TY - JOUR
T1 - Fully Discrete Schemes with First- and Second-Order Temporal Accuracy for the Incompressible Magnetohydrodynamic Flow Based on the Generalized Scalar Auxiliary Variable Approach
AU - Ma , Huimin
AU - Huang , Pengzhan
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 109
EP - 113
PY - 2025
DA - 2025/10
SN - 18
DO - http://doi.org/10.4208/aamm.OA-2023-0325
UR - https://global-sci.org/intro/article_detail/aamm/24521.html
KW - Magnetohydrodynamic model, stability analysis, generalized scalar auxiliary variable, vector penalty projection.
AB - <p style="text-align: justify;">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.</p>