STABILITY AND ERROR ANALYSIS OF IMEX SAV SCHEMES FOR THE MAGNETO-HYDRODYNAMIC EQUATIONS

被引：40

作者：

LI, Xiaoli ^{[1
]}

Wang, Weilong ^{[2
,3
]}

Shen, J. I. E. ^{[2
,3
,4
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[3] Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Fujian, Peoples R China

[4] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2022年 / 60卷 / 03期

基金：

中国国家自然科学基金;

关键词：

  magneto-hydrodynamic equations; implicit-explicit schemes; energy stability; error estimates; NAVIER-STOKES EQUATIONS; FINITE-ELEMENT-METHOD; MHD; EFFICIENT; CONVERGENT; ALGORITHMS;

D O I：

10.1137/21M1430376

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct and analyze first-and second-order implicit-explicit schemes based on the scalar auxiliary variable approach for the magneto-hydrodynamic equations. These schemes are linear, only require solving a sequence of linear differential equations with constant coefficients at each time step, and are unconditionally energy stable. We derive rigorous error estimates for the velocity, pressure, and magnetic field of the first-order scheme in the two-dimensional case without any condition on the time step. Numerical examples are presented to validate the proposed schemes.

引用

页码：1026 / 1054

页数：29

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