Improved discrete-time modeling of multi-dimensional wave propagation using the interpolated digital waveguide mesh

The digital waveguide mesh is an extension of the one-dimensional digital waveguide technique. Waveguide meshes are used for simulation of two- and three-dimensional wave propagation in musical instruments and acoustic spaces. The original waveguide mesh algorithm suffers from direction-dependent dispersion. In this paper we show that this problem may be reduced by using an interpolated rectilinear mesh. In the analysis part we show the analytical solution for the wave propagation speed and numerical simulations of the magnitude response and phase speed in both the original and the interpolated two-dimensional waveguide mesh algorithms. We demonstrate by simulation that the wave propagation characteristics of the proposed interpolated waveguide mesh are independent of direction and thus the remaining errors caused by dispersion may be corrected with a postprocessor.