A Conservative Cell-Based Unsplit Volume of Fluid Advection Scheme for Three-Dimensional Atomization Simulations

The Volume of Fluid (VoF) method is widely used for capturing the interface motion in multi-phase flow simulations. In particular, unsplit geometrical advection schemes have proved well-suited for flows with complex topologies. In the cell-based approach, the computational cell is followed along its Lagrangian trajectories and provides a conceptually simple framework for advancing the interface. Thus, this is a semi-Lagrangian method, and enforcing conservation is difficult. This paper presents a cell-based three-dimensional (3D) unsplit advection scheme that is conservative. The method relies on the Hybrid Lagrangian Eulerian Method (HyLEM) of Le Chenadec and Pitsch [3] but additionally ensures discrete conservation by introducing a correction of the projected cell, which is inspired by the 3D flux-based method of Owkes and Desjardins [14] and the two-dimensional cell-based method of Comminal et al. [4]. While the projected cell vertices are evaluated as in HyLEM, additional vertices are introduced to modify the projected cell faces. The positions of those are obtained from conservative flux volumes. The proposed method provides the same accuracy as the method of Owkes and Desjardins [14], but is more efficient. The proposed method is tested in various benchmark cases and applied in an atomization case.