Unconditional stability and error analysis of an Euler IMEX-SAV scheme for the micropolar Navier-Stokes equations

TL;DR

This paper introduces a new unconditionally energy stable Euler IMEX-SAV scheme for the micropolar Navier-Stokes equations, providing rigorous error analysis and numerical verification of its effectiveness.

Contribution

The paper develops a decoupled, linear, unconditionally energy stable scheme for the micropolar Navier-Stokes equations using SAV and IMEX methods, with proven error estimates.

Findings

The scheme is unconditionally energy stable.

Error estimates are rigorously derived in 2D.

Numerical examples confirm theoretical results.

Abstract

In this paper, we consider numerical approximations for solving the micropolar Navier-Stokes (MNS) equations, that couples the Navier-Stokes equations and the angular momentum equation together. By combining the scalar auxiliary variable (SAV) approach for the convective terms and some subtle implicit-explicit (IMEX) treatments for the coupling terms, we propose a decoupled, linear and unconditionally energy stable scheme for this system. We further derive rigorous error estimates for the velocity, pressure and angular velocity in two dimensions without any condition on the time step. Numerical examples are presented to verify the theoretical findings and show the performances of the scheme.