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.

翻译：我们提出一种混合有限体积法-谱元法，基于Lighthill声学类比模拟气动声学现象。首先采用有限体积法计算流体解，然后将声源项投影至声学网格，并利用谱元法求解非齐次Lighthill波动方程。该新型投影方法通过离线计算声学网格与流体网格的交集以保持精度。所提出的交集算法被证明具有鲁棒性、可扩展性，并能高效计算任意多面体单元的几何交集。随后我们分析了投影误差的特性，证明当流体网格足够精细时，可充分发挥声学求解器的精度，并对理论估计进行数值验证。最后，我们针对两个典型气动声学基准问题——共转涡对及层流绕过方柱引起的噪声，实际展示了该投影方法在处理高阶求解器时的有效性。流体计算采用开源有限体积库OpenFOAM[46]完成，而非齐次Lighthill波动方程则通过开源谱元库SPEED[31]求解。