Numerical simulation of turbulent flows in industrial settings is often realized by Reynolds-averaged Navier-Stokes equations (RANS). These algorithms produce stationary, time-averaged solutions. On the other hand, the physical processes in industry, especially those concerning the noise generation and aero-acoustics, are time dependent. Thus, in the current project, we use Large Eddy Simulation (LES). The aero-acoustic design of industrial applications is targeted. Two different approaches are considered. The one is a fully coupled aero-acoustics simulation on the basis of a highly local space-time accurate Discontinous Galerkin scheme of high order which covers the small scale structures of the flow as well as the large scale acoustic propagation within one single simulation. The code uses local time steps as well as spatially inhomogeneous unstructured meshes. The other approach is a weakly coupled scheme, where first the turbulent flow field is calculated with a second order Finite Volume scheme on block-structured grids and a distinct acoustic simulation with the flow results as sources afterwards. The 2 approaches are compare w.r.t. to numerical and computational efficiency on the basis of industrial testcases.