Large Eddy Simulation of Engineering and Geophysical Turbulent Flows

Large Eddy Simulation (LES) is one of the most successful approaches in the numerical simulation of turbulent flows. LES aims at approximating the large structures in the flow, while modeling the effect of the small structures which are not captured on the numerical mesh.

This introductory talk will present some of the achievements and challenges in LES of engineering and geophysical applications.
In particular, we will focus on the closure problem and the boundary conditions in LES.

First, we will present a rigorous numerical analysis for a bounded artificial viscosity model for the numerical simulation of turbulent flows. In practice, the commonly used Smagorinsky model is overly dissipative, and yields unphysical results. To date, several methods for ``clipping'' the Smagorinsky viscosity have proved useful in improving the physical characteristics of the simulated flow. However, such heuristic strategies rely strongly upon a priori knowledge of the flow regime. The bounded artificial viscosity model relies on a highly nonlinear, but monotone and smooth, semilinear elliptic form for the artificial viscosity.
For such a bounded model, we have introduced a variational computational strategy, provided finite element error convergence estimates, and included several computational examples indicating its improvement over the overly diffusive Smagorinsky model.

Second, we will introduce new boundary conditions for LES based on approximate deconvolution. An advantage of these Approximate Deconvolution Boundary Conditions (ADBC) is that they are suited for turbulent flows with time-dependent boundary conditions. One such application is flow control, where for example, blowing and suction on the surface of an airfoil can be used to reduce the skin-friction drag. Note that current LES boundary conditions are not up to this task: they either lead to a prohibitively high computational cost or need boundary layer theory which might not be available. Our new boundary conditions avoid these two roadblocks - they are efficient and general.