Petö, Márton ; Juhre, Daniel ; Eisenträger, Sascha (2023)
Code verification of non‐linear immersed boundary simulations using the method of manufactured solutions.
In: PAMM - Proceedings in Applied Mathematics and Mechanics, 23 (4)
doi: 10.1002/pamm.202300068
Article, Bibliographie
This is the latest version of this item.
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2023 |
| Creators: | Petö, Márton ; Juhre, Daniel ; Eisenträger, Sascha |
| Type of entry: | Bibliographie |
| Title: | Code verification of non‐linear immersed boundary simulations using the method of manufactured solutions |
| Language: | English |
| Date: | December 2023 |
| Place of Publication: | Weinheim |
| Publisher: | Wiley-VCH |
| Journal or Publication Title: | PAMM - Proceedings in Applied Mathematics and Mechanics |
| Volume of the journal: | 23 |
| Issue Number: | 4 |
| Collation: | 8 Seiten |
| DOI: | 10.1002/pamm.202300068 |
| Corresponding Links: | |
| 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. |
| Identification Number: | Artikel-ID: e202300068 |
| Additional Information: | Special Issue: 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics 600 Technology, medicine, applied sciences > 624 Civil engineering and environmental protection engineering |
| Divisions: | 13 Department of Civil and Environmental Engineering Sciences 13 Department of Civil and Environmental Engineering Sciences > Mechanics 13 Department of Civil and Environmental Engineering Sciences > Mechanics > Numerical Mechanics |
| Date Deposited: | 03 Jun 2024 05:19 |
| Last Modified: | 03 Jun 2024 05:19 |
| PPN: | |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
Available Versions of this Item
-
Code verification of non‐linear immersed boundary simulations using the method of manufactured solutions. (deposited 28 May 2024 12:10)
- Code verification of non‐linear immersed boundary simulations using the method of manufactured solutions. (deposited 03 Jun 2024 05:19) [Currently Displayed]
 |
Send an inquiry |
Options (only for editors)
 |
Show editorial Details |
Drucken
Impressum