Mathematics

This work discusses a stabilization technique for the compressible Euler equations with application in the atmospheric flow dynamics.Despite the computational resources available, a Direct Numerical Simulation (DNS) for the atmospherical flow 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 also to the restriction of the time step in order to fulfill the CFL condition.One of the remedies to these issues is the LES (Large Eddy Simulation) technique, which consists in simulating the large structures, while the smallest are modeled by a "sub-grid model".Inspired by the LES methodology, another approach to stabilize the oscillations in the domain is the Evolve-Filer-Relax algorithm (EFR) 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 atmospheric flow dynamics when the spatial scales are on the order of tens of kilometers (mesoscale flows).The collocated finite volume method (FVM) is employed for space discretization with a third order centered scheme for the convection terms. A segregated pressure-based solver is used for the pressure-velocity coupling.The characteristics of three different filter types will be analyzed: Linear, Smagorinski-like and Deconvolution-type filters.The three filters are tested on two different benchmarks: the non-linear density current and the rising thermal bubble.Numerical results confirm the selectivity of the deconvolution-based filter while the linear filter is the most dissipative.All filters give perfectly comparable results to those in the literature obtained with high-order methods.