  We present a filter stabilization technique for the mildly compressible Euler
equations that relies on a linear or nonlinear indicator function to identify
the regions of the domain where artificial viscosity is needed and determine
its amount. For the realization of this technique, we adopt a three step
algorithm called Evolve-Filter-Relax (EFR), which at every time step evolves
the solution (i.e., solves the Euler equations on a coarse mesh), then filters
the computed solution, and finally performs a relaxation step to combine the
filtered and non-filtered solutions. We show that the EFR algorithm is
equivalent to an eddy-viscosity model in Large Eddy Simulation. Three indicator
functions are considered: a constant function (leading to a linear filter), a
function proportional to the norm of the velocity gradient (recovering a
Smagorinsky-like model), and a function based on approximate deconvolution
operators. Through well-known benchmarks for atmospheric flow, we show that the
deconvolution-based filter yields stable solutions that are much less
dissipative than the linear filter and the Samgorinsky-like model and we
highlight the efficiency of the EFR algorithm.
