Higher-order impedance boundary conditions for finite difference solutions to the wave equation.

Abstract

Higher-order finite difference methods for the solution of the wave equation are well established. The interchangeability of temporal and spatial derivatives allows for exact representations of the differential equation in difference forms to the order of accuracy desired. Realistic impedance conditions, however, germane to problems of an architectural acoustics origin, are typically given as ratios of pressure and velocity in the frequency domain. This work develops fourth order-accurate time domain boundary conditions for the types of materials typically encountered in the architectural acoustics field. Accuracy and agreement of numerical simulations to scale model measurements are compared and discussed, as is computational cost relative to lower-order methods.