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Abstract We investigate the temporal accuracy of two generalized‐ schemes for the incompressible Navier‐Stokes equations. In a widely‐adopted approach, the pressure is collocated at the time steptn + 1while the remainder of the Navier‐Stokes equations is discretized following the generalized‐ scheme. That scheme has been claimed to besecond‐order accurate in time. We developed a suite of numerical code using inf‐sup stable higher‐order non‐uniform rational B‐spline (NURBS) elements for spatial discretization. In doing so, we are able to achieve high spatial accuracy and to investigate asymptotic temporal convergence behavior. Numerical evidence suggests that onlyfirst‐order accuracyis achieved, at least for the pressure, in this aforesaid temporal discretization approach. On the other hand, evaluating the pressure at the intermediate time step recovers second‐order accuracy, and the numerical implementation is simplified. We recommend this second approach as the generalized‐ scheme of choice when integrating the incompressible Navier‐Stokes equations.
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New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis
We construct new first- and second-order pressure correctionschemes using the scalar auxiliary variable approach for the Navier-Stokes equations. These schemes are linear, decoupled and only require solving a sequence of Poisson type equations at each time step. Furthermore, they are unconditionally energy stable. We also establish rigorous error estimates in the two dimensional case for the velocity and pressure approximation of the first-order scheme without any condition on the time step.
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- Award ID(s):
- 2012585
- PAR ID:
- 10329244
- Date Published:
- Journal Name:
- Mathematics of Computation
- Volume:
- 91
- Issue:
- 333
- ISSN:
- 0025-5718
- Page Range / eLocation ID:
- 141 to 167
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1090/mcom/3651
