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**On the analysis and construction of perfectly matched layers for the linearized Euler equations.**
*(English)*
Zbl 0933.76063

Summary: We present a detailed analysis of a recently proposed perfectly matched layer (PML) method for the absorption of acoustic waves. The split set of equations is shown to be only weakly well-posed, and ill-posed under small low-order perturbations. This analysis provides the explanation for the stability problems associated with the split field formulation and illustrates why applying a filter has a stabilizing effect. Utilizing recent results obtained within the context of electromagnetics, we develop strongly well-posed absorbing layers for the linearized Euler equations. The schemes are shown to be perfectly absorbing independent of frequency and angle of incidence of the wave in the case of a non-convecting mean flow. In the general case of a convecting mean flow, a number of techniques is combined to obtain absorbing layers exhibiting PML-like behavior. The efficiency of the absorbing layers is illustrated through the solution of aero-acoustic benchmark problems. \(\copyright\) Academic Press.

### MSC:

76M22 | Spectral methods applied to problems in fluid mechanics |

76Q05 | Hydro- and aero-acoustics |

76N15 | Gas dynamics (general theory) |

### Keywords:

absorption of acoustic waves; split field formulation; strongly well-posed absorbing layers
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\textit{J. S. Hesthaven}, J. Comput. Phys. 142, No. 1, 129--147 (1998; Zbl 0933.76063)

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