Variational multi-scale modeling of interfacial flows with a balanced-force surface tension model

In this paper, we present a level-set based formulation to simulate interfacial flows on unstructured meshes. The residual-based variational multiscale formulation (VMS) is employed to solve the coupled Navier-Stokes and level-set convection equations as well as the re-distancing problem based on an Eikonal equation. To suppress the nonphysical currents, we embed a balanced-force surface tension model in the VMS formulation. We compare traditional Brackbill's continuous surface force (CSF) model and the balanced-force CSF model by simulating a series of bubble dynamics on unstructured meshes. We assess the accuracy of both models by comparing with benchmark results, which shows that the VMS formulation with the balanced-force CSF model possesses improved performance. At last, we simulate a droplet impact and crown propagation problem with the balanced-force CSF model. Good agreement with the experimental result is achieved.