Vortex Spline Method for Two-Dimensional Rayleigh-Taylor Interfaces Between Inviscid and Perfect Dielectric Fluids with External Electric Fields

Abstract

Interfacial fluid instabilities are widespread in industrial applications. They often lead to mixing between different fluids and play an important role in industrial processes. How to control such interfacial instabilities between dielectric fluids by external electric fields have been actively explored. To understand the effects of external electric fields on the unstable interface and precisely control it, a numerical method capable of providing accurate results is indispensable and highly desired. In this paper, we present a numerical method for systems containing unstable material interfaces between incompressible, inviscid and perfect dielectric fluids in the presence of gravity and external electric fields in two dimensions. We extend the formulation of vortex sheets in the literature from hydrodynamics to electrohydrodynamics, and derive a numerical method in which the computation of both velocity and electric field is only conducted at the one-dimensional material interface. Non-uniform one-dimensional meshes are used to represent the interface shape, which captures the dominant features with fewer nodes. High-order regularization for the Birkhoff-Rott integral in the literature [1] is implemented to control the numerical instabilities. We implement a dynamic mesh adjustment algorithm to further improve the efficiency and robustness of numerical solutions. Validation studies on the convergence and accuracy are conducted.