Assessment of a sponge layer as a non-reflective boundary treatment with highly accurate gust–airfoil interaction results

This paper deals with the numerical performance of a sponge layer as a non-reflective boundary condition. This technique is well known and widely adopted, but only recently have the reasons for a sponge failure been recognised, in analysis by Mani. For multidimensional problems, the ineffectiveness of the method is due to the self-reflections of the sponge occurring when it interacts with an oblique acoustic wave. Based on his theoretical investigations, Mani gives some useful guidelines for implementing effective sponge layers. However, in our opinion, some practical indications are still missing from the current literature. Here, an extensive numerical study of the performance of this technique is presented. Moreover, we analyse a reduced sponge implementation characterised by undamped partial differential equations for the velocity components. The main aim of this paper relies on the determination of the minimal width of the layer, as well as of the corresponding strength, required to obtain a reflection error of no more than a few per cent of that observed when solving the same problem on the same grid, but without employing the sponge layer term. For this purpose, a test case of computational aeroacoustics, the single airfoil gust response problem, has been addressed in several configurations. As a direct consequence of our investigation, we present a well documented and highly validated reference solution for the far-field acoustic intensity, a result that is not well established in the literature. Lastly, the proof of the accuracy of an algorithm for coupling sub-domains solved by the linear and non-liner Euler governing equations is given. This result is here exploited to adopt a linear-based sponge layer even in a non-linear computation.