A discontinuous Petrov-Galerkin method for compressible Navier-Stokes equations in three dimensions
Authors:
- Waldemar Rachowicz,
- Adam Zdunek,
- Witold Cecot
Abstract
Application of a Discontinuous Petrov-Galerkin (DPG) method for simulation of compressible viscous flows in three dimensions is presented. The approach enables construction of stable schemes for problems with a small perturbation parameter. The main idea of the method is a weak formulation with a relaxed interelement continuity of the solution. The formulation satisfies the inf-sup condition with the stability constant independent of the small perturbation parameter, which here is the viscosity constant for the compressible Navier-Stokes equations. The DPG discrete formulation uses the specially designed so-called optimal test functions. They do not compromise the inf-sup stability of the continuous formulation. DPG does not use any artificial dissipation for the compressible Navier-Stokes equations. Being a residual minimization method it has got a built-in a posteriori error estimation which allows for mesh adaptivity leading to resolving reliable viscous fluxes, the major difficult task in simulations of viscous flows. We illustrate the method with a few steady state laminar solutions.
- Record ID
- CUTa191410a8471455bb85594ab5239ef3f
- Publication categories
- ;
- Author
- Journal series
- Computers & Mathematics With Applications, ISSN 0898-1221, e-ISSN 1873-7668
- Issue year
- 2021
- Vol
- 102
- Pages
- 113-136
- Other elements of collation
- rys.; tab.; wykr.; Bibliografia (na s.) - 135-136; Bibliografia (liczba pozycji) - 29; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 102
- Keywords in English
- finite element method, compressible Navier-Stokes equations, discontinuous Petrov-Galerkin, h-adaptivity, error estimation
- DOI
- DOI:10.1016/j.camwa.2021.10.010 Opening in a new tab
- URL
- https://www.sciencedirect.com/science/article/pii/S0898122121003588 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 140
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTa191410a8471455bb85594ab5239ef3f/
- URN
urn:pkr-prod:CUTa191410a8471455bb85594ab5239ef3f
* 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.