New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis

Li, Xiaoli; Shen, Jie; Liu, Zhengguang

doi:10.1090/mcom/3651

New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis
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Math. Comp. 91 (2022), 141-167 Request permission

Abstract:

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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