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The acoustic black-hole (ABH) effect is a well-known way of controlling structural vibrations in solid beams and plates. The theory behind this effect is to reduce the velocity of waves by altering the physical properties of the domain according to a power-law profile. For an ideal ABH, this leads to vanishing reflections from the end of the termination. In practice, there will be a truncation in the profile, which leads to some reflections. A well-known way of minimizing this truncation error is to add damping material to the end of the ABH termination.

For a waveguide embedding a set of rings with retarding inner radius according to a power-law profile, the velocity of sound waves tends to zero. However, unlike the structural counterpart, experimental results in the literature show that adding damping material to reduce the truncation error is not effective for waveguides. Here, we present a finite element simulation of the considered cylindrical setup. Our results confirm that the addition of damping material to the end of the waveguide is ineffective while suggesting that the local absorption effects at the lateral surface of the cylinder are a primary source of damping to achieve the ABH effect.