In this paper, we mainly focus on the numerical approximations of the electro-hydrodynamic system, which couples the Poisson-Nernst-Planck equations and the Navier-Stokes equations. A novel linear, fully-decoupled and energy-stable finite element scheme for solving this system is proposed and analyzed. The fully discrete scheme developed here is employed by the stabilizing strategy, implicit-explicit (IMEX) scheme and a rotational pressure-correction method. One particular feature of the scheme is adding a stabilization term artificially in the conservation of charge density equation to decouple the computations of velocity field from electric field, which can be treated as a first-order perturbation term for balancing the explicit treatment of the coupling term. We rigorously prove the unique solvability, unconditional energy stability and error estimates of the proposed scheme. Finally, some numerical examples are provided to verify the accuracy and stability of the developed numerical scheme.

中文翻译：

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一种用于电流体动力学方程的高效无条件能量稳定有限元方法


在本文中，我们主要关注电流体动力学系统的数值近似，它耦合了泊松-能斯特-普朗克方程和 Navier-Stokes 方程。提出并分析了一种新颖的线性、全解耦和能量稳定的有限元方案来求解该系统。这里开发的完全离散方案被稳定策略、隐式显式 （IMEX） 方案和旋转压力校正方法采用。该方案的一个特点是在电荷密度守恒方程中人为地添加了一个稳定项，以将速度场的计算与电场解耦，这可以被视为一阶扰动项，用于平衡耦合项的显式处理。我们严格证明了所提出的方案的独特可解性、无条件能量稳定性和误差估计。最后，提供了一些数值算例来验证所提数值方案的准确性和稳定性。