Analysis and optimization of numerical sponge layers as a nonreflective boundary treatment

The aim of this work is to provide practical guidelines for designing sponge layers considering applications in computational fluid dynamics and computational aeroacoustics. We present the analysis of sponge/flow interactions and provide a characterization of its basic reflectivity mechanisms. While sponges are perfect absorbers in one-dimensional systems, they can cause their own reflection when encountering oblique sound or oblique vorticity waves. To minimize this adverse effect, sponge strength and profile need to be selected optimally. Also for a fixed desired accuracy, sponge length should be above a minimum threshold. Our analysis quantifies these requirements for a wide range of conditions in terms of inflow/outflow Mach number, incident frequencies, incident angles, and desired accuracy, and covers main concerns with sponges such as sound/sponge interactions and vortex/sponge interactions. As a test case, we present a nonlinear Euler calculation of a convecting vortex interacting with sponges with different lengths. We show that sponges designed by our guidelines achieve accuracies comparable to perfectly matched layers for the same cost, over moderate to high accuracy demands. The results of the presented analysis can be used to determine sponge requirements for a wide range of CFD applications. A summary of these guidelines are listed in the paper.