# Mixed modeling for large-eddy simulation: The minimum-dissipation-Bardina-model

Streher, L. B., **Silvis**, M. H., Verstappen, R.

In: *Proceedings of the 7th European Conference on Computational Fluid Dynamics*. Ed. by Owen, R., De Borst, R., Reese, J., Pearce, C. International Center for Numerical Methods in Engineering, Barcelona, Spain, pp. 335–345 (2018).

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## Abstract

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.