A 2.5-dimensional acoustic wave solver: Modeling simplified vocal tract geometries with reduced computational load

High-fidelity three-dimensional (3D) wave solvers accurately simulate acoustic wave propagation in complex vocal tract geometries but are computationally demanding, limiting their usage in real-time applications. In contrast, low-dimensional models are efficient but limited to cylindrical tracts, neglecting higher-order modes in their frequency responses. This paper introduces a lightweight lumped two-dimensional (2.5D) solver that combines the efficiency of low-dimensional models with the accuracy of 3D approaches to model straight tracts constrained to mid-sagittal symmetry. Like 3D, the 2.5D model captures transverse wave propagation and accounts for higher-order modes. We validate the model by comparing its transfer functions and pressure distributions against those of a conventional two-dimensional (2D) solver and a high-fidelity 3D finite element model for six straight tract geometries of varying complexity. This analysis demonstrates the abilities and limitations of the proposed method. The results show that the 2.5D solver closely matches the 3D model's transfer functions up to 12 kHz, with correlation coefficients exceeding 0.8 for symmetric tracts. For asymmetric geometries, it still performs significantly better than the 2D model. Additionally, the 2.5D solver achieves over two orders of magnitude computational speed-up compared to the 3D model, offering a better trade-off between accuracy and efficiency for vocal tract acoustic modeling.