Stability and error analysis of IMEX SAV schemes for the magneto-hydrodynamic equations

TL;DR

This paper develops and analyzes linear IMEX SAV schemes for magneto-hydrodynamic equations, demonstrating their unconditional energy stability and providing rigorous error estimates, validated through numerical examples.

Contribution

The paper introduces first- and second-order IMEX SAV schemes that are linear, unconditionally energy stable, and come with rigorous error analysis for MHD equations.

Findings

Schemes are linear and require solving linear equations with constant coefficients.

The first-order scheme has proven error estimates in 2D without time step restrictions.

Numerical examples confirm the theoretical stability and accuracy of the schemes.

Abstract

We construct and analyze first- and second-order implicit-explicit (IMEX) schemes based on the scalar auxiliary variable (SAV) approach for the magneto-hydrodynamic equations. These schemes are linear, only require solving a sequence of linear differential equations with constant coefficients at each time step, and are unconditionally energy stable. We derive rigorous error estimates for the velocity, pressure and magnetic field of the first-order scheme in the two dimensional case without any condition on the time step. Numerical examples are presented to validate the proposed schemes.