Merging Filtering, Modeling and Discretization to Simulate Large Eddies In Burgers’ Turbulence

Abstract The research presented seeks to advance large-eddy simulation (LES) through the integration of its three core components - filtering, modeling and discretization. The integrated approach is developed for LES of Burgers’ turbulence in one spatial dimension, serving as an initial step toward future extensions to three-dimensional turbulent flows. Too small scales of motion 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 the cell-to-face interpolation used to evaluate fluxes on cell faces. The interpolation-induced filter sets the effective resolution of the flux and thereby determines the large eddies. The net effect of smaller scales is modeled in a way that aligns physical and numerical interpretations, treating filtering, modeling and discretization as a coherent whole. The two spatial filters partition kinetic energy into three: a subgrid part, the energy of the large eddies and that of the supergrid scales filtered-out by the cell-to-face interpolation. The latter scales do not contribute to the convective flux and 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.