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Wave-based time-domain methods for room acoustics auralisation are computationally intensive, but performance at an audio rate is coming within reach in special-purpose hardware. In this talk, the focus will be on the various problems and challenges posed by such methods, including computational cost, techniques for ensuring numerical stability under realistic room geometries and wall conditions, and the inherent problem of numerical dispersion in time domain methods. Alongside these basic considerations, some special topics will be discussed, including higher order accuracy, and source/receiver modeling. Many sound and video demonstrations will be presented.