  The Navier-Stokes equations describe the motion of viscous fluids. In order
to predict turbulent flows with reasonable computational time and accuracy,
these equations are spatially filtered according to the large-eddy simulation
(LES) approach. The current work applies a volume filtering procedure according
to Schumann (1975). To demonstrate the procedure the Schumann filter is first
applied to a convection-diffusion equation. The Schumann filter results in
volume-averaged equations, which are not closed. To close these equations a
model is introduced, which represents the interaction between the resolved
scales and the small subgrid scales. Here, the anisotropic minimum-dissipation
model of Rozema et al. (2015) is considered. The interpolation scheme necessary
to evaluate the convective flux at the cell faces can be viewed as a second
filter. Thus, the convection term of the filtered convection-diffusion equation
can be interpreted as a double-filtered term. This term is approximated by the
scale similarity model of Bardina et al. (1983). Thus, a mixed
minimum-dissipation-Bardina model is obtained. Secondly, the mathematical
methodology is extended to the Navier-Stokes equations. Here, the pressure term
is analyzed separately and added to the convection-diffusion equation as a sink
term. Finally, spatially filtered Navier-Stokes equations that depend on both
the anisotropic minimum-dissipation (AMD) model proposed by Rozema et al.
(2015) and the scale similarity model of Bardina et al. (1983) are obtained.
Hence, a mathematically consistent method of mixing the AMD model and the
Bardina model is achieved.
