The efficiency of time-domain acoustic simulations is improved immensely if the degrees of freedom imparted by the spatial discretization are reduced. Time-stable model order reduction strategies achieve this by ensuring that frequency-domain system realizations transform in a physical manner after reduction. Frequency dependent damping matrices add to the challenge and require additional consideration. Handling the associated boundary condition imposition in the time domain is one way to approach the problem. Convolution complicates this strategy but the obstacle can be surmounted using a recursive formulation. This work proposes such a method, combining Krylov subspace projection based model order reduction with an efficient time domain-impedance boundary condition implementation. The mass and stiffness matrices are frequency independent and reduced using a second-order Arnoldi algorithm. As Arnoldi iterations implicitly match the moments of the system transfer function, the complex damping matrix must still be contended with. Discussion is included on when reduced order, time-domain, simulations bear fruit. Comparison with full-order time and frequency-domain calculations demonstrate the effectiveness of the proposed algorithms with system degrees of freedom decreased from NDOF= 13125 to RDOF= 63, and simulation time reductions of 9197%.
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