Seepage equation and relative resistance scaling law considering high Reynolds number flow in porous media

Based on the volume averaging method, the local linearized macroscopic flow equation in porous media with inertia effect is derived, and the solution of Navier-Stokes equation with large Re can be obtained recursively, thus avoiding the problems of high computational cost and poor computational stability caused by solving Navier-Stokes equation directly. An example of a square periodic array model shows that the average velocity direction is not always consistent with the direction of the macroscopic pressure gradient.