Shallow flows, characterized by having a thickness much smaller than their lateral extent, can often be modeled by a depth-averaged (shallow-water or 2.5 dimensional) approximation.
Average fluid velocities are computed in the layer and the top fluid surface is free to move, which leads to a changing fluid-layer thickness. The advantages of this approach are its speed
and simplicity over full three-dimensional simulations.
One complication, however, is how to efficiently account for dynamic contact-line effects at lateral boundaries of the fluid. These boundaries are free to move over the underlying solid
surface. Furthermore, the fluid contact angle at these boundaries depends on the local dynamic flow conditions.
In this paper we present a new shallow-flow computational method based on the Volume-of-Fluid (VOF) technique, which conserves fluid mass, while allowing for general wetting and
drying behavior. Non-uniform surface tension and fluid-substrate interactions, defined by a static contact angle, are included in the model. No special prescriptions are needed to locate
contact line locations or define dynamic contact angles.