不可压缩磁流体方程的全解耦和无条件能量稳定格式  

Fully Decoupled and Unconditionally Energy Stable Scheme for Incompressible MHD Equations

作　　者：周帅 陈建华 王琨 张国栋 ZHOU Shuai;CHEN Jianhua;WANG Kun;ZHANG Guodong(School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China)

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2024年第1期1-11,共11页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(12171415,12271468)。

摘　　要：提出了一个一阶线性、无条件能量稳定、全解耦格式来求解非线性耦合的磁流体方程。该格式基于鞍点系统的压力投影方法,非线性耦合项隐式-显式处理和引入稳定项来稳定磁场与速度场解耦计算进行构造。该格式将磁流体动力系统转化为几个线性椭圆型问题求解,具有高效、易实现、稳定等优点。同时证明了格式的时间半离散形式和全离散形式都是无条件能量稳定的。最后,通过几组数值实验验证了格式的稳定性和收敛性。In this paper,we propose a first order linear,unconditional energy stable and fully decoupled scheme to solve coupled,nonlinear magnetohydrodynamics equations.The scheme is based on the pressure projection method of saddle point system,the implicit-explicit treatment of nonlinear coupling terms and the introduction of stable terms to stabilize the decoupling calculation of magnetic field with velocity field.The scheme transforms the MHD dynamic system into several linear elliptic problems,which is efficient,easy-to-implement and stable.We prove that the time semi-discrete form and the fully discrete form of the scheme are unconditionally energy stable.Finally,the stability and convergence of the scheme are verified by several numerical experiments.

关 键 词：磁流体动力系统 能量稳定 解耦格式 投影方法 

分 类 号：O242.21[理学—计算数学]