Development and Evaluation of a Complete 3D FDTD Computational Algorithm for the Numerical Approximation of Guided Acoustic Wave Propagation in Lossy Media

The suggestion of a complete and reliable numerical scheme for the description and study of acoustic wave propagation in confined regions of space with complex geometric characteristics and irrespective of lossless or lossy media comprises the objective of this contribution. Specifically, the fundamental principles of the Finite-Difference Time-Domain method (FDTD) are utilized in order to build an optimum computational domain and solve the acoustic equations in the interior of various structures such as pipes, ducts and waveguides regardless their shape and the individual properties. The proposed methodology is also supplemented by the competent and widely tested absorbing boundary condition of the Generalized Perfectly Matched Layer (GPML) developed by the authors in acoustics, for the successful absorption of the travelling waves at the limits and thus the proper termination of the used computational domain. The whole theory is implemented in the case of the rectangular duct with rigid walls in order to compare the simulation results with the exact analytical solution that can be properly derived in such a case and thus to evaluate and verify the effectiveness of the suggested numerical scheme. Numerous simulations of multimodal sound propagation in straight or bent ducts clearly indicate the substantial capabilities of the method as a valuable computational tool in acoustics which can effectively replace the prevailing but costly and cumbersome experimental approaches.