Estimates of surface normal and curvature, reconstruction of continuum surface force model, and elimination of spurious currents

Abstract

SUMMARYA reconstructed continuum surface force (CSF) model is presented for the volume‐of‐fluid (VOF) method in numerical simulations of surface tension‐driven flow. The gradient of VOF function yielded by the one‐direction difference (ODD) algorithm has second‐order accuracy in one direction and exhibits unit pulse function in the other direction. Use of our ODD algorithm for surface normal and curvature improves the accuracy of surface tension force estimate and meets the necessary condition of a circular droplet free of spurious currents. The immersed length, a physical depth of grid cell center introduced in this paper, is computed from VOF function and surface orientation. It is chosen instead of VOF function as weight parameters in the evaluations of density and volumetric surface tension force between interfacial grid cells. Grid cells and control cells are classified into interfacial, sublayer, and interior cells according to their distances to interface. Surface tension is thus constructed within interfacial or sublayer cells. The numerical approach is modified so that flow pressure solutions are sought only at those immersed grid cell centers. The transitional region from one fluid to the other is compressed. Spurious currents by no means grow on free surface in the numerical simulations using our algorithms and reconstructed CSF model. The simulation results agree with the Laplace pressure jump across a static circular free surface or experimental observations. Copyright © 2014 John Wiley & Sons, Ltd.