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ABSTRACT Numerical stabilization techniques are often employed in under‐resolved simulations of convection‐dominated flows to improve accuracy and mitigate spurious oscillations. Specifically, the evolve–filter–relax (EFR) algorithm is a framework that consists of evolving the solution, applying a filtering step to remove high‐frequency noise, and relaxing through a convex combination of filtered and original solutions. The stability and accuracy of the EFR solution strongly depend on two parameters, the filter radius and the relaxation parameter . Standard choices for these parameters are usually fixed in time, and related to the full order model setting, that is, the grid size for and the time step for . The key novelties with respect to the standard EFR approach are: (i) time‐dependent parameters and , and (ii) data‐driven adaptive optimization of the parameters in time, considering a fully‐resolved simulation as reference. In particular, we propose three different classes of optimized‐EFR (Opt‐EFR) strategies, aiming to optimize one or both parameters. The new Opt‐EFR strategies are tested in the under‐resolved simulation of a turbulent flow past a cylinder at . The Opt‐EFR proved to be more accurate than standard approaches by up to 99, while maintaining a similar computational time. In particular, the key new finding of our analysis is that such accuracy can be obtained only if the optimized objective function includes: (i) aglobalmetric (as the kinetic energy), and (ii)spatial gradients' information. 

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.