Computation of the curvature field in numerical simulation of multiphase flow

An essential ingredient in the simulation of multiphase fluid flow with surface tension is the accurate computation of the interface curvature. Curvature effects become more significant as we decrease the length scale of the problem at hand and thus accurate computation of curvature is especially important when considering microscale multiphase flows. We compared the curvature field calculated by three methods: the front capturing approach exemplified by the Level Set Method, the front tracking approach exemplified by Tryggvason’s original Front Tracking method and a new Hybrid approach used in the context of the Level Contour Reconstruction Method, LCRM [S. Shin, S.I Abdel-Khalik, V. Daru and D. Juric, Accurate representation of surface tension using the level contour reconstruction method, JCP 203 (2005) 493–516]. We find that both the Level Set and Hybrid LCRM show great improvement if curvature is first calculated directly on the phase boundary and then redistributed back to the underlying grid.