变密度MHD方程完全解耦且无条件能量稳定的数值算法  

Fully Decoupled and Unconditionally Energy-stable Schemes for MHD Equations with Variable Density

作　　者：王兆伟 王旦霞 WANG Zhaowei;WANG Danxia(School of Mathematics,Taiyuan University of Technology,Jinzhong Shanxi 030600,China)

机构地区：[1]太原理工大学数学学院,山西晋中030600

出　　处：《广西师范大学学报(自然科学版)》2025年第2期193-206,共14页Journal of Guangxi Normal University:Natural Science Edition

基　　金：山西省基础研究计划(202203021211129);山西省回国留学人员科研资助项目(2021-029);山西省国际合作平台项目(202104041101019)。

摘　　要：本文致力于对变密度不可压缩磁流体动力学方程建立全解耦且无条件能量稳定的数值算法。首先,引入辅助中间速度变量,分别与Gauge-Uzawa方法的对流形式和守恒形式相结合,建立2个一阶半离散数值算法。2个算法成功地解耦所有耦合项,使得只需在离散级求解线性化子问题,所以大大提高计算效率。其次,证明2个算法都是无条件能量稳定的,并且对流形式的有限元全离散化算法也是无条件能量稳定的。最后,用数值实验验证解耦方案的准确性和有效性。This article is dedicated to establishing fully decoupled and unconditionally energy-stable numerical algorithms for the incompressible magnetohydrodynamics(MHD)equations with variable density.The overall idea is as follows:Firstly,two first-order semi-discrete numerical algorithms are developed based on the Gauge-Uzawa method in both convective and conserved forms.Since both algorithms successfully decouple all coupled terms,only the linearized subproblems need to be solved at the discrete level,which significantly improve computational efficiency.Secondly,it is demonstrated that both algorithms are unconditionally energy-stable,and the finite element fully discrete algorithm in convective form is also unconditionally energy-stable.Finally,numerical experiments confirm the accuracy and effectiveness of the decoupled schemes.

关 键 词：磁流体动力学 全解耦 无条件能量稳定 变密度 Gauge-Uzawa方法 

分 类 号：O242[理学—计算数学]