Time-Domain Modeling of the Acoustic Impedance of Porous Surfaces

A time-domain boundary condition (TDBC) for acoustic reflections from a rigid-frame porous material is derived. The TDBC is the time-domain counterpart of the familiar, linear, frequency-dependent surface impedance for locally reacting surfaces. Although the TDBC is developed from a rather simple, two-parameter phenomenological model, it is shown to apply to a broad range of frequencies and to agree closely with predictions from more sophisticated models that do not have readily derivable time-domain formulas. The TDBC gives the pressure as the sum of two terms involving the particle velocity normal to the surface of the material: one term is directly proportional to the particle velocity at the present time, whereas the other involves a convolution of the particle velocity with a slowly decaying response function. Numerical implementation of the TDBC is discussed and illustrated with example finite-difference, time-domain calculations involving propagation over a porous ground surface.