A consistent and parallelized height function based scheme for applying contact angle to 3D volume-of-fluid simulations

A height function based numerical scheme has been developed to apply contact angle in the parallel computational framework of 3D volume-of-fluid method. Given that most of the reported height function methods are implemented in 2D, the differences between the implementations of 2D and 3D height function methods are first focused. Then, a novel scheme is proposed to preserve the accuracy and consistency of height function for the calculation of interface curvature near the contact line. Finally, the extension to parallel computation is presented in details because it is not a trivial task as it appears, e.g., the information transmission among the cells neighboring two intersecting boundaries requires careful treatment. Numerical tests reveal that with the proposed scheme, accurate estimations of interface curvature and normal vector are obtained for a spherical interface, and such a numerical strategy allows the spurious currents to decrease to machine accuracy for a 3D stationary droplet. Moreover, by simulating a droplet spreading on a solid wall with 3D Cartesian grid, either from a static state driven by capillary force or with an initial impact velocity, the numerical results verify that the contact line can maintain an axi-symmetric shape during the dynamic spreading.