An improved level set method with hyperbolic tangent regularization and a potential-form interfacial force

Level set method has long been renowned for its ease of use and it can be easily extended to higher dimensions. Level set method is deemed as a sharp interface method and uses the signed distance function as the kernel. However, level set method is facing a couple of challenges, including the discretization of the curvature-based interfacial tension, and the regularization of the Heaviside function, which is used to indicate phases. In this paper, an improved level set method is presented. The key improvements lie in the regularization of the Heaviside function and the use of the interfacial force model. Given the complexity of the curvature-based interfacial tension model, the potential-form model, which is often employed in phase field method and is much simpler in form, is utilized. The improved level set model is then coupled with the Navier-Stokes equation for two-phase flow simulations. The model was tested in two cases, one about droplet impact and the other about the spurious flow in a static droplet. The performance of the two interfacial force models was compared.