  Performing geometry-resolved simulations of flows over rough and porous walls
is highly expensive due to their multiscale characteristics. Effective models
that circumvent this difficulty are often used to investigate the interaction
between the free-fluid and such complex walls. These models, by construction,
employ an intrinsic averaging process and capture only macroscopic physical
processes. However, physical experiments or direct simulations yield micro- and
macroscale information, and isolating the macroscopic effect from them is
crucial for rigorously validating the accuracy of effective models. Despite the
increasing use of effective models, this aspect received the least attention in
the literature. This paper presents an efficient averaging technique to extract
macroscopic interface data from the flowfield obtained via direct simulations
or physical experiments. The proposed methodology employs a combination of
signal processing and polynomial interpolation techniques to capture the
macroscopic information. Results from the ensemble averaging are used as the
reference to quantify the accuracy of the proposed method. Compared to the
ensemble averaging, the proposed method, while retaining accuracy, is
cost-effective for rough and porous walls. To the best of our knowledge, this
is the only averaging method that works for poroelastic walls, for which the
ensemble averaging fails. Moreover, it applies equally to viscous- and
inertia-dominated flows over irregular surfaces.

Fluid Dynamics