不可压缩MHD-Boussinesq方程基于ESAV方法的一阶Euler解耦算法研究

doi:10.12677/aam.2026.1510403

期刊菜单

不可压缩MHD-Boussinesq方程基于ESAV方法的一阶Euler解耦算法研究
Study of a First-Order Euler Decoupled Algorithm for the Incompressible Magnetohydrodynamics-Boussinesq Equations Based on the Exponential Scalar Auxiliary Variable Approach

DOI: 10.12677/aam.2026.1510403, PDF,
作者: 康妍, 李媛：温州大学数理学院，浙江温州
关键词: 不可压缩MHD-Boussinesq方程；ESAV方法；无条件稳定性；最优误差估计；Incompressible MHD-Boussinesq Equations； ESAV Scheme； Unconditional Stability； Optimal Error Estimates

摘要: 本文研究了一类基于指数型标量辅助变量(ESAV)方法的二维不可压缩MHD-Boussinesq方程的一阶Euler时间离散格式，证明了所提出格式的无条件稳定性，得到了速度、磁场和温度的最优误差估计。最后，给出了数值例子来证明这些收敛速度。

Abstract: In this paper, we study a first-order Euler finite element time-discrete scheme based on the exponential scalar auxiliary variable (ESAV) approach for the two-dimensional incompressible magnetohydrodynamics-Boussinesq equations. The unconditional stability of the proposed scheme is proved. Then we obtain optimal error estimates for the velocity, magnetic field and temperature. Finally, numerical examples are provided to demonstrate these convergence rates.

文章引用：康妍, 李媛. 不可压缩MHD-Boussinesq方程基于ESAV方法的一阶Euler解耦算法研究[J]. 应用数学进展, 2026, 15(10): 137-155. https://doi.org/10.12677/aam.2026.1510403

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