A generalized level-set immersed interface method with application

The level-set based immersed interface method (IIM) for the elliptic interface problem is generalized to accommodate the interface intersecting the boundary. Finite difference schemes accounting for the jump conditions together with Neumann/periodic boundary condition are derived. It is easy for implementation. Numerical evidence indicates that the generalized IIM achieves the second-order accuracy in both solution and gradient. The method is coupled with a continuum surface method for simulating electrohydrodynamics with moving contact lines. Simulations demonstrate rich behaviors of the droplet. The effect of the electric field is studied. Although the method is presented in 2D, its extension to 3D is straight forward.