A homogenization approach for unsteady porous media flows approximates the memory kernel in the macroscale Darcy law as a sum of exponentials to convert the nonlocal problem into a solvable local system of differential equations.
Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems, Springer Science & Business Media
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Computational homogenization of unsteady flows in a periodic porous medium
A homogenization approach for unsteady porous media flows approximates the memory kernel in the macroscale Darcy law as a sum of exponentials to convert the nonlocal problem into a solvable local system of differential equations.