Consistant velocity-pressure coupling for second-order L2-penalty and direct-forcing methods

Arthur Sarthou (1) , Stéphane Vincent (2) , Jean-Paul Caltagirone (2)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 TREFLE - Transferts, écoulements, fluides, énergétique

The present work studies the interactions between fictitious-domain methods on structured grids and velocity-pressure coupling for the resolution of the Navier-Stokes equations. The pressure-correction approaches are mainly used in this context but the corrector step is generally not modified consistently to take into account the fictitious domain. A consistent modification of the pressure-projection for a high-order penalty (or penalization) method close to the Hikeno-Kajishima modification for the Immersed Boundary Method is presented here. Compared to the first-order correction required for the $L^2$-penalty methods, the small values of the penalty parameters do not lead to numerical instabilities in solving the Poisson equation. A comparison of the corrected rotational pressure-correction method with the augmented Lagrangian approach which does not require a correction is carried out.

Mots clés: Navier-Stokes equations; Fictitious domain; Velocity-pressure coupling; Augmented Lagrangian; Pressure-correction methods; Projection methods; Fractionnal-step methods; Penalty method; Penalization method; Immersed boundary method; Incompressible flows

Domaines: Modélisation et simulation; Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Arthur Sarthou, Stéphane Vincent, Jean-Paul Caltagirone. Consistant velocity-pressure coupling for second-order L2-penalty and direct-forcing methods. 2011. ⟨hal-00592079⟩