  We review models for unsteady porous media flow in the volume-averaging
framework and we discuss the theoretical relations between the models and the
definition of the model coefficients (and the uncertainty therein). The
different models are compared against direct numerical simulations of
oscillatory flow through a hexagonal sphere pack. The model constants are
determined based on their definition in terms of the Stokes flow, the potential
flow and steady nonlinear flow. Thus, the discrepancies between the model
predictions and the simulation data can be attributed to shortcomings of the
models' parametrisation.
  We found that an extension of the dynamic permeability model of Pride et al.
[Physical Review B 47(9), 1993] with a Forchheimer-type nonlinearity performs
very well for linear flow and for nonlinear flow at low and medium frequencies,
but the Forchheimer term with a coefficient obtained from the steady-state
overpredicts the nonlinear drag at high frequencies. The model reduces to the
unsteady Forchheimer equation with an acceleration coefficient based on the
static viscous tortuosity for low frequencies.
  The unsteady Forchheimer equation with an acceleration coefficient based on
the high frequency limit of the dynamic tortuosity has large errors for linear
flow at medium and high frequencies, but low errors for nonlinear flow at all
frequencies. This is explained by an error cancellation between the inertial
and the nonlinear drag.
