Applying contact angles based on a continuously moving contact line in 2D VOF simulations

A height-function-based numerical approach is developed for enforcing contact angles on flat and curved solid surfaces within two-dimensional volume-of-fluid simulations. This method incorporates the contact line position into the curvature estimation in the contact line cell, where the interface normal is constrained to the prescribed angle to ensure smooth contact line motion. On flat solid surfaces, the proposed model achieves higher accuracy than the conventional vertical height-function method for enforcing very small and very large contact angles. Moreover, it extends naturally to curved solid surfaces represented by the embedded boundary method, enabling the imposition of arbitrary contact angles without inducing significant spurious currents near the contact line. Numerical validations confirm the accuracy and robustness of the proposed method, demonstrating its applicability to multiphase flows involving complex wall geometries and contact-line dynamics.