A surface marker algorithm coupled to an area-preserving marker redistribution method for three-dimensional interface tracking

In this work we present a coupled marker and local area conservation algorithm for reconstruction and advection of interfaces in three-dimensional space. The interface is described by a set of closed lines which define a coarse Lagrangian quadrangular mesh in the fixed computational grid. Fixed markers are located where the lines cross and are maintained during the whole simulation. At each time step the interface is first reconstructed and then all markers are advected by following streamlines. In the reconstruction step, new markers are determined by computing the intersections of the interface lines with the grid cell faces and by adding area conservation markers between fixed and grid intersection markers. Intersection and conservation markers defined at the previous time step are discarded. The method maintains a smooth geometrical description of the interface for both two-dimensional and three-dimensional tests with accurate volume conservation even in very challenging situations where the fluid bodies progressively deform and stretch developing localized regions with very high curvature and thin fluid filaments. The method compares favorably with front capturing methods, such as Volume-of-Fluid and level set, and other hybrid techniques, such as the particle level set method.