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**Well-posed perfectly matched layers for advective acoustics.**
*(English)*
Zbl 0947.76076

Using a mathematical framework originally design for the development of perfectly matched layer (PML) schemes in computational electromagnetics, the authors develop a set of strongly well-posed PML equations for the absorption of acoustic and vorticity waves in two-dimensional convective acoustics under the assumption of a spatially constant mean flow. A central piece is the development of a variable transformation that conserves the dispersion relation of the physical space equations. The PML equations are given for layers being perpendicular to the direction of the mean flow as well as for layers being parallel to the mean flow. The efficacy of the PML scheme is illustrated by solving the equations of acoustics using a fourth-order scheme, confirming the accuracy as well as stability of the proposed scheme.

Reviewer: Qian Zuwen (Beijing)

### MSC:

76Q05 | Hydro- and aero-acoustics |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

### Keywords:

perfectly matched layers; absorbing boundary conditions; fourth-order scheme; strongly well-posed equations; convective acoustics; variable transformation; dispersion relation
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\textit{S. Abarbanel} et al., J. Comput. Phys. 154, No. 2, 266--283 (1999; Zbl 0947.76076)

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### References:

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