Error analysis of the SAV-MAC scheme for the Navier-Stokes equations

TL;DR

This paper introduces an energy-stable SAV-MAC numerical scheme for Navier-Stokes equations, providing rigorous error analysis and confirming second-order accuracy through numerical experiments.

Contribution

It develops a novel SAV-MAC scheme that is unconditionally energy stable and achieves second-order accuracy for velocity and pressure approximations.

Findings

Scheme is unconditionally energy stable.

Achieves second-order accuracy in time and space.

Numerical results verify theoretical error estimates.

Abstract

An efficient numerical scheme based on the scalar auxiliary variable (SAV) and marker and cell scheme (MAC) is constructed for the Navier-Stokes equations. A particular feature of the scheme is that the nonlinear term is treated explicitly while being unconditionally energy stable. A rigorous error analysis is carried out to show that both velocity and pressure approximations are second-order accurate in time and space. Numerical experiments are presented to verify the theoretical results.