Nonlinear filtering stabilization of convection-dominated flows

The Direct Numerical Simulation (DNS) of the equations governing fluid dynamics phenomena computes the evolution of all the significant flow structures by resolving them with a properly refined computational grid. However, such an approach is unaffordable from a computational standpoint for the flow fields where the convection effects become dominant with respect to the diffusive ones because in these configurations very fine meshes are required. Therefore, the simulation of turbulent flows is performed by introducing different models. In particular, the equations can be properly averaged (quite often in time) or filtered (usually in space). In this work, we focus on the latter approach, leading to the so-called Large Eddy Simulation (LES) techniques. In this context, we consider an alpha model equipped with a nonlinear differential low-pass filter for the simulation of fluid flows at moderately large Reynolds numbers with under-refined meshes. This allows to obtain accurate numerical solutions and, at the same time, to keep under control the computational cost. We consider several test cases coming from geophysical fluid dynamics. Moreover, we will show some new outcomes related to the extension of this pipeline to a multiphysics context, involving magnetohydrodynamics.