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Physical and Spurious Modes in Mixed Finite Element Formulation for the Galbrun Equation

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Sound propagation in moving media can be described by the Galbrun equation for the oscillating component of the fluid displacement. A displacement based finite element formulation using standard Lagrangian elements produces spurious modes, which renders it unfeasible for any numerical purpose. Herein, the quadratic eigenvalue problem for the mixed formulation in 2D using Mini elements and Taylor-Hood elements is set up and solved. Solution confirms that both element types are suitable for low Mach numbers and under certain conditions. Although the formulation is not free from spurious results, it is shown that physical and spurious modes are well separated for low Mach numbers in non-dissipative systems. Vorticity modes, such as those arising from the linearized Euler equations, could not be identified. If absorbing walls are considered, separation of physical and spurious modes becomes less clear. Then, eigenvalues of both types of modes are located closer to each other in the complex plane. Examples include the one-dimensional duct problem, for which the spurious modes are discussed for the energy conserving problem, and an annular duct under two conditions: first subjected to a shear flow and with a rigid boundary, and secondly with an absorbing boundary, which allows investigating the dissipative case.
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Document Type: Research Article

Publication date: May 1, 2014

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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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