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Unconditionally energy stable, splitting schemes for magnetohydrodynamic equations
Author(s) -
Wang Kun,
Zhang GuoDong
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4934
Subject(s) - magnetohydrodynamic drive , magnetohydrodynamics , mathematics , nonlinear system , projection (relational algebra) , stability (learning theory) , energy (signal processing) , projection method , flow (mathematics) , saddle point , mathematical optimization , computer science , algorithm , physics , geometry , magnetic field , statistics , quantum mechanics , machine learning , dykstra's projection algorithm
In this article, we propose first‐order and second‐order linear, unconditionally energy stable, splitting schemes for solving the magnetohydrodynamics (MHD) system. These schemes are based on the projection method for Navier–Stokes equations and implicit–explicit treatments for nonlinear coupling terms. We transform a double saddle points problem into a set of elliptic type problems to solve the MHD system. Our schemes are efficient, easy to implement, and stable. We further prove that time semidiscrete schemes and fully discrete schemes are unconditionally energy stable. Various numerical experiments, including Hartmann flow and lid‐driven cavity problems, are implemented to demonstrate the stability and the accuracy of our schemes.