A new article on free-surface problems with moving contact line by Ivan Fumagalli, Nicola Parolini and Marco Verani has appeared on Journal of Computational Physics.
The article can be downloaded at the following link
https://authors.elsevier.com/a/1WD4K508Haf6U
Title: On a free-surface problem with moving contact line: From variational principles to stable numerical approximations
Authors: Ivan Fumagalli, Nicola Parolini, Marco Verani
Abstract: We analyze a free-surface problem described by time-dependent Navier–Stokes equations. Surface tension, capillary effects and wall friction are taken into account in the evolution of the system, influencing the motion of the contact line – where the free surface hits the wall – and of the dynamics of the contact angle. The differential equations governing the phenomenon are first derived from the variational principle of minimum reduced dissipation, and then discretized by means of the ALE approach. The numerical properties of the resulting scheme are investigated, drawing a parallel with the physical properties holding at the continuous level. Some instability issues are addressed in detail, in the case of an explicit treatment of the geometry, and novel additional terms are introduced in the discrete formulation in order to damp the instabilities. Numerical tests assess the suitability of the approach, the influence of the parameters, and the effectiveness of the new stabilizing terms.
