Volume conservation method for the three-dimensional front-tracking method

Abstract

A method to conserve the volume of dispersed components (e.g. bubbles and droplets) in a viscous fluid is proposed for the front-tracking method (Unverdi and Tryggvason, 1992; Tryggvason et al., 2001). The method adjusts the coordinates of each nodal points on the interface (or Lagrangian markers) along the velocity vector. A simplified algorithm determines the new position of the marker independently from those of the surrounding nodes, which allows the volume correction to be accomplished efficiently. The results show that the volume of a deformed fluid particle is kept constant within errors of O(10⁻⁷) ～ O(10⁻⁶). The effects of the time step size and the frequency of the volume correction are investigated. The method is applicable to enclosed structures of non-spherical geometry (e.g. oblate/prolate/spherical-cap fluid particles).