Time-domain impedance boundary conditions for liners that are not based on parameter fitting continue to pose a significant numerical challenge in computational aeroacoustics. This work presents a superposition-based time-domain impedance boundary condition for acoustic liners, including multiple-degree-of-freedom designs and acoustic metamaterials. Three discrete convolution formulations are examined: one using an admittance transfer function, and two using a reflection coefficient transfer function, applied explicitly and implicitly. The study is carried out in one dimension, and the accuracy of each method is assessed by simulating the interaction between an acoustic wave and a liner. Results for a single-degree-of-freedom analytical liner show agreement with frequency-domain benchmark solutions, demonstrating the accuracy of the method. The approach is then extended to two non-analytical realistic liner configurations by reconstructing the required transfer-function data from numerical impedance tube simulations. The framework is applied to both configurations and exhibits consistent behaviour across all three formulations. The findings support the use of this approach for broadband, non-linear, and experimentally derived impedance models. ... Read more