  We consider a Leray model with a nonlinear differential low-pass filter for
the simulation of incompressible fluid flow at moderately large Reynolds number
(in the range of a few thousands) with under-refined meshes. For the
implementation of the model, we adopt the three-step algorithm
Evolve-Filter-Relax (EFR). The Leray model has been extensively applied within
a Finite Element (FE) framework. Here, we propose to combine the EFR algorithm
with a computationally efficient Finite Volume (FV) method. Our approach is
validated against numerical data available in the literature for the 2D flow
past a cylinder and against experimental measurements for the 3D fluid flow in
an idealized medical device, as recommended by the U.S. Food and Drug
Administration. We will show that for similar levels of mesh refinement FV and
FE methods provide significantly different results. Through our numerical
experiments, we are able to provide practical directions to tune the parameters
involved in the model. Furthermore, we are able to investigate the impact of
mesh features (element type, non-orthogonality, local refinement, and element
aspect ratio) and the discretization method for the convective term on the
agreement between numerical solutions and experimental data.
