A sixth-order finite volume scheme for the steady-state incompressible Stokes equations on staggered unstructured meshes

schema volume fini d'ordre six pour le probleme de probleme de Stokes stationaire

Ricardo Costa (1) , Stéphane Clain (1) , Gaspar Machado (1)

1 CMAT - Centro de Matemática [Minho]

We propose a new sixth-order finite volume scheme to solve the bidimensional linear steady-state Stokes problem on staggered unstructured meshes and complex geometries. The method is based on several classes of polynomial reconstructions to accurately eva-luate the diffusive fluxes, the pressure gradient, and the velocity divergence. The main difficulty is to handle the div-grad duality to avoid numerical locking and oscillations. A new preconditioning technique based on the construction of a pseudo-inverse matrix is also proposed to dramatically reduce the computational effort. Several numerical simulations are carried out to highlight the performance of the new method.

On propose un nouveau schema volume fini d'ordre 6 pour le probleme de Stokes. La principale difficulté est le traintement de la dualité div-grad qui provient de la condition d'incompressibilité

Mots clés: finite volume; high-order scheme; preconditioning; incompressible fluid; Stokes equations

Domaines: Analyse numérique [math.NA]

Ricardo Costa, Stéphane Clain, Gaspar Machado. A sixth-order finite volume scheme for the steady-state incompressible Stokes equations on staggered unstructured meshes. 2015. ⟨hal-01107313⟩