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Consistent Velocity-Pressure Coupling for Second-Order L 2 -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 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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-02862463
Contributor : Stéphane Vincent <>
Submitted on : Tuesday, June 9, 2020 - 3:23:21 PM
Last modification on : Monday, August 31, 2020 - 9:36:05 AM

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Arthur Sarthou, Stéphane Vincent, Jean-Paul Caltagirone. Consistent Velocity-Pressure Coupling for Second-Order L 2 -Penalty and Direct-Forcing Methods. Fluids, MDPI, 2020, ⟨10.3390/fluidsxx010005⟩. ⟨hal-02862463⟩

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