LAUSR

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.