论文标题
无吸引的MHD方程的SAV方案的稳定性和误差分析
Stability and error analysis of the SAV schemes for the inductionless MHD equations
论文作者
论文摘要
在本文中，我们考虑了用于求解无诱导磁水动力学（MHD）方程的数值近似值。通过利用标量辅助变量（SAV）方法来处理对流和耦合术语，我们为该系统提出了一些一阶和二阶方案。这些方案是线性的，分离的，无条件的能量稳定，只需要在每个时间步骤求解具有恒定系数的一系列微分方程。我们进一步为一阶方案得出了严格的误差分析，并在二维情况下建立了速度，压力，电流密度和电势的最佳收敛速率。提出了数值示例以验证理论发现并显示方案的性能。
In this paper, we consider numerical approximations for solving the inductionless magnetohydrodynamic (MHD) equations. By utilizing the scalar auxiliary variable (SAV) approach for dealing with the convective and coupling terms, we propose some first- and second-order schemes for this system. These schemes are linear, decoupled, unconditionally energy stable, and only require solving a sequence of differential equations with constant coefficients at each time step. We further derive a rigorous error analysis for the first-order scheme, establishing optimal convergence rates for the velocity, pressure, current density and electric potential in the two-dimensional case. Numerical examples are presented to verify the theoretical findings and show the performances of the schemes.
