The Arbitrary Lagrangian-Eulerian (ALE) framework coupled with a direct boundary tracking technique is proven as an effective method for simulation of capillary jet breakup. In this paper, an alternative derivation of ALE is proposed by introducing instantaneous inertial coordinates. Several improvements for simulations are made, including a linear implicit time scheme, a compact scheme for dynamic boundary conditions, and an iterative direct boundary tracking technique for kinematic boundary conditions. Numerical results are verified and improvements are demonstrated. (C) 2010 Elsevier Ltd. All rights reserved.