The 1998 Summer Program contained seven projects in LES involving fifteen scientists. The interest in LES continues to grow, and the findings from the Summer Programs have found increased utility in setting the direction for research in LES. The project by Carati and Rogers was the first application of the `Ensemble Averaged LES' concept developed at the 1996 Summer Program to an inhomogeneous flow, the time evolving plane wake. In this procedure, one executes several realizations of a turbulent flow on the same number of computer processors simultaneously. Thus, at each time step the ensemble averaged field is available, which could be used in parameterization of the subgrid scale stresses. Such parameterization can lead to improved and economical models as well as being useful for building a bridge between LES and Reynolds averaged approach, RANS. As with homogeneous flows, it appears that only about sixteen realizations are sufficient. Interestingly, the three models tested led to similar results for low order turbulence statistics which were in good agreement with the DNS data. One of the important and relatively unattended areas for research in subgrid scale modeling is for high speed compressible flows. The LES equations contain several terms without counterparts in incompressible flows. Adams et al used DNS data of a M=3 compression corner with a shock to compute and evaluate the relative importance of the subgrid scale terms. In addition, as with numerous other studies, they demonstrated that scale similarity type models perform better in a priori tests. An important issue addressed in this report is the treatment of shock wave as a subgrid scale entity. A new and very promising approach for subgrid scale modeling, in general, and for the treatment of shocks, in particular, was introduced. This is an algorithmic procedure, as opposed to phenomenological modeling, which uses regularized deconvolution of the velocity field to estimate the unfiltered flow field. If this methodology turns out to be robust, especially when applied to high Reynolds number flows, it will have far reaching consequences in the development of modern LES in the years to come. The deconvolution strategy is very similar to Domaradzki's subgrid scale estimation model and is also related to Leonard's (AIAA Paper 97-0204) estimate of the filtered advection term in the Navier Stokes equations. Domaradzki's approach, which was extended to compressible turbulence during the Summer Program, appears to be a bit more involved than the deconvolution approach and has an adjustable model parameter, but its results appear to be equally impressive. Like the scale similarity models, the estimation model yields high correlations with the DNS data and, additionally, appears to provide correct level of subgrid scale dissipation which the scale similarity models tend to be incapable of. Winckelmans et. al conducted a thorough evaluation of Leonard's model in both the isotropic decay problem and turbulent channel flow. It was quickly discovered that the model does not provide sufficient dissipation, and hence the Smagorinsky model was added to the model. The model coefficient was computed using the dynamic procedure, which is now much better behaved in terms of lower variability in space and positive values. The principal deficiency of the Leonard model without the Smagorinsky component is manifested in incorrect distribution in the energy spectrum. Another improved feature of the Leonard model is the higher values of subgrid scale shear stress near walls. Cottet & Vasilyev implemented an integral formulation of Leonard's model. This formulation allows for a simple method to distinguish forward and backscatter of energy and allows for a more rigorous control of backscatter, which is essential for stabilization of the computations. Apparently, the backscatter control feature is the reason for not requiring additional dissipation through added Smagorinsky model or other means. An important pacing item for application of LES to complex flows is the resolution of the wall layer. For high Reynolds number attached boundary layers, the resolution of the wall layer is too demanding of computer resources, and development of lower dimensional modeling approaches for this region is an active area of research in LES. The wall modeling problem is divided into two parts: the actual modeling of the wall layer by a lower dimensional dynamic system, and the transfer of the appropriate information to the outer layer LES. In an attempt to focus on the mathematical boundary condition aspect of the problem and to avoid the particular complications of the wall region, Jiménez and Vasco considered a novel simulation of a channel half by prescribing boundary conditions on the centerline. They confirmed the earlier results by Baggett and the previous experience from the prescription of inflow conditions in LES, that prescription of random fluctuations, even with correct second order statistics, is inadequate as boundary conditions. They attribute the difficulty to large pressure fluctuations at the boundary which induce artificial energy fluxes across it. Nicoud et al. use the scaled velocity field at an interior plane in LES of channel flow to supply turbulence structures at the boundary. A dynamic procedure was developed to relate the time scales of the velocity in the interior plane and at the boundary. The ratio of the two time scales appear to be near one rather than that deduced from the log layer scaling. The results are encouraging, but further refinements are needed.