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  4. Code verification of non-linear immersed boundary simulations using the method of manufactured solutions
 
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Code verification of non-linear immersed boundary simulations using the method of manufactured solutions

Citation Link: https://doi.org/10.15480/882.8895
Publikationstyp
Journal Article
Date Issued
2023
Sprache
English
Author(s)
Petö, Márton  
Juhre, Daniel  
Eisenträger, Sascha  
TORE-DOI
10.15480/882.8895
TORE-URI
https://hdl.handle.net/11420/44435
Citation
93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2023)
Contribution to Conference
93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)
Publisher DOI
10.1002/pamm.202300068
Non-standard finite element technologies, such as immersed boundary approaches, are typically based on novel algorithms and advanced methods, which require reliable testing of the implemented code. For this purpose, the method of manufactured solutions (MoMS) offers a great framework, enabling an easy and straightforward derivation of closed-form reference solutions. In this contribution, the focus is kept on non-linear analysis via the finite cell method (FCM), which is typically based on an unfitted geometry discretization and higher-order shape functions. The code verification via MoMS generally requires the application of boundary conditions to all boundaries of the simulation domain, which need to be enforced in a weak sense on the immersed boundaries. To avoid this, we propose a novel way of deriving manufactured solutions, for which the necessary constraints on the embedded boundaries are directly fulfilled. Thus, weak boundary conditions can be eliminated from the FCM simulation, and the simulation complexity is reduced when testing other relevant features of the immersed code. In particular, we focus on finite strain analysis of 3D structures with a Neo-Hookean material model, and show that the proposed technique enables a reliable code verification approach for all load steps throughout the deformation process.
DDC Class
620: Engineering
510: Mathematics
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
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