四川大学学报（自然科学版）2025，Vol.62Issue(4)：831-837,7.DOI:10.19907/j.0490-6756.240037
磁流体方程保持严格无散条件的有限元
A finite element for magneto-hydrodynamic equation preserving divergence-free condition
摘要
Abstract
In this paper,a finite element is established for the magneto-hydrodynamics equation.In the finite element,the implicit Euler method is utilized for the time discretization and the Picard linearization method is utilized for the decoupling and linearization processing.For the spatial discretization,the continuous piecewise linear elements are employed to approximate the density,flow velocity and pressure,and the NE0 and RT0 el-ements are used to approximate the electric field and magnetic field,respectively.Besides,a stabilization term is added to compensate the lack of dissipation.The unconditional energy stability of the semi-discrete scheme as well as the preservation of divergence-free condition of the fully discrete scheme are proved.Nu-merical examples demonstrate the convergence,energy stability and preservation of divergence-free condition of the finite element.关键词
有限元/磁流体方程/无散条件/Euler方法Key words
Finite element/Magneto-hydrodynamics equation/Divergence-free/Euler method分类
数理科学引用本文复制引用
唐豪杰,代佳佳,张世全,贺巧琳..磁流体方程保持严格无散条件的有限元[J].四川大学学报（自然科学版）,2025,62(4):831-837,7.基金项目
四川省自然科学基金(2023NSFSC0075) （2023NSFSC0075）
