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：本文研究求解无感磁流体力学（MHD）方程组的数值逼近方法。通过引入标量辅助变量（SAV）技术处理对流项与耦合项，本文为该方程组构造了一阶与二阶格式。所提格式满足线性解耦、无条件能量稳定性，且每个时间步仅需求解一系列常系数微分方程。进一步，本文对一阶格式开展了严格的误差分析，在二维情形下建立了速度、压力、电流密度及电势的最优收敛阶。数值算例验证了理论分析的正确性并展示了格式的数值表现。