In its 2025 report on environmental noise in Europe, the European Environmental Agency stated that more than 30 % of the European population (about 150 Millionen Menschen) are exposed to long-term unhealthy noise levels from transport sources, such as road traffic, railways, and air traffic. Noise exposure has a greater health impact than better-known risks such as second-hand smoke, and overall is just behind air pollution and climatic factors. One countermeasure for noise pollution is the construction of noise barrier walls, for which precise acoustic simulation methods are necessary to ensure the effectiveness of the measure. To date, sound propagation simulations are based on geometrical methods that do not account for wave effects, such as diffraction or refraction, yielding incorrect results, especially for low frequencies. These low frequencies often cause disturbances and discomfort in humans and can be responsible for pathologies such as hypertonia. In contrast, an alternative approach is based on solving the wave equation, fully resolving all wave-based phenomena. These wave-based methods yield more accurate results than geometrical methods, particularly for low frequencies. The Finite Element Method is used with a Continuous Galerkin and a Discontinuous Galerkin approach to compute outdoor noise propagation in two application examples: Application example 1 presents a simple noise barrier geometry over a flat plane, and serves as a test case used to highlight differences between the results of geometry-based and wave-based methods. Application example 2 resembles a real-world geometry of an alpine valley with a dominant traffic noise source. A geometry-based simulation, a Continuous Galerkin, and a Discontinuous Galerkin Finite Element simulation are performed and the results are compared to each other.
Another area, where acoustic behavior at low frequencies plays an important role, is room acoustics, for which two application examples are presented. Application example 3 represents an empty room. To simulate the acoustic field in an empty room, both the Continuous Galerkin and the Discontinuous Galerkin Finite Element Method are used. The simulation results of the empty room are validated against reverberation time measurements in a real room. Application example 4 presents a common approach to improving low-frequency room acoustics, namely, the installation of so-called edge absorbers. These are porous acoustic absorbers positioned along room edges that have good absorption properties in the low-frequency range. To predict the effect of edge absorbers on the acoustic field, a Continuous Galerkin Finite Element model is presented, where the absorber is modeled as an equivalent fluid using the Johnson-Champoux-Allard-Lafarge model. The simulation model allows to study interaction mechanisms between room and absorber. The Finite Element model of the room with edge absorbers is validated against transfer function measurements in a real room. In conclusion, this work underlines the importance of using wave-based simulation methods for low-frequency acoustic simulations.

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