Accuracy and convergence of the curvature and normal vector discretizations for 3D static and dynamic front-tracking interfaces

In this work, three classes of numerical methods are investigated to evaluate the mean curvature, the unit normal vector and the surface tension on a front tracking interface encountered in the simulation of multiphase flows with separated phases. The Laplace-Beltrami Operator discretization, the Integral Formulation of the surface tension and the Surface Reconstruction technique are well-known methods used in the literature, but whose accuracy, robustness and convergence properties are seldom studied. In a first step, different variants of these methods are presented and compared against each other on a static analytical surface to measure their sensitivity to the size and regularity of the mesh. Then, to assess the influence of the surface advection scheme and the remeshing procedures, two original and time dependent analytical surfaces have been developed, leading to a ligament formation or the birth of a drop/bubble on a flat surface/liquid film. Comparisons to such dynamical surfaces are especially useful and significant, since they highlight the sensitivity of numerical methods for the interface property calculation to the errors produced by the Lagrangian transport of the front-tracking surface. Finally, the accuracy of the different approximations is correlated to their computation time, so that the user may choose the most appropriate method according to the desired accuracy and cost.