Reinitialization of the Level-Set Function in 3d Simulation of Moving Contact Lines (Communications in Computational Physics, 2020)
The level set method is one of the most successful methods for the simulationof multi-phase flows. To keep the level set function close the signed distance function,the level set function is constantly reinitialized by solving a Hamilton-Jacobi typeof equation during the simulation. When the fluid interface intersects with a solid wall,a moving contact line forms and the reinitialization of the level set function requiresa boundary condition in certain regions on the wall. In this work, we propose to usethe dynamic contact angle, which is extended from the contact line, as the boundarycondition for the reinitialization of the level set function. The reinitialization equationand the equation for the normal extension of the dynamic contact angle form a coupledsystem and are solved simultaneously. The extension equation is solved on thewall and it provides the boundary condition for the reinitialization equation; the levelset function provides the directions along which the contact angle is extended fromthe contact line. The coupled system is solved using the 3rd order TVD Runge-Kuttamethod and the Godunov scheme. The Godunov scheme automatically identifies theregions where the angle condition needs to be imposed. The numerical method is illustratedby examples in three dimensions.