A PLIC volume tracking method for the simulation of two-fluid flows

Abstract

Numerical methodologies for computer simulations of two-fluid flows are presented. These methodologies fall into the category of volume tracking methods with piecewise-linear interface calculation (PLIC). The scope of this work is limited to laminar flows of immiscible, non-reacting, incompressible Newtonian fluids, without phase change, in planar two-dimensional geometries. The following novel or enhanced procedures are proposed: a parallelogram scheme for multidimensional advection of the volume-fraction field; a circle-fit technique for the orientation of the interface segments and the calculation of curvature; a novel contact angle treatment; and a staggered formulation for volumetric body forces that can accurately balance pressure forces in the vicinity of the interface. In addition, surface-tension-derived and hydrostatic-derived pressure adjustments are introduced as a means of accurately calculating pressure forces in cells that contain the interface, so as to minimize the non-physical flows that afflict many available volume tracking methods. The proposed method is validated using four test problems that involve simulations of pure advection, a static drop, an oscillating bubble, and a static meniscus. Copyright © 2006 John Wiley & Sons, Ltd.