@Article{AAMM-18-109,
author = {Ma , Huimin and Huang , Pengzhan},
title = {Fully Discrete Schemes with First- and Second-Order Temporal Accuracy for the Incompressible Magnetohydrodynamic Flow Based on the Generalized Scalar Auxiliary Variable Approach},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2025},
volume = {18},
number = {1},
pages = {109--113},
abstract = {<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>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2023-0325},
url = {http://global-sci.org/intro/article_detail/aamm/24521.html}
}