the dead volume is analyzed. The inertia-viscous cross phenomena are shown to be negligible when the flow structure is clearly nonperiodic.