Spectral element method for wave propagation on irregular domains
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A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the physical space are mapped according to the length scale of the beeline segment or the curve segment. Using the Bubnov–Galerkin method, some acoustic problems with two kinds of irregular domains are simulated in detail. First, the basic problem with analytical solution is analysed numerically. Numerical results show that the SEM integrated with the length-scale method has the same precision as the isoparametric SEM. Also, it can save nearly half of the time cost. Additionally, the acoustic propagations with inlet flow are simulated numerically. All the results indicate that the SEM integrated with the length-scale method has the ability to simulate the acoustic problems with irregular domains. It is shown that the mapping method maintains the curve edges and provides a useful alternative for isoparametric element, which represents a curved edge with a straight edge.
KeywordsSpectral element method curved quadrilateral element isoparametric element Chebyshev polynomial mapping method
The authors would like to acknowledge the support by the National Fundamental Research Program of China (No. 2012CB026004).
- 7.Goldstein M E 1974 Unified approach to aerodynamic sound generation in the presence of sound. J. Acoust. Soc. Am. 56(5): 499–509Google Scholar
- 8.Kim J W and Lee D J 2000 Fourth computational aeroacoustics (CAA) workshop on benchmark problems. In: Proceedings of the NASA Conference, ClevelandGoogle Scholar
- 9.Kosec G 2016 A local numerical solution of a fluid-flow problem on an irregular domain. Adv. Eng. Softw. 1–9Google Scholar
- 18.Pozrikidis C 2014 The finite element method in two dimensions. In: Introduction to Finite and Spectral Element Methods Using MATLAB. Hoboken: CRC PressGoogle Scholar
- 20.Tam C K W and Hardin J C 1996 Second computational aeroacoustic (CAA) workshop on benchmark problems. In: Proceedings of the NASA Conference, TallahasseeGoogle Scholar
- 22.Vosse F N V D and Minev P D 1996 Spectral element methods: theory and applications. Eindhoven: Eindhoven University of TechnologyGoogle Scholar