Large-Eddy Simulation: A Synthesis of Filtering, Modeling, and Discretization

Large Eddy Simulation (LES) is conceptualized as a synthesis of filtering, modeling, and discretization. Small-scale motions are removed by applying conservation laws over control volumes of user-defined size, establishing the computational grid. Two spatial filters emerge: one from grid-cell averaging and another from interpolating fluxes at cell faces. The interpolation filter defines the large eddies, while a model captures the net effect of smaller scales. This model bridges physical and numerical interpretations which converge when filtering, modeling, and discretization are treated coherently (constitute a unified methodological approach). To separate large eddies, the model must disrupt the nonlinear coupling across scales. The two filters partition kinetic energy into three: the subgrid part, the large-eddy part, and the part associated with supergrid scales filtered-out by cell-to-face interpolation. The latter scales are subordinate to the large eddies, while subgrid scales are truncated by the grid, simplifying modeling. The model ensures that large eddies do not generate smaller scales, with consistency enhanced via Richardson extrapolation. The approach is validated on 1D decaying Burgers' turbulence and provides a foundation for future LES of 3D turbulent flows.