Connectivity-free front tracking method for multiphase flows with free surfaces

In this study, a connectivity-free front tracking method is developed to simulate multiphase flows with free surfaces. This method is based on the point-set method which does not require any connectivities between interfacial points to represent the interface. The main advantage of the connectivity-free approach is the easiness in re-constructing the interface when large topology change occurs. It requires an indicator field to be constructed first based on the existing interface and the surface curvature and normal are then computed using the indicator field. Here, we adopt the reproducing kernel particle method (RKPM) interpolation function that provides the ability to deal with free-surface flows and the flexibility of using non-uniform meshes when local fine resolution is needed. A points regeneration scheme is developed to construct smooth interfaces and to automatically handle topology changes. The mass conservation is verified by performing a single vortex advection test. Several 2-D and 3-D numerical tests including an oscillating droplet, dam-breaking, two droplet impacting and multi-bubble merging are presented to show the accuracy and the robustness of the method.