In the present work, we are interested in the direct numerical simulation of the compressible Euler and Navier Stokes equations at low Mach number regime. First, we propose a review of existing work on the subject in order to identify the issues raised by the simulation of in this kind of flow, and the existing relevant solutions. Then, we will test different selected compressible low Mach solvers using the discontinuous Galerkin space discretisation and discuss about their behaviour.