Convergence results for the vector penalty-projection and two-step artificial compressibility methods

Philippe Angot (1) , Pierre Fabrie (2)

1 analyse appliquée
2 Équipe EDP et Physique Mathématique

In this paper, we propose and analyze a new artificial compressibility splitting method which is issued from the recent vector penalty-projection method for the numerical solution of unsteady incompressible viscous flows introduced in [1], [2] and [3]. This method may be viewed as an hybrid two-step prediction-correction method combining an artificial compressibility method and an augmented Lagrangian method without inner iteration. The perturbed system can be viewed as a new approximation to the incompressible Navier- Stokes equations. In the main result, we establish the convergence of solutions to the weak solutions of the Navier-Stokes equations when the penalty parameter tends to zero.

Mots clés: Artificial compressibility; Navier-Stokes equations; Vector penalty-projection; Pseudo-compressibility; Penalty method

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Dynamique des Fluides [physics.flu-dyn]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Philippe Angot, Pierre Fabrie. Convergence results for the vector penalty-projection and two-step artificial compressibility methods. 2011. ⟨hal-00653113v1⟩