A Shallow Water Model with Contact Line Capturing via a Color Function for Partially Wetting Films

This paper follows on from previous work on the development of a shallow-water model to simulate partial wetting phenomena at large scale [1]. The originality of this model lies in the use of a scalar quantity (called the color function), advected by the liquid film speed, to locate the position of the contact line between the film and the wall. The advantage of this function is that it allows to easily calculate (via its gradient) the macroscopic resultant of the capillary forces acting in the vicinity of the contact line, without the need to introduce a disjoining pressure model as in [2, 3, 4] that is necessarily associated with a regularization parameter h * for numerical purpose. Using the hyperbolic structure of the system of equations, we show that we can build an HLLC-type solver that preserves the positivity of the film thickness and the maximum principle on the color function under a CFL-like condition. Finally, a series of 1D and 2D numerical results demonstrating the robustness and accuracy of the proposed numerical method is presented.