A Discontinuous Galerkin Method is applied to unstructured grids to simulate aeroacoustic propagation, modelled by the Linearized Euler Equations. On triangular and tetrahedral elements with straight edges, the quadrature-free form of the Discontinuous Galerkin Method is used. In addition to the classical linear treatment of wall boundaries, two treatments involving a second-order representation of the geometry are presented. The simulation of acoustic scattering problems shows that the linear treatment can limit the accuracy at high order, and demonstrates how the boundary treatment involving curved elements overcomes this restriction. The benefits of higher-order treatments are also assessed for more realistic geometries, namely a high-lift airfoil and an elliptical muffler.