Numerical stabilization of the Stokes problem in vorticity–velocity–pressure formulation

• Published in: Computer methods in applied mechanics and engineering Vol. 196; no. 9; pp. 1767 - 1786
• Main Authors: Salaün, Michel, Salmon, Stéphanie
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2007; Elsevier
• Subjects: Bubble functions; Computational techniques; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Inf–sup conditions; Mathematical methods in physics; Mathematics; Mixed finite elements method; Numerical Analysis; Physics; Rotational flow and vorticity; Stokes problem; Stream function-vorticity formulation; Vorticity–velocity–pressure formulation; Mixed finite elements method; Inf–sup conditions; Stokes problem; Vorticity–velocity–pressure formulation; Bubble functions; 65N30; Stream function-vorticity formulation; Unstructured mesh; Stream function; Stabilization; Bubble function; Vorticity-velocity-pressure formulation; Inf-sup conditions; Mixed method; Finite element method; Incompressible flow; Vorticity; Dirichlet problem; Boundary-value problems; Modelling; Vortex flow; Incompressible fluid; Mesh generation
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2006.09.015

We work on a vorticity, velocity and pressure formulation of the bidimensional Stokes problem for incompressible fluids. In previous papers, the authors have developed a natural implementation of this scheme. We have then observed that, in case of unstructured meshes with Dirichlet boundary conditions on the velocity, the convergence is not optimal. In this paper, we propose to add “bubble” velocity functions with compact support along the boundary to improve convergence. We then prove a convergence theorem and illustrate by numerical results better behaviour of the scheme in general cases.