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

## TL;DR

This paper develops a geometrical Volume-of-Fluid method for accurately simulating contact line advection in dynamic wetting, ensuring correct contact angle transport and analyzing convergence properties of different interface reconstruction techniques.

## Contribution

It introduces a boundary-adapted VOF method for contact line advection that achieves linear convergence of the contact angle, improving upon existing methods.

## Key findings

- Boundary ELVIRA method achieves linear convergence.
- Boundary Youngs method exhibits oscillations and does not converge.
- The proposed method correctly transports the contact angle with prescribed velocity.

## Abstract

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