A Characteristic Finite Element Analysis with a Level Set Method for an Electrohydrodynamic Flow

Abstract

A numerical simulation of an electrohydrodynamic flow is performed. The purpose of this analysis is to establish a scheme for accurate and robust analyses of electrohydrodynamic problems. The method used here is a level set method based on the finite element method. In our problem we have two material derivatives, one in the Navier-Stokes equations, the other in the advection equation for the interface of two fluids, air and a liquid. We apply a first order characteristic method to approximate these material derivatives, where an integral including upstream information is calculated with an accurate computation. Some results including the surface tension effect are presented comparing with the Lagrangian method that the author previously obtained.