A new defect-correction method for the stationary Navier-Stokes equations based on pressure projection

2017 ◽  
Vol 41 (1) ◽  
pp. 250-260 ◽  
Author(s):  
Juan Wen ◽  
Yinnian He
Keyword(s):  
Stokes Equations ◽  
Correction Method ◽  
Navier Stokes ◽  
Defect Correction ◽  
Navier Stokes Equations ◽  
Pressure Projection ◽  
Stationary Navier Stokes Equations

scholarly journals A TWO-LEVEL DEFECT–CORRECTION METHOD FOR NAVIER–STOKES EQUATIONS

2009 ◽  
Vol 81 (3) ◽  
pp. 442-454 ◽  
Author(s):  
QINGFANG LIU ◽  
YANREN HOU
Keyword(s):  
Stokes Equations ◽  
Correction Method ◽  
Navier Stokes ◽  
Stability Factor ◽  
Defect Correction ◽  
Navier Stokes Equations ◽  
Level Method ◽  
High Reynolds ◽  
Standard Galerkin Method ◽  
Correction Step

AbstractA two-level defect–correction method for the steady-state Navier–Stokes equations with a high Reynolds number is considered in this paper. The defect step is accomplished in a coarse-level subspace Hm by solving the standard Galerkin equation with an artificial viscosity parameter σ as a stability factor, and the correction step is performed in a fine-level subspace HM by solving a linear equation. H1 error estimates are derived for this two-level defect–correction method. Moreover, some numerical examples are presented to show that the two-level defect–correction method can reach the same accuracy as the standard Galerkin method in fine-level subspace HM. However, the two-level method will involve much less work than the one-level method.

scholarly journals Consistent Velocity–Pressure Coupling for Second-Order L2-Penalty and Direct-Forcing Methods

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 92
Author(s):  
Arthur Sarthou ◽  
Stéphane Vincent ◽  
Jean-Paul Caltagirone
Keyword(s):  
Stokes Equations ◽  
Correction Method ◽  
Navier Stokes ◽  
Fictitious Domain ◽  
Immersed Boundary ◽  
Navier Stokes Equations ◽  
Pressure Correction ◽  
Numerical Instabilities ◽  
Pressure Projection ◽  
Velocity Pressure

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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