摘要
本文对理想磁流体方程建立了一个有限元.该有限元在时间上采用隐式欧拉离散并利用Picard线性化方法进行解耦和线性化处理,在空间上则分别采用连续分片线性元逼近密度、流速及压力,用NE0元和RT0元逼近电场和磁场.此外该有限元还添加了稳定项以弥补缺失的耗散项.本文证明,半离散格式是无条件能量稳定的,全离散格式能够保持磁场无散条件.数值算例验证了有限元的收敛性、能量稳定性及保持磁场无散条件的能力.
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 NE_(0) and RT_(0) elements 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.Numerical examples demonstrate the convergence,energy stability and preservation of divergence-free condition of the finite element.
作者
唐豪杰
代佳佳
张世全
贺巧琳
TANG Hao-Jie;DAI Jia-Jia;ZHANG Shi-Quan;HE Qiao-Lin(School of Mathematics,Sichuan University,Chengdu 610065,China;School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)
出处
《四川大学学报(自然科学版)》
北大核心
2025年第4期831-837,共7页
Journal of Sichuan University(Natural Science Edition)
基金
四川省自然科学基金(2023NSFSC0075)。
关键词
有限元
磁流体方程
无散条件
EULER方法
Finite element
Magneto-hydrodynamics equation
Divergence-free
Euler method
