Validation of a Discontinuous Galerkin Implementation of the Time-Domain Linearized Navier–Stokes Equations for Aeroacoustics

The propagation of small perturbations in complex geometries can involve hydrodynamic-acoustic interactions, coupling acoustic waves and vortical modes. A propagation model, based on the linearized Navier–Stokes equations, is proposed. It includes the mechanism responsible for the generation of vorticity associated with the hydrodynamic modes. The linearized Navier–Stokes equations are discretized in space using a discontinuous Galerkin formulation for unstructured grids. Explicit time integration and non-reflecting boundary conditions are described. The linearized Navier–Stokes (LNS) model is applied to two test cases. The first one is the time-harmonic source line in an incompressible inviscid two-dimensional mean shear flow in an infinite domain. It is shown that the proposed model is able to capture the trailing vorticity field developing behind the mass source and to represent the redistribution of the vorticity. The second test case deals with the analysis of the acoustic propagation of an incoming perturbation inside a circular duct with a sudden area expansion in the presence of a mean flow and the evaluation of its scattering matrix. The computed coefficients of the scattering matrix are compared to experimental data for three different Mach numbers of the mean flow, M0 = 0.08, 0.19 and 0.29. The good agreement with the experimental data shows that the proposed method is suitable for characterizing the acoustic behavior of this kind of network.