Implicit Turbulence Modeling for Large-Eddy Simulation

Turbulence modeling and the numerical discretization of the Navier-Stokes equations are strongly coupled in large-eddy simulations. The truncation error of common approximations for the convective terms can outweigh the effect of a physically sound subgrid-scale model. The subject of this thesis is the analysis and the control of local truncation errors in large-eddy simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic procedures, a nonlinear discretization method has been developed where numerical and turbulence-theoretical modeling are fully merged. The truncation error itself functions as an implicit turbulence model accurately representing the effects of unresolved turbulence. Various applications demonstrate the efficiency and reliability of the new method as well as the superiority of an holistic approach.

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