A level-set-based sharp-interface method for moving contact lines

This work elaborates on modeling of multi-phase flows with moving contact lines at no-slip walls. We propose a method that is based on the level-set-based sharp-interface method for compressible multifluids of Hu and Khoo [1]. The method has two main components: (i) a dynamic-contact-angle, level-set boundary condition, (ii) an extrapolation equation for obtaining the interface velocities at the dynamically evolving contact line at sub-cell resolution. It reduces spurious currents that form at the blind spot and deteriorate numerical simulations. The theory of Cox [2] provides the basis for the model development. The resulting sharp-interface method for moving contact lines is physically motivated and straightforward to implement into a finite-volume scheme. The method is verified against analytical solutions, and its convergence and stability is demonstrated. The method is robust for extreme contact angles. We explore the range of applicability through benchmark examples and a cross-method comparison for generic 2D test cases. Moreover, experimental reference cases are reproduced with considerably low resolution requirements.