A discrete duality finite volume discretization of the vorticity-velocity-pressure formulation of the 2D Stokes problem on almost arbitrary two-dimensional grids

Sarah Delcourte (1, 2) , Pascal Omnes (3, 4)

1 MMCS - Modélisation mathématique, calcul scientifique
2 KALiFFE - Kinetic models AppLIed for Future of Fusion Energy
3 LAGA - Laboratoire Analyse, Géométrie et Applications
4 DM2S - Département de Modélisation des Systèmes et Structures

We present an application of the discrete duality finite volume method to the numerical approximation of the vorticity-velocity-pressure formulation of the 2D Stokes equations, associated to various non-standard boundary conditions. The finite volume method is based on the use of discrete differential operators obeying some discrete duality principles. The scheme may be seen as an extension of the classical MAC scheme to almost arbitrary meshes, thanks to an appropriate choice of degrees of freedom. The efficiency of the scheme is illustrated by numerical examples over unstructured triangular and locally refined non-conforming meshes, which confirm the theoretical convergence analysis led in the article.

Mots clés: Stokes equations; vorticity-velocity-pressure formulation; boundary conditions; discrete duality; finite volumes; arbitrary meshes; a priori estimates

Domaines: Analyse numérique [math.NA]

Sarah Delcourte, Pascal Omnes. A discrete duality finite volume discretization of the vorticity-velocity-pressure formulation of the 2D Stokes problem on almost arbitrary two-dimensional grids. Numerical Methods for Partial Differential Equations, 2015, pp.1-30. ⟨10.1002/num.21890⟩. ⟨cea-00772972v2⟩