On the Modeling of Surface Tension and its Applications by the Generalized Interpolation Material Point Method

This paper presents a numerical procedure to model surface tension using the Generalized Interpolation Material Point (GIMP) method which employs a background mesh in solving the equations of motion. The force due to surface tension is formulated at the mesh grid points by using the continuum surface force (CSF) model and then added to the equations of motion at each grid point. In GIMP, we use the grid mass as the color function in CSF and apply a moving average smoothing scheme to the grid mass to improve the accuracy in calculating the surface interface. The algorithm, named as GIMP-CSF, is implemented using the software package Uintah and benchmarked by three numerical examples: static equilibrium of a 2D liquid drop, dynamic evolution of a square drop in 2D and 3D, and the capillary rise. The benchmark results, when compared to analytical solutions and those obtained by other approaches, demonstrated the accuracy and effectiveness of the GIMP-CSF algorithm.