In this paper, we propose and analyze first-order time-stepping pressure-correction projection scheme for the Navier-Stokes-Planck-Nernst-Poisson equations. By introducing a governing equation for the auxiliary variable through the ionic concentration equations, we reconstruct the original equations into an equivalent system and develop a first-order decoupled and linearized scheme. This scheme preserves non-negativity and mass conservation of the concentration components and is unconditionally energy stable. We derive the rigorous error estimates in the two dimensional case for the ionic concentrations, electric potential, velocity and pressure in the $L^2$- and $H^1$-norms. Numerical examples are presented to validate the proposed scheme.

翻译：本文针对 Navier-Stokes-Planck-Nernst-Poisson 方程，提出并分析了一阶时间步进的压力校正投影格式。通过离子浓度方程引入辅助变量的控制方程，我们将原方程重构为一个等价系统，并发展了一种一阶解耦线性化格式。该格式保持了浓度分量的非负性与质量守恒性，并且是无条件能量稳定的。我们在二维情形下，对离子浓度、电势、速度与压力在 $L^2$-范数与 $H^1$-范数下导出了严格的误差估计。数值算例验证了所提格式的有效性。