(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
Based on the generalized scalar auxiliary variable approach and vector penalty projection method, some fully discrete schemes with first- and second-order accuracy in time direction are constructed for solving the incompressible magnetohydrodynamic model. It is a combination of mixed finite element approximation for spatial discretization and first-order backward Euler/second-order backward differential formula for temporal discretization. The proposed schemes own several features: it decouples unknown physical variables and linearizes the nonlinear terms, then it only needs to solve some linear equations at each temporal level; although the divergence of numerical velocity is not exactly equal to zero, it can approximately meet the mass conservation when one takes small penalty parameter; while the computation of the velocity and pressure are decoupled, numerical results show that the velocity and pressure can reach second-order accuracy in time. The resulting schemes are supported by numerical analysis and simulation.