Abstract
The Arbitrary Lagrangian Eulerian (ALE) framework coupled with some boundary tracking techniques is proven to be an effective method for simulation of freeโsurface flows. In this paper, a special ALE framework is derived with clarification of three velocities, the notion of meshโfrozen and fieldโfrozen, and the notion of tentatively inertial coordinates. A weighted integral ALE governing equations are formulated on generic coordinates and discretized with a finite element method and linear implicit time scheme. The system is solved with a discrete operator splitting technique and superpositionโbased logistic parallelization. The formulation and implementation are verified through several fixedโgeometry problems and a reasonably good parallel performance is observed. Capillary jet flow is the main problem of the paper and the numerical techniques for boundary tracking are elaborated, which include an indirect boundary tracking of flux method and an iterative direct boundary tracking method. Also, a highโorder compact scheme for dynamic boundary condition and a squeeze technique for kinematic boundary condition are adopted. The axisymmetric jet breakup is studied in detail and numerical results match with the published data very well. Numerical accuracy and sensitivity are studied, including effects of element type, time scheme, compact scheme, and boundary tracking techniques. Copyright ยฉ 2010 John Wiley & Sons, Ltd.