A wavelet-based multiresolution approach to large-eddy simulation of turbulence

The wavelet-based multiresolution analysis (MRA) technique is used to develop a modelling approach to large-eddy simulation (LES) and its associated subgrid closure problem. The LES equations are derived by projecting the Navier–Stokes (N–S) equations onto a hierarchy of wavelet spaces. A numerical framework is then developed for the solution of the large and the small-scale equations. This is done in one dimension, for the Burgers equation, and in three dimensions, for the N–S problem. The proposed methodology is assessed in a priori tests on an atmospheric turbulent time series and on data from direct numerical simulation. A posteriori (dynamic) tests are also carried out for decaying and force-driven Burgers turbulence.