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.

翻译：本文考虑数值逼近求解无感磁流体力学方程的方法。采用标量辅助变量（SAV）法来处理对流和耦合项，提出一些一阶和二阶格式。这些格式是线性的、分离的、无条件能量稳定的，并且每个时间步只需要解一系列常系数的微分方程。进一步给出了一阶格式的严密误差分析，证明了在二维情形下，速度、压力、电流密度和电势的最优收敛率。通过数值实验验证了理论结果，并展示了数值格式的性能。