Filter stabilization for the compressible Navier Stokes equations with applications to atmosphere dynamics

This thesis is about on a stabilization technique for the compressible Euler equations with application in the atmospherical flow dynamics. Despite the computational resources available, a Direct Numerical Simulation (DNS) in the atmospherical flow simulations is still far away from our possibilities, this is not only due to the mesh size requirement in terms of storage and computational power, but this is also due to the restriction of the time step in order to respect the CFL condition. One of the remedy of this issue is the LES (Large-eddy-simulation) which is a technique that consists to simulate the large structures while the smallest are modelled by a "sub-grid model". Inspired by the LES methodology,another approach to stabilize the oscillations in the domain is the so called Evolve-Filer-Relax algorithm that is well investigated in the literature only for the incompressible flows. The main objective of this thesis is to extend the methodology to the compressible framework.In particular to test the method in the context of the atmospherical flow dynamics when the spatial scales are tens of kilometers (mesoscale modelling). The finite volume method (FVM) is employed for the space discretization while a segre- gated pressure-based solver is used for the resolution of the equations. Three different types of filters will be investigated: a Linear filter, a Smago-like and a Deconvolution-type. The three filters are tested for two different benchmark: The non linear density current and the rising thermal bubble. Numerical results confirm the selectiveness of the deconvolution-based filter while the linear is the most dissipative. All the filters compares well with the results present in literature both qualitatively and quantitatively