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

2021/03/31 by Xiaoli Li, Jie Shen, Zhengguang Liu · 6 citations
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations

paper · pdf · doi:10.1090/mcom/3651

Abstract

We construct new first- and second-order pressure correction schemes 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.

Citations

• Numerical solution of the Navier-Stokes equations

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