@Article{CiCP-20-1163,
author = {Shixin Xu and Weiqing Ren},
title = {Reinitialization of the Level-Set Function in 3d Simulation of Moving Contact Lines},
journal = {Communications in Computational Physics},
year = {2018},
volume = {20},
number = {5},
pages = {1163--1182},
abstract = {<p style="text-align: justify;">The level set method is one of the most successful methods for the simulation
of 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 type
of 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 requires
a boundary condition in certain regions on the wall. In this work, we propose to use
the dynamic contact angle, which is extended from the contact line, as the boundary
condition for the reinitialization of the level set function. The reinitialization equation
and the equation for the normal extension of the dynamic contact angle form a coupled
system and are solved simultaneously. The extension equation is solved on the
wall and it provides the boundary condition for the reinitialization equation; the level
set function provides the directions along which the contact angle is extended from
the contact line. The coupled system is solved using the 3rd order TVD Runge-Kutta
method and the Godunov scheme. The Godunov scheme automatically identifies the
regions where the angle condition needs to be imposed. The numerical method is illustrated
by examples in three dimensions.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.210815.180316a},
url = {http://global-sci.org/intro/article_detail/cicp/11186.html}
}