An interface-preserving level-set method for interfacial flows with moving contact lines

It is well-known that the level-set methods have poor mass conservation properties, mostly due to the shift of the zero level set during the reinitialization process. In this talk, we present an interface-preserving discontinuous Galerkin method to solve the Hamilton-Jacobi equation for the level-set reinitialization. This reinitialization method essentially causes no mass loss as long as the interface curvature can be resolved by the computational mesh. More importantly, it allows for an easy implementation of the artificial boundary conditions that arise when the interfaces intersect the domain boundaries at non-90 degree angles. We solve the level-set and flow equations by finite element methods based on the finite-element library deal.II. A generalized Navier condition is adopted to relax the moving contact line singularity. We first compute a rising bubble for code validation as well as an illustration of the mass conservation performance. We then compute the advancing menisci in a Poiseuille flow, which are validated against Cox’s hydrodynamic theory. We will also present some preliminary results on a non-iterative model for contact-angle hysteresis.