Large-Eddy Simulation of the Navier-Stokes Equations: Deconvolution, Particle Methods, and Super-Resolution

The technique of large-eddy simulation (LES) continues to play an important role in the numerical simulation of fluid dynamic processes in engineering and scientific applications. This paper will review and discuss a few of the various schemes for LES applied to the incompressible Navier-Stokes equations and to the scalar advection-diffusion equation. In particular, subgrid models based on deconvolution will be discussed. An interesting connection between the tensor diffusivity model, a particular version of a deconvolution model, and Lagrangian particle methods for the vorticity transport equation and for the scalar convection-diffusion equation will be explored. In addition, the possibility of using super-resolution, i.e. recovering fine-scale information knowing only coarse-scale information, in LES will be investigated.