In this work, we propose a lattice Boltzmann method to model the electrohydrodynamic (EHD) conduction phenomenon in dielectric liquids. To incorporate the effect of the source term appeared in the charge conservation equations, some unified force terms that can be implemented locally are delicately designed in the charge evolution equations. We further validate the present model against some analytical solutions as well as experimental data for several problems, and a good agreement is obtained. Then it is used to study the fluid circulation in a square cavity generated by EHD conduction phenomenon, and the numerical results indicate that the geometric scale and the difference in the mobilities of the positive and negative charges could play an important role in studying EHD conduction phenomenon. Further, to analyze the characteristics of the EHD conduction mechanisms in the ohmic and saturation regimes, the influences of the conduction number $W_0$ as well as the parameter $\beta ,$ which is related to Onsager effect, are also investigated, and the numerical results fit well with previous work.

在这项工作中，我们提出了一种格子Boltzmann方法来模拟介电液体中的电流体动力学（EHD）传导现象。为了合并电荷守恒方程中出现的源项的影响，在电荷演化方程中精心设计了一些可以局部实现的统一力项。我们针对一些分析解决方案以及一些问题的实验数据进一步验证了本模型，并获得了良好的共识。然后用于研究由EHD传导现象产生的方腔内的流体循环，数值结果表明，几何尺度和正负电荷迁移率的差异可能对研究EHD传导现象起重要作用。 。进一步，${\mathrm{w\; ^}}_0$ 以及参数 $\beta ，$ 还对与Onsager效应有关的数值进行了研究，数值结果与以前的工作非常吻合。