New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis
Numerical Analysis
2020-02-24 v1 Numerical Analysis
Analysis of PDEs
Abstract
We construct new first- and second-order pressure correction schemes using the scalar auxiliary variable (SAV) approach for the Navier-Stokes equations. These schemes are linear, decoupled and only require a sequence of solving Poisson type equations at each time step. Furthermore, they are unconditionally energy stable. We also establish rigorous error estimates for the velocity and pressure approximation of the first-order scheme without any condition on the time step.
Cite
@article{arxiv.2002.09090,
title = {New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis},
author = {Xiaoli Li and Jie Shen and Zhengguang Liu},
journal= {arXiv preprint arXiv:2002.09090},
year = {2020}
}