In this paper, we present a three-dimensional (3D) reconstruction algorithm for Cartesian grids and a split advection algorithm which is based on a two-dimensional (2D) Eulerian-Lagrangian scheme that conserves mass exactly for incompressible flows. In the Volume-of-Fluid/Piecewise Linear Interface Calculation (VOF/PLIC) method a linear function in every grid cell cut by the interface approximates the free surface or the surface between two immiscible phases. The reconstruction is not continuous, and not accurate in regions with high surface curvature or when the interface develops thin filaments. Therefore, we have developed a new 2D mixed markers and VOF algorithm that follows the motion of a smooth interface with a good conservation of volume. Results are shown for flows with nonconstant vorticity.

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