A second-order scheme based on blended BDF for the incompressible MHD system

For the incompressible MHD equations, we present a fully discrete second-order-in-time scheme based on a blended BDF and extrapolation treatments for nonlinear terms. The proposed scheme is more accurate than the two-step BDF with additional nominal computational time and is still A-stable. Then, unconditional stability, long-time stability, and optimal convergence rate of the scheme are presented. At last, the numerical findings are verified by comparison with the two-step BDF scheme in several 2D and 3D numerical experiments.

Automated summary

In this paper, a fully discrete second-order-in-time scheme for the incompressible MHD equations is proposed, which utilizes blended BDF and extrapolation treatments for nonlinear terms. The scheme is shown to be more accurate than the traditional two-step BDF scheme, while maintaining A-stability. The unconditional stability, long-time stability, and optimal convergence rate of the scheme are discussed, and numerical experiments with comparison to the two-step BDF scheme are conducted to verify the findings.