A High Order Discontinuous Galerkin Spectral Element Solver for the Lighthill’s Wave Equation

We propose a high fidelity solver based on hybrid Finite Volume (FV) - Discontinuous Galerkin Spectral Element Method (DGSEM) for solving the Lighthill's acoustic wave equation that models aeroacoustic problems. The flow solution is firstly computed by employing a FV method. The noise source term is then projected onto the acoustic space. We finally solve the inhomogeneous acoustic Lighthill's wave equation to predict the aeroacoustic noise propagation by employing a DGSEM solver. The aim of this work is to show the discretization flexibility introduced by the DG strategy and the high accuracy provided by the SEM when solving aeroacoustic problems featuring complex geometries. The DGSEM discretization simplifies the meshing strategy for the user, granting the flexibility of non conformal methods while preserving the high order accuracy. We validate the introduced hybrid aeroacoustic solver by computing the noise generated by a laminar flow around a circular cylinder. Then, we address the problem of the noise generated by a side view mirror, where we fully exploit the flexibility allowed by the DGSEM strategy.