Volume‐tracking of subgrid particles

A new PLIC‐VOF method is proposed to track deformable particles, such as bubbles and liquid droplets, that can be smaller than the grid spacing. The idea is to replace the surface normal (SN) calculation used in the PLIC, by the SN vector obtained from partial differential equations that are solved together with the advection algorithm. The equations for the evolution of SN vector are derived, and examined by using the first‐order and the second‐order upwind schemes. Since the normal vector is defined in every cell, the method generally improves the accuracy at low grid resolution. It is found that a normal vector of zero magnitude is located at the centroid of a particle, to second‐order accuracy for small particles. The motion of a subgrid particle is controlled by the arrival of the zero vector in the present PLIC/SN method, so that the particle can be translated at the right speed without any additional treatment. This has been numerically verified by simulating a particle of one‐tenth of grid spacing traveling in three different directions, in addition to a few typical test cases. Copyright © 2010 John Wiley & Sons, Ltd.