Different strategies regarding the simulation of sound generation and propagation are explored. A hydrodynamic/acoustic splitting method for computational aeroacoustics in low Mach number flows with variable density, temperature gradients and heat conduction is described. The resulting equations can be formulated as linearized Euler equations plus source terms and reduce to the linear acoustic wave equation, if convection speeds can be neglected. In contrast, a direct approach based on the coupling of different grids, time steps and equations allows a simulation of both flow and acoustics in one single calculation. For acoustic domains, the ADER discontinuous Galerkin and the conforming face finite element discretizations are efficient high order methods for unstructured grids. The proposed methods are validated and applied to complex test cases such as the simulation of an aero-engine inlet and the scattering of sound waves at a solid sphere.