Level set reinitialization at a contact line

When a level-set signed distance function is reinitialized in the vicinity of a contact line, there is a “blind spot” that prevents an accurate reconstruction of a signed distance function. The numerical method can create parasitic velocity currents near this region. If additional contact-line physics are included, the parasitic velocity currents would pollute the solution and alter the physical behavior. In this study, a modified reinitialization routine is proposed that combines the standard Hamilton–Jacobi equation with a relaxation equation for those grid cells along a wall in the blind spot. Two test cases, an angled fluid wedge (zero curvature) and a circular fluid arc (constant curvature), are used to evaluate the numerical error induced by different methods. The proposed method has less numerically-induced interface distortion than other techniques examined. Furthermore, this routine can be easily extended to three dimensions. Drops sliding on a wall are simulated in both two and three dimensions to demonstrate the advantages of this method. A spreading fluid interface further shows that this method allows contact lines to merge naturally.