Advanced and high-order numerical discretization methods for large-eddy simulation that maximize subgrid-scale model resolution

We present a new family of discretization methods designed for efficient and enhanced resolution of the subgrid-scale model contribution term in the governing equations of large-eddy simulation (LES). The new numerical discretization family overcomes some of the difficulties experienced in LES where very high-order of accuracy or extreme cutoff-to-grid resolution separation is required to achieve convergence of the turbulence statistics. The new method employs bilinear stencils of high-order of accuracy, but with compact or narrow-band support, to discretize second-order derivatives with variable coefficients, such as those present in the Smagorinsky model; with fixed or dynamic coefficient. The new method is discretely conservative, preserves invariance properties of second-order elliptic operators, and it is optimized for bandwidth resolution. Actual LES results of homogeneous turbulence at high Reynolds numbers confirm that the error in the statistics can be made extremely small with the new discretization. In addition, the extension of the discretization approach to wall-bounded flows will be discussed and their performance in high-order stress closures will be presented.