This paper presents a fully explicit two-dimensional electrohydrodynamics (EHD) numerical model, which scrutinizes multiphase flows’ dynamics and interactions when exposed to an external electric field. The electrostatic phenomena are interconnected with hydrodynamics through the resolution of the Maxwell’s equations, which are simplified along with its boundary conditions based on the leaky dielectric model. An explicit smoothed particle hydrodynamics formulation is developed to discretize the Poisson equation in order to calculate the electric potential and the consequent forces that are derived through the divergence of the Maxwell’s equations. This approach offers the advantage of having low computational costs while simultaneously simplifying its implementation. Furthermore, to interpolate the physical properties on the discretized domain, particles, our recently proposed quartic-spiky kernel function is used. Comparisons with both analytical and numerical data from literature are performed. Then, various test cases are presented and new benchmarks are incorporated. This includes the EHD of a drop deformation within a fluid, interactions between two and three drops, as well as the Rayleigh–Taylor instability under an external electric field. The results herein presented clearly illustrate the strong capability of the proposed method and its robustness in simulating multiphase flows with intricate interfaces under a constant external electric field.

中文翻译：

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基于漏介电模型的二维电流体动力学多相流完全显式不可压缩平滑粒子流体动力学方法


本文提出了一个完全明确的二维电流体动力学（EHD）数值模型，该模型仔细研究了暴露于外部电场时多相流的动力学和相互作用。静电现象通过麦克斯韦方程组的解析与流体动力学相互关联，麦克斯韦方程组及其基于漏介电模型的边界条件得到了简化。开发了显式平滑粒子流体动力学公式来离散泊松方程，以便计算通过麦克斯韦方程组的散度导出的电势和随之而来的力。这种方法具有计算成本低、同时简化其实现的优点。此外，为了在离散域、粒子上插值物理属性，使用了我们最近提出的四次尖峰核函数。与文献中的分析数据和数值数据进行比较。然后，提出各种测试用例并纳入新的基准。这包括流体内液滴变形的 EHD、两个和三个液滴之间的相互作用，以及外部电场下的瑞利-泰勒不稳定性。本文给出的结果清楚地说明了所提出的方法的强大能力及其在恒定外部电场下模拟具有复杂界面的多相流的鲁棒性。