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Compact Higher-Order Time-Domain Schemes for the Unconditionally Stable Modeling of Generalized 3-D Acoustic Propagation Problems

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A higher-order curvilinear finite-difference time-domain (FDTD) technique, combined with the alternating-direction implicit (ADI) concept, is presented in this paper for the unconditionally stable characterization and optimal design of modern 3-D acoustic propagation arrangements. Departing from a compact non-standard discretization discipline, applied directly to the general form of the linearized Euler's equations, the novel method develops a family of accurate spatial/temporal operators and introduces a dual-mesh framework for the correct association of velocity components and pressure values. Moreover, the presence of an arbitrary mean flow vector in lossy regions is efficiently treated via a stencil control process that selects the appropriate candidate according to the problem, under study. On the other hand, different media interfaces, not necessarily aligned with grid's cells, are elaborately analyzed in terms of a convergent algorithm which satisfies the physical continuity conditions and exhibits enhanced directional sensitivity. To truncate open-boundary regions and ensure satisfactory annihilation rates for the intricate vorticity and entropy waves, the higher-order technique introduces a parameterized perfectly matched layer (PML) absorber. Finally, the frequent case of bent ducts with flexible or rigid walls and changeable cross-section is rigorously manipulated by a multimodal decomposition process that decouples non-separable modes. Hence, the detrimental dispersion errors of customary approaches are drastically subdued and the prolonged duration of time-domain simulations is safely circumvented through time increments far above the Courant criterion. Numerical results, concerning various modern acoustic structures as well as extensive comparisons with reference data, confirm the preceding merits and yield optimized configurations.
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Document Type: Research Article

Publication date: November 1, 2007

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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