This paper focuses on the numerical modeling of the acoustic response of perforated-plate liners at high sound pressure levels in the time domain. In order to do so, a porous-based description of the perforated plate is used to represent the visco-thermal processes occurring inside the perforated plate. It is done through the use of the equivalent fluid model (EFM) containing two irrational transfer functions described herein by a generic model covering the Johnson Champoux Allard Pride Lafarge model (JCAPL), the JCAL and JCA models. The nonlinear phenomena occurring at high sound pressure levels are taken into account by using the Forchheimer's correction in the time-domain EFM, introducing a quadratic nonlinearity in the equations. The formulation of the nonlinear EFM equations in the time domain leads to an augmented system for which a proof of stability is given. From the nonlinear EFM, an approximate model is built for numerical simulations with a multipole approximation of the transfer functions. Sufficient stability conditions are provided for the nonlinear multipolebased approximate EFM. A numerical scheme using a discontinuous Galerkin method is developed to validate the model against experiments with perforated-plate liners.