Consistent Velocity-Pressure Coupling for Second-Order L 2 -Penalty and Direct-Forcing Methods

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

1 I2M - Institut de Mécanique et d'Ingénierie
2 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

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 widely 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 Ikeno-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: Mécanique des fluides [physics.class-ph]

Arthur Sarthou, Stéphane Vincent, Jean-Paul Caltagirone. Consistent Velocity-Pressure Coupling for Second-Order L 2 -Penalty and Direct-Forcing Methods. Fluids, 2020, ⟨10.3390/fluids5020092⟩. ⟨hal-02862463⟩