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  4. Code verification of immersed boundary techniques using the method of manufactured solutions
 
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Code verification of immersed boundary techniques using the method of manufactured solutions

Citation Link: https://doi.org/10.15480/882.9599
Publikationstyp
Journal Article
Date Issued
2024-06
Sprache
English
Author(s)
Petö, Márton  
Gorji, Mahan  
Konstruktion und Festigkeit von Schiffen M-10  
Duvigneau, Fabian  
Düster, Alexander  
Konstruktion und Festigkeit von Schiffen M-10  
Juhre, Daniel  
Eisenträger, Sascha  
TORE-DOI
10.15480/882.9599
TORE-URI
https://hdl.handle.net/11420/47609
Journal
Computational mechanics  
Volume
73
Issue
6
Start Page
1283
End Page
1309
Citation
Computational Mechanics 73 (6): 1283-1309 (2024)
Publisher DOI
10.1007/s00466-023-02411-x
Scopus ID
2-s2.0-85177599761
Publisher
Springer
ISSN
01787675
Peer Reviewed
true
Code verification plays a crucial role for all finite element applications, especially for non-standard ones, such as immersed boundary approaches, which are typically based on novel algorithms and often error-prone in-house implementations. Instead of relying on rarely available analytical solutions or overkill FEM simulations, in this article, the capabilities of the method of manufactured solutions (MoMS) are explored, enabling an easy and straightforward derivation of closed-form reference solutions. The focus is kept on immersed problems, in particular, on the finite cell method (FCM), and manufactured solutions are derived for 2D and 3D problems involving voids and single/multiple inclusions. We propose several approaches for the construction of the manufactured solutions, where zero traction conditions for void regions and continuous normal stresses along material interfaces are directly fulfilled. Thus, no weak boundary conditions are required for reproducing the manufactured solution via FCM. This not only enables code verification for FCM implementations that lack the option of applying weak boundary conditions, but also keeps the simulation complexity low, when testing other relevant features, e.g., different integration schemes or the implementation of enrichment functions. The flexibility and wide application range of the MoMS in the context of immersed boundary simulations is demonstrated using static, quasi-static, and transient problems in the context of linear elasticity. Finally, the analytical derivations of the manufactured solutions used in this paper are provided as supplementary material.
Subjects
Extended finite element method
Finite cell method
Immersed boundary methods
Material interfaces
Method of manufactured solutions
DDC Class
620: Engineering
510: Mathematics
624: Civil Engineering, Environmental Engineering
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by-nc/4.0/
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