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Keywords = fractionnal-step methods

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23 pages, 2099 KB  
Article
Consistent Velocity–Pressure Coupling for Second-Order L2-Penalty and Direct-Forcing Methods
by Arthur Sarthou, Stéphane Vincent and Jean-Paul Caltagirone
Fluids 2020, 5(2), 92; https://doi.org/10.3390/fluids5020092 - 10 Jun 2020
Cited by 1 | Viewed by 2849
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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