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Within OpenFOAM, we develop a pressure-based solver for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations are used to describe non-hydrostatic atmospheric flow. For the stabilization of the Euler equations and to capture sub-grid processes, we consider two Large Eddy Simulation models: the classical Smagorinsky model and the one equation eddy-viscosity model. To achieve high computational efficiency, our solver uses a splitting scheme that decouples the computation of each variable. The numerical results obtained with our solver are validated against numerical data available in the literature for two classical benchmarks: the rising thermal bubble and the density current. Through qualitative and quantitative comparisons, we show that our approach is accurate. This paper is meant to lay the foundation for a new open-source package specifically created for the quick assessment of new computational approaches for the simulation of atmospheric flows at the mesoscale level. 

Abstract This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition, and manifold interpolation, the proposed approach allows to accurately recover field solutions from a few large-scale simulations. Numerical experiments for the Rayleigh-Bénard cavity problem show the effectiveness of such multi-step procedure in two parametric regimes, i.e., medium and high Grashof number. The latter regime is particularly challenging as it nears the onset of turbulent and chaotic behavior. A major advantage of the proposed method in the context of time-periodic solutions is the ability to recover frequencies that are not present in the sampled data.