document: A fully-coupled numerical framework for two-phase flows with an implicit implementation of surface tension has been introduced in this article. This fully-coupled framework has then been used to compare the influence of the surface tension treatment on the time-step restrictions resulting from capillary waves. The conducted study demonstrates that restrictions on the numerical time-step resulting from capillary waves are valid and unchanged regardless of the numerical treatment of surface tension. Since surface tension is not a function of pressure or velocity, the change in implementation does not affect the matrix coefficients of the primitive variables and, thus, numerical stability is independent of the treatment of surface tension. Further analysis shows that the capillary time-step constraint is a requirement imposed by the spatiotemporal sampling of capillary waves, which is independent of the applied numerical methodology.
extractive_keyphrases: applied numerical methodology capillary waves compare the influence numerical treatment of surface tension surface tension
abstractive_keyphrases: fully-coupled framework fully-coupled numerical framework restrictions on the numerical time-step resulting from capillary waves spatiotemporal sampling of capillary waves surface tension treatment time-step restrictions resulting from capillary waves treatment of surface tension two-phase flows