A comparison of fictitious domain methods appropriate for spectral/ hp element discretisations

The fictitious domain, finite cell and fat boundary method, which are commonly adopted for fluid–structure interaction (FSI) problems, have been considered and implemented in a spectral/ hp element code for a 1D test problem. The finite cell and fat boundary method are extended for the general case...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2008-04, Vol.197 (25), p.2275-2289
Main Authors: Vos, P.E.J., van Loon, R., Sherwin, S.J.
Format: Article
Language:English
Subjects:
Fat boundary method
Fictitious domains
Finite cell method
Fluid–structure interaction
Lagrange multipliers
Spectral/ hp element method
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Summary:The fictitious domain, finite cell and fat boundary method, which are commonly adopted for fluid–structure interaction (FSI) problems, have been considered and implemented in a spectral/ hp element code for a 1D test problem. The finite cell and fat boundary method are extended for the general case of a deformable solid in a fluid, and analysed. Furthermore, a new implicit variation of the fat boundary method is proposed. The 1D framework allows for a clear and detailed analysis of the different approaches and to highlight the similarities and differences between the methods. Exponential p-convergence, which is typical for smooth solutions discretised with spectral/ hp elements, is demonstrated for all methods except the classic fictitious domain formulation. This overview can be considered as a starting point to study the capability, advantages and disadvantages of these methods for fluid–structure interaction problems in a more realistic setting and in higher dimensions.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2007.11.023