An adaptive two-grid solver for DPG formulation of compressible Navier-Stokes equations in 3D
Authors:
- Waldemar Rachowicz,
- Witold Cecot,
- Adam Zdunek
Abstract
We present an overlapping domain decomposition iterative solver for linear systems resulting from the discretization of compressible viscous flows with the Discontinuous Petrov–Galerkin (DPG) method in three dimensions. It is a two-grid solver utilizing the solution on the auxiliary coarse grid and the standard blockJacobi iteration on patches of elements defined by supports of the coarse mesh base shape functions. The simple iteration defined in this way is used as a preconditioner for the conjugate gradient procedure. Theoretical analysis indicates that the condition number of the preconditioned system should be independent of the actual finite element mesh and the auxiliary coarse mesh, provided that they are quasiuniform. Numerical tests confirm this result. Moreover, they show that presence of strongly flattened or elongated elements does not slow the convergence. The finite element mesh is subject to adaptivity, i.e. dividing the elements with large errors until a required accuracy is reached. The auxiliary coarse mesh is adjusting to the nonuniform actual mesh.
- Record ID
- CUT02bef33cb66f48e880d703c6e4be4285
- Publication categories
- ;
- Author
- Journal series
- Computational Methods in Applied Mathematics, ISSN 1609-4840, e-ISSN 1609-9389
- Issue year
- 2024
- Vol
- 24
- No
- 1
- Pages
- 141-172
- Other elements of collation
- rys.; tab.; wykr.; Bibliografia (na s.) - 171-172; Bibliografia (liczba pozycji) - 22; Oznaczenie streszczenia - Abstr.; Data udostępnienia on-line - 2023-07-12; Numeracja w czasopiśmie - Vol. 24, Iss. 1
- Keywords in English
- Finite Element Method, compressible Navier-Stokes equations, discontinuous Petrov-Galerkin, iterative solver, domain decomposition
- ASJC Classification
- ; ;
- DOI
- DOI:10.1515/cmam-2022-0206 Opening in a new tab
- URL
- https://www.degruyter.com/document/doi/10.1515/cmam-2022-0206/html 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
- Score (nominal)
- 70
- Score source
- journalList
- Score
- Publication indicators
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT02bef33cb66f48e880d703c6e4be4285/
- URN
urn:pkr-prod:CUT02bef33cb66f48e880d703c6e4be4285
* 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.