A locally extended finite element method for the simulation of multi-fluid flows using the Particle Level Set method

The simulation of immiscible two-phase flows on Eulerian meshes requires the use of special techniques to guarantee a sharp definition of the evolving fluid interface. This work describes the combination of two distinct technologies with the goal of improving the accuracy of the target simulations. First of all, a spatial enrichment is employed to improve the approximation properties of the Eulerian mesh. This is done by injecting into the solution space new features to make it able to correctly resolve the solution in the vicinity of the moving interface. Then, the Lagrangian Particle Level Set (PLS) method is employed to keep trace of the evolving solution and to improve the mass conservation properties of the resulting method. While the local enrichment can be understood in the general context of the XFEM, we employ an element-local variant, which allows preserving the matrix graph, and hence highly improving the computational efficiency.