In this paper, we present two linear time-marching methods for an electrohydrodynamic model of charge transport with variable density dielectric fluid. The model is a highly coupled nonlinear system and an energy dissipation law of the system is discovered. The main feature of the proposed methods is that energy stability is preserved at the fully discrete level by using suitable reformulations of the continuous equations and implicit-explicit time discretization schemes. The mixed finite element method is employed for the spatial discretization. Numerical experiments are carried out to validate the convergence rates and the energy stability of the schemes. To further demonstrate the robustness of the proposed schemes, the effects of injected charges for Rayleigh-Taylor instability and the electro-convection phenomenon between two concentric half-cylinders are simulated. Results show that the injected charges can accelerate the evolutions of Rayleigh-Taylor instability and the number of vortices increases in the electro-convective flow when the inner radius increases.

在本文中，我们为可变密度介电流体的电荷传输电流体动力学模型提供了两种线性时间步长方法。该模型是一个高度耦合的非线性系统，并发现了系统的能量耗散规律。所提出方法的主要特征是通过使用连续方程式的适当重新公式化和隐式-显式时间离散化方案，将能量稳定性保持在完全离散的水平上。混合有限元法用于空间离散化。进行了数值实验，验证了方案的收敛速度和能量稳定性。为了进一步证明所提出方案的鲁棒性，模拟了注入电荷对瑞利-泰勒不稳定性的影响以及两个同心半圆柱体之间的对流现象。结果表明，当内半径增大时，注入的电荷可加速瑞利-泰勒不稳定性的演化，并且电对流中的涡旋数增加。