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The Navier-Stokes equations describe the motion of viscous fluids. In orderto 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 accordingto Schumann (1975). To demonstrate the procedure the Schumann filter is firstapplied to a convection-diffusion equation. The Schumann filter results involume-averaged equations, which are not closed. To close these equations amodel is introduced, which represents the interaction between the resolvedscales and the small subgrid scales. Here, the anisotropic minimum-dissipationmodel of Rozema et al. (2015) is considered. The interpolation scheme necessaryto evaluate the convective flux at the cell faces can be viewed as a secondfilter. Thus, the convection term of the filtered convection-diffusion equationcan be interpreted as a double-filtered term. This term is approximated by thescale similarity model of Bardina et al. (1983). Thus, a mixedminimum-dissipation-Bardina model is obtained. Secondly, the mathematicalmethodology is extended to the Navier-Stokes equations. Here, the pressure termis analyzed separately and added to the convection-diffusion equation as a sinkterm. Finally, spatially filtered Navier-Stokes equations that depend on boththe 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 theBardina model is achieved.

Mixed modeling for large-eddy simulation: the minimum-dissipation-bardina model