A stabilized finite volume method based on the rotational pressure correction projection for the time-dependent incompressible MHD equations

Abstract

This paper presents an efficient numerical scheme for solving the time-dependent incompressible Magnetohydrodynamics (MHD) equations based on the rotational pressure correction projection method within the finite volume framework. Utilizing the lowest equal-order mixed finite element pair ($P_1-P_1-P_1$) to approximate the velocity, magnetic and pressure fields, our numerical scheme satisfies the discrete inf–sup condition by the pressure projection stabilization. To tackle the coupling inherent in the time-dependent incompressible MHD equations,the rotational pressure correction projection method is introduced to split the original problem into several linear subproblems. The unconditional stability of numerical schemes are provided,optimal error estimates in both $L^2$ and $H^1$-norms of numerical solutions are also presented. Finally, some numerical results are given to verify the established theoretical findings and show the performances of the considered numerical schemes.