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We consider the interface advection problem by a prescribed velocity field inthe special case when the interface intersects the domain boundary, i.e. in thepresence of a contact line. This problem emerges from the discretization ofcontinuum models for dynamic wetting. The kinematic evolution equation for thedynamic contact angle (Fricke et al., 2019) expresses the fundamentalrelationship between the rate of change of the contact angle and the structureof the transporting velocity field. The goal of the present work is to developan interface advection method that is consistent with the fundamentalkinematics and transports the contact angle correctly with respect to aprescribed velocity field. In order to verify the advection method, thekinematic evolution equation is solved numerically and analytically (forspecial cases). We employ the geometrical Volume-of-Fluid (VOF) method on astructured Cartesian grid to solve the hyperbolic transport equation for theinterface in two spatial dimensions. We introduce generalizations of the Youngsand ELVIRA methods to reconstruct the interface close to the domain boundary.Both methods deliver first-order convergent results for the motion of thecontact line. However, the Boundary Youngs method shows strong oscillations inthe numerical contact angle that do not converge with mesh refinement. Incontrast to that, the Boundary ELVIRA method provides linear convergence of thenumerical contact angle transport.

Contact line advection using the geometrical Volume-of-Fluid method