Digital waveguide mesh models have provided an accurate and efficient method of modelling the properties of many resonant structures, including acoustic spaces. 2-D rectilinear and triangular mesh structures have been used extensively in the past to model plates and membranes and are presented here as potential analogues to 2-D acoustic spaces. Impulse response measurements are taken and comparisons are made regarding the spectral content and the associated properties when compared with standard room acoustic parameters. Enhanced mesh structures are examined using frequency warping techniques and high-resolution sampling rates. The 2-D triangular mesh is shown to be considerably superior to the rectilinear mesh in terms of the measurements taken, with a further significant improvement being made by using the same mesh oversampled to a much higher resolution to improve the bandwidth of the measured impulse responses.