An Immersed Interface Method for Axisymmetric Electrohydrodynamic Simulations in Stokes flow

A numerical scheme basedon the immersed interfacemethod (IIM) is devel- oped to simulate the dynamics of an axisymmetric viscous drop under an electric field. In this work, the IIM is used to solve both the fluid velocity field and the electric po- tential field. Detailed numerical studies on the numerical scheme show a second-order convergence. Moreover, our numerical scheme is validated by the good agreement with previous analytical models (1,31,39), and numerical results from the boundary integral simulations (17). Our method can be extended to Navier-Stokes fluid flow with nonlinear inertia effects. AMS subject classifications: 76W05, 65M06, 65M12