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Computational Constrains on Large Eddy Simulation of Inhomogeneous Turbulent Complex Geometry Flows

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This paper presents a systematic approach for large eddy simulation to be consistent, i.e. to satisfy all the assumptions used in the derivation of the LES equations. We demonstrated that a solution, consistent with the true filtered Navier-Stokes equations, can be achieved by means of explicit filtering. We have shown that explicit filtering not only provides the means for both assessing and minimizing the effects of numerical error in practical simulations, but also allows the filter shape and size to be chosen independently of the computational mesh. Having the ability to control the filter shape opens whole new horizons in LES modelling, since it makes it feasible to look at SGS modelling and filtering as one inseparable issue. The success of explicit filtering strongly depends on the ability to construct discrete filters that commute with differentiation. We have described the general theory of construction of such filters and developed a tool for assessing the local spectrum of the commutation error. Although tremendous progress has recently been made in the development of the explicit filtering approach, a lot of fundamental research needs to be done before researchers and engineers can take full advantage of this new mathematical tool. Among the issues which definitely need to be addressed in the near future are the development of the SGS models that correspond to specific filters and their subsequent verification with experimental and DNS results.

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  • Fluid Mechanics

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