Traffic noise in urban environments constitutes a significant health hazard, creating potential for proactive noise management and auralization as tool for modern urban planning. However, state-of-the-art raybased Geometrical Acoustics (GA) models utilized in current auralization pipelines struggle to predict the sound propagation across grounds featuring varying acoustic properties, known as Impedance Discontinuity (ID). Relying just on Specular Reflection (SR) leads to unphysical, abrupt spectral changes when a geometric reflection point moves across an ID. To resolve such discontinuities, this thesis proposes extensions to the reflection and diffraction propagation simulation of sound propagation based on GA. First, the reflection filter is extended to incorporate the Weyl-Van der Pol approximation, accounting for spherical wavefront curvature over finite impedances. Second, the M-UTD is introduced. The M-UTD treats an ID as a diffractive edge by adapting electromagnetic diffraction models incorporating extensions by Luebbers, Holm, and Schettino to acoustic propagation. The M-UTD is evaluated against Boundary Element Method (BEM) simulations and experimental measurements. These investigations cover single and multiple IDs scenarios on flat surfaces, angled wedges, and a dynamic auralization scenario. The results demonstrate that the M-UTD successfully compensates for the magnitude and phase differences at material boundaries. By computing a continuous diffraction component driven by the impedance mismatch, the model reduces discrete amplitude fluctuations during dynamic source movement, yielding a much smoother and more physically plausible time-variant spectrogram. While limitations remain at low frequencies and grazing angles, the proposed M-UTD provides an efficient, reciprocal, and robust solution. Ultimately, it improves the agreement of the calculated sound field over discontinuous surfaces with BEM simulations and measurements.

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