A hybrid finite volume -- spectral element method for aeroacoustic problems

TL;DR

This paper introduces a hybrid finite volume and spectral element method for aeroacoustic modeling, combining fluid dynamics and sound wave solutions with a novel intersection algorithm for accuracy and efficiency.

Contribution

It presents a new hybrid FV-SEM approach with an innovative projection method for accurate coupling of fluid and acoustic grids in aeroacoustic simulations.

Findings

Accurate projection method for fluid-acoustic grid coupling

Robust and scalable intersection algorithm

Successful application to aeroacoustic benchmarks

Abstract

We propose a hybrid Finite Volume (FV) - Spectral Element Method (SEM) for modelling aeroacoustic phenomena based on the Lighthill's acoustic analogy. First the fluid solution is computed employing a FV method. Then, the sound source term is projected onto the acoustic grid and the inhomogeneous Lighthill's wave equation is solved employing the SEM. The novel projection method computes offline the intersections between the acoustic and the fluid grids in order to preserve the accuracy. The proposed intersection algorithm is shown to be robust, scalable and able to efficiently compute the geometric intersection of arbitrary polyhedral elements. We then analyse the properties of the projection error, showing that if the fluid grid is fine enough we are able to exploit the accuracy of the acoustic solver and we numerically assess the obtained theoretical estimates. Finally, we address two relevant aeroacoustic benchmarks, namely the corotating vortex pair and the noise induced by a laminar flow around a squared cylinder, to demonstrate in practice the effectiveness of the projection method when dealing with high order solvers. The flow computations are performed with OpenFOAM [46], an open-source finite volume library, while the inhomogeneous Lighthill's wave equation is solved with SPEED [31], an opensource spectral element library.