In this work modifications for the aeroacoustic solver NoisSol are presented. This code applies the high order ADER-Discontinuous Galerkin scheme for the solution of linearized acoustic equations in inhomogeneous mean flow conditions. At first, the problems, that can arise under certain mean flow conditions, are discussed. Then different approaches are shown to solve those problems. These include variable Jacobi matrices, the so called Taylor-DG time integration method and a modified surface integration based on a nodal data basis. In the last part some results are shown. These include a convergence test to show the operability of the modified schemes and a Single Cylinder Scattering test case with an inhomogeneous background flow to show the potential of the new schemes.