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A Spectral Collocation Method for Confined Unsteady Flows with Oscillating Boundaries

✍ Scribed by D. Mateescu; M.P. Paı̈doussis; W.G. Sim

Book ID
102971453
Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
686 KB
Volume
8
Category
Article
ISSN
0889-9746

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✦ Synopsis

This paper presents a spectral collocation method especially developed for the study of confined unsteady flows with periodically oscillating boundaries. It is based on suitable expansions of the fluid-dynamic parameters, using Chebyshev polynomials and Fourier functions for the spatial expansions and exponential functions of time, and containing (a) priori unknown coefficients which are determined using a collocation method. As a special feature, complex exponential functions of time and frequency are used in this method for the time discretization. The method is validated by comparison with analytical solutions for several test problems of typical steady and unsteady confined flows with oscillating boundaries. Excellent agreement has been found in all cases. The solution of nonlinear problems using this spectral method is exemplified by the calculation of the unsteady viscous flow in an eccentric annular space, generated by the oscillatory rotation of the inner boundary.

📜 SIMILAR VOLUMES

Spectral collocation methods for the pri
Spectral collocation methods for the primary two-point boundary value problem in modelling viscoelastic flows
✍ A. Karageorghis; T. N. Phillips; A. R. Davies 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 433 KB

Expansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two-point boundary value problem within a spectral collocation formulation. The performance of the methods is analysed in terms of accuracy and robustness relative to the level of non-lineari