The use of a Discontinuous Galerkin framework to perform a compressible Large Eddy Simulation is an effective and accurate way to simulate complex turbulent flows. However, since the turbulent scales size is not known a priori, assumptions during the grid generation must be made. With the aim of reducing the influence of such assumptions, lowering the computational effort required to perform the LES and moving towards the adaptive LES postulated by Pope, New J Phys, 6(1):35, 2004, , we introduced a polynomial adaptive framework in Tugnoli, J Comput Phys, 349:33–58, 2017, . In the present work we employ the aforementioned procedure to assess the effects of a varying Mach number in a flow around a square section cylinder, a configuration of interest for example for flame holders in combustors. Since most of the reference data on this kind of flows is obtained by incompressible computations (e.g. Rodi et al, J Fluids Eng, 119(2):248–262, 1997, ) and experiments (e.g. Lyn et al, J Fluid Mech, 304:285–319, 1995, ) the aim is to assess what are the effects of slightly higher Mach numbers in such flows, and what is the error involved into comparing compressible simulations results with incompressible reference data.
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