Contact line treatment with the sharp interface method

• We presented a method to treat contact points using a sharp interface method.
• The contact point position is controlled by a user-defined function.
• Boundary conditions ensure coupling between the interface and the contact point.
• Curvature approximation ensures coupling between NS-equations and contact point.
• Interpolation for curvature computation must omit discontinuity in distance function.

A technique to handle contact points in a sharp interface method based on the level set method is presented. The contact points are tracked explicitly. The coupling between the contact points and the zero level set is enforced by boundary conditions during reinitialisation of the distance function. For sharp interface methods an accurate approximation of the curvature is important. However, this cannot be obtained by using the conventional central difference methods adjacent to walls since the level set functions are not defined therein. Therefore we propose to use the tracked contact point and the intersection points of the first two grid lines parallel to the wall with the zero contour line of the signed distance function to approximate the contact angle and curvature adjacent to the walls. The method is verified using a capillary rise and a gravity driven two phase channel flow.