Applications for complex acoustic environments exist in, e.g., hearing research, architectural planning, and entertainment. Geometrical acoustics (GA) offers a high computational efficiency, as required for dynamic real-time renderings. However, the assumed ray-like propagation does not directly account for perceptually relevant effects of diffraction, which are particularly noticeable for occluded sound sources. In typical indoor environments, finite objects and apertures like, e.g., tables, billboards, and doors form an important category of entities, for which computationally efficient diffraction modelling is of interest. Here, we apply a recent approach for integrating diffraction in the framework of GA to a flat finite object. The underlying universal diffraction filter approximation (UDFA) uses (fractional-order) filter functions with physically-based parameters to account for first-order edge diffraction. Higher-order diffraction, i.e., repeated diffraction at the same object leads to additional spectral effects at low frequencies which are modelled in a simplified way using additional filters. The suggested filter approach and topology offer a computationally highly efficient and spatially smooth infinite impulse response (IIR) implementation for modelling diffraction. Results are compared to a state-of-art higher-order diffraction simulation.