We developed a finite difference ink jet simulation code based on the coupled level set projection method on nonrectangular grids. A slipping contact model was applied to resolve the contradiction of the moving contact point and the no-slip condition. For practical applications, the code was connected to an equivalent circuit which receives a dynamic voltage and simulates the ink behavior in the supply channel under the influence of ink cartridge, vibration plate, and PZT actuator. Simulation results of continuous droplet ejections are given and discussed.