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

Abstract : 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.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [42 references]

https://hal.archives-ouvertes.fr/hal-00592079
Contributor : Arthur Sarthou <>
Submitted on : Wednesday, May 11, 2011 - 11:11:53 AM
Last modification on : Monday, June 15, 2020 - 7:08:43 PM
Long-term archiving on: : Friday, August 12, 2011 - 2:39:11 AM

### File

SMPM_corr_press_sarthou.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00592079, version 1

### Citation

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

Record views