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A time domain boundary element method for acoustic scattering by lined surfaces in a subsonic uniform mean flow

A time domain boundary integral equation with Burton-Miller reformulation is presented for acoustic scattering by surfaces with liners in a uniform mean flow. The Ingard-Myers impedance boundary condition is implemented using a broadband multipole impedance model which is in turn converted into time domain differential equations to augment the boundary integral equation. The coupled integral-differential equations are solved numerically by a March-On-in-Time (MOT) scheme. While the Ingard-Myers condition is known to support Kelvin-Helmholtz instability due to its use of a vortex sheet interface between the flow and the lined surface, it is found that by neglecting a second-order derivative term in the current time domain impedance boundary condition formulation, the instability can be effectively avoided in computation. Proposed formulation and implementation are validated with numerical examples. Moreover, a minimization procedure for finding the poles and coefficients of the broadband multiple impedance expansion is formulated by which, unlike the commonly used vector-fitting method, passivity of the model is ensured. Numerical tests show the proposed minimization approach is effective for modeling liners that are commonly used in aeroacoustic applications.