Enhanced Numerical Equivalent Acoustic Material (eNEAM): Analytical and Numerical Framework for Porous Media with Thermo-Viscous Effects for Time Domain Simulations

Accurate prediction of sound propagation in porous and dissipative media remains challenging when classical models struggle to capture the microscopic material characteristics. This work introduces the Enhanced Numerical Equivalent Acoustic Material (eNEAM) framework, extending the original NEAM formulation by combining analytical and numerical approaches. The analytical formulation provides closed-form expressions for effective impedance, complex wavenumber, and absorption coefficient under normal incidence, with and without thermo-viscous effects, enabling a direct validation against impedance-tube data and efficient initialization of finite-difference time-domain (FDTD) simulations. A parameter optimization strategy, focused on the thermolabile coefficient (ΨB), significantly improves low-frequency absorption predictions. Robustness studies reveal that even substantial variations in model parameters generally remain within an optimal ±10% range. Additionally, a comparison between models with and without thermo-viscous losses was performed and shows that differences are negligible at macroscopic scales, which can be useful to reduce computational costs. Following computational time reduction, the adaptive mesh refinement technique employed also reduces time costs by over 50% in 1-D FDTD simulations, even without GPU acceleration. Taken together, these developments demonstrate that eNEAM provides a versatile, accurate, and computationally efficient framework for modeling porous materials, bridging experimental characterization, analytical formulations, and numerical simulations while maintaining robustness against parameter variations.