Petö, Márton ; Juhre, Daniel ; Eisenträger, Sascha (2024)
Code verification of non‐linear immersed boundary simulations using the method of manufactured solutions.
In: PAMM - Proceedings in Applied Mathematics and Mechanics, 2023, 23 (4)
doi: 10.26083/tuprints-00027196
Artikel, Zweitveröffentlichung, Verlagsversion
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Kurzbeschreibung (Abstract)
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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Petö, Márton ; Juhre, Daniel ; Eisenträger, Sascha |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Code verification of non‐linear immersed boundary simulations using the method of manufactured solutions |
| Sprache: | Englisch |
| Publikationsjahr: | 28 Mai 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | Dezember 2023 |
| Ort der Erstveröffentlichung: | Weinheim |
| Verlag: | Wiley-VCH |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | PAMM - Proceedings in Applied Mathematics and Mechanics |
| Jahrgang/Volume einer Zeitschrift: | 23 |
| (Heft-)Nummer: | 4 |
| Kollation: | 8 Seiten |
| DOI: | 10.26083/tuprints-00027196 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/27196 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (Abstract): | 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. |
| ID-Nummer: | Artikel-ID: e202300068 |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-271963 |
| Zusätzliche Informationen: | Special Issue: 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik 600 Technik, Medizin, angewandte Wissenschaften > 624 Ingenieurbau und Umwelttechnik |
| Fachbereich(e)/-gebiet(e): | 13 Fachbereich Bau- und Umweltingenieurwissenschaften 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Numerische Mechanik |
| Hinterlegungsdatum: | 28 Mai 2024 12:10 |
| Letzte Änderung: | 29 Mai 2024 11:43 |
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| Suche nach Titel in: | TUfind oder in Google |
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- Code verification of non‐linear immersed boundary simulations using the method of manufactured solutions. (deposited 28 Mai 2024 12:10) [Gegenwärtig angezeigt]
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