Contact Line Advection using the Level Set Method

In this work, we consider the geometrical problem of the numerical advection of a hypersurface by a prescribed velocity field in the special case when the hypersurface intersects the domain boundary. This problem emerges from the discretization of continuum models for dynamic wetting. The kinematic evolution equation [1], [2] expresses the fundamental relationship between the rate of change of the contact angle and the structure of the transporting velocity field. We employ a simple version of the Level Set method to numerically solve the hyperbolic transport equation for the interface in two dimensions. The results are validated against an analytic solution of the kinematic evolution equation. Full access to the data and C++‐implementations is provided via an open research data repository [3].