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We present a filter stabilization technique for the mildly compressible Eulerequations that relies on a linear or nonlinear indicator function to identifythe regions of the domain where artificial viscosity is needed and determineits amount. For the realization of this technique, we adopt a three stepalgorithm called Evolve-Filter-Relax (EFR), which at every time step evolvesthe solution (i.e., solves the Euler equations on a coarse mesh), then filtersthe computed solution, and finally performs a relaxation step to combine thefiltered and non-filtered solutions. We show that the EFR algorithm isequivalent to an eddy-viscosity model in Large Eddy Simulation. Three indicatorfunctions are considered: a constant function (leading to a linear filter), afunction proportional to the norm of the velocity gradient (recovering aSmagorinsky-like model), and a function based on approximate deconvolutionoperators. Through well-known benchmarks for atmospheric flow, we show that thedeconvolution-based filter yields stable solutions that are much lessdissipative than the linear filter and the Samgorinsky-like model and wehighlight the efficiency of the EFR algorithm.

Filter stabilization for the mildly compressible Euler equations with application to atmosphere dynamics simulations