A staggered scheme with non-conforming refinement for the Navier-Stokes equations

Fabrice Babik (1) , Jean-Claude Latché (2) , Bruno Piar (3) , Khaled Saleh (4, 5, 6)

1 IRSN/PSN-RES/SA2I/LIE - Laboratoire de l'Incendie et des Explosions
2 IRSN/PSN-RES/SA2I - Service des Agressions Internes et des risques Industriels
3 IRSN - Institut de Radioprotection et de Sûreté Nucléaire
4 ICJ - Institut Camille Jordan
5 UCBL - Université Claude Bernard Lyon 1
6 MMCS - Modélisation mathématique, calcul scientifique

We propose a numerical scheme for the incompressible Navier-Stokes equations. The pressure is approximated at the cell centers while the vector valued velocity degrees of freedom are localized at the faces of the cells. The scheme is able to cope with unstructured non-conforming meshes, involving hanging nodes. The discrete convection operator, of finite volume form, is built with the purpose to obtain an L 2-stability property, or, in other words, a discrete equivalent to the kinetic energy identity. The diffusion term is approximated by extending the usual Rannacher-Turek finite element to non-conforming meshes. The scheme is first order in space for energy norms, as shown by the numerical experiments.

Mots clés: General Quadrangle; Hanging Node; Dual Cell; Dual Mesh; Initial Face

Domaines: Mathématiques [math]

Fabrice Babik, Jean-Claude Latché, Bruno Piar, Khaled Saleh. A staggered scheme with non-conforming refinement for the Navier-Stokes equations. Finite volumes for complex applications VII, Jun 2014, Berlin, Germany. pp.87-95, ⟨10.1007/978-3-319-05684-5_7⟩. ⟨hal-04095021⟩