Coupling of smoothed particle hydrodynamics and finite volume method for electrohydrodynamic droplet deformation simulation

Abstract

In the numerical simulation of droplet electrohydrodynamic deformation, the grid-based method is difficult to handle the large topological deformation of the droplet interface, while the meshless method is challenging in the enforcement of boundary conditions. Therefore, a coupling method of the smoothed particle hydrodynamics (SPH) method and the finite volume method (FVM) is developed in this paper. In the present coupling method, the SPH method is used to solve the governing equations of the two-phase flow, while the FVM is used to solve the governing equations of the electric field. The realization of the coupling method is based on the information transfer between particles and grids. In order to accurately transfer the electric field force of interface grid nodes to SPH particles, a particle splitting interpolation method is developed. The influences of electrical capillary number, electrical conductivity ratio, and permittivity ratio on droplet deformation are studied. The simulation results are in good agreement with the theoretical predictions, and the coupling method can obtain more accurate numerical results than the pure SPH method. The coupling method can provide a reliable way to investigate complex electrohydrodynamic problems.