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Títol: Discontinuous Galerkin methods for the Stokes equations using divergence-free approximations
Autor: Villardi de Montlaur, Adeline de
Fernandez Mendez, Sonia
Huerta, Antonio
Altres autors/autores: Universitat Politècnica de Catalunya. Escola Politècnica Superior de Castelldefels (EPSC); Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. LACÀN - Centre Específic de Recerca de Mètodes Numèrics en Ciències Aplicades i Enginyeria
Matèries: Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Galerkin methods
Stokes equations
Galerkin, Mètodes de
Equacions de Navier-Stokes
Tipus de document: Article
Descripció: A discontinuous Galerkin (DG) method with solenoidal approximation for the simulation of incompressible flow is proposed. It is applied to the solution of the Stokes equations. The interior penalty method is employed to construct the DG weak form. For every element, the approximation space for the velocity field is decomposed as the direct sum of a solenoidal space and an irrotational space. This allows to split the DG weak form into two uncoupled problems: the first one solves for the velocity and the hybrid pressure (pressure along the mesh edges) and the second one allows the computation of the pressure in the element interior. Furthermore, the introduction of an extra penalty term leads to an alternative DG formulation for the computation of solenoidal velocities with no presence of pressure terms. Pressure can then be computed as a post-process of the velocity solution. Numerical examples demonstrate the applicability of the proposed methodologies.
Peer Reviewed
This is the pre-peer reviewed version of the following article: Montlaur, A.; Fernandez, S.; Huerta, A. Discontinuous Galerkin methods for the Stokes equations using divergence-free approximations. "International journal for numerical methods in fluids", Juliol 2008, vol. 57, núm. 9, p. 1071-1092., which has been published in final form at http://www3.interscience.wiley.com/journal/117953707/abstract?CRETRY=1&SRETRY=0
Postprint (author’s final draft)
Altres identificadors i accés: Montlaur, A.; Fernandez, S.; Huerta, A. Discontinuous Galerkin methods for the Stokes equations using divergence-free approximations. "International journal for numerical methods in fluids", Juliol 2008, vol. 57, núm. 9, p. 1071-1092.
0271-2091
http://hdl.handle.net/2117/8152
10.1002/fld.1716
Disponible al dipòsit:E-prints UPC
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