A discontinuous Petrov-Galerkin method for compressible viscous flows in three dimensions
Authors:
- Waldemar Rachowicz,
- Adam Zdunek,
- Witold Cecot
Abstract
The Discontinuous Petrov-Galerkin (DPG) method allows one to construct stable finite element schemes for some classes of singularily perturbed problems like, for instance, convection-dominated diffusion. The central ingredient of the method is a special weak formulation characterized by a relaxed interelement continuity of approximation. It satisfies the inf-sup stability condition with the stability constant independent of the small parameter of perturbation. This technology was applied by Chan et al. in [1] to develop a scheme for simulation of the two-dimensional compressible Navier-Stokes equations. In this paper we extend that work to three dimensions. We present the necessary modifications, the details of the functional setting, the discrete trial and test finite element spaces, and the final form of the algorithm. The issues of a posteriori error estimation and h-adaptivity of finite element meshes are addressed. The technique is illustrated with a few preliminary numerical examples.
- Record ID
- CUT091bc4f374984462b877ba9aa8a3fa31
- Publication categories
- ; ;
- Author
- Pages
- [1-15]
- Other elements of collation
- il.; Bibliografia (na s.) - 15; Bibliografia (liczba pozycji) - 11; Oznaczenie streszczenia - Abstr.
- Book
- Cecot Witold, Witold Cecot Kozień Marek, Marek Kozień Lisowski Wojciech Wojciech Lisowski [et al.] (eds.): 4th Polish Congress of Mechanics and the 23rd International Conference on Computer Methods in Mechanics, AIP Conference Proceedings, no. 2239, 2020, [Melville], American Institute of Physics, AIP Publishing, ISBN 978-0-7354-1998-8
- Keywords in English
- discontinuous Petrov-Galerkin, finite element method, compressible viscous flows
- DOI
- DOI:10.1063/5.0008211 Opening in a new tab
- URL
- https://aip.scitation.org/doi/10.1063/5.0008211 Opening in a new tab
- Related project
- Nieciągła aproksymacja Petrova-Galerkina do równań Naviera-Stokesa dla przepływów ściśliwych. . Project leader at PK: , ,
Projects financed by NSC [Projekty finansowane przez NCN] - Language
- eng (en) English
- License
- Score (nominal)
- 20
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT091bc4f374984462b877ba9aa8a3fa31/
- URN
urn:pkr-prod:CUT091bc4f374984462b877ba9aa8a3fa31
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.