Second order unconditional linear energy stable, rotational velocity correction method for unsteady incompressible magneto-hydrodynamic equations

In this paper, we present a second order decoupled time discretization method for solving the unsteady incompressible magneto-hydrodynamic (M H D) equations. The method is mainly based on the rotational velocity correction projection scheme and extrapolation algorithm. The semi-implicit and extrapolation treatments are used to deal with the hydrodynamic equation and the magnetic equation nonlinear terms respectively. We prove the unconditional energy stability for the proposed scheme by means of a key technique Gauge-Uzawa format. To verify the effectiveness of the presented scheme, we test a series of numerical experiments: accuracy test, stability test, flow around a cylinder test and driven cavity flow problem.

Automated summary

In this paper, a second order decoupled time discretization method for solving the unsteady incompressible magneto-hydrodynamic equations is presented. The method utilizes rotational velocity correction projection scheme and extrapolation algorithm to handle the hydrodynamic equation and the magnetic equation nonlinear terms respectively. The unconditional energy stability of the proposed scheme is proven using the Gauge-Uzawa format. Numerical experiments including accuracy test, stability test, flow around a cylinder test and driven cavity flow problem are conducted to verify the effectiveness of the presented scheme.