A modified continuum surface force (M-CSF) model for two-phase flow problems in smoothed particle hydrodynamics

This work proposes a modified interfacial tension model based on the continuum surface force (M-CSF) in the context of smoothed particle hydrodynamics. This correction aims to enhance computational stability, improve force evaluation precision, and increase symmetry around the interface. Several two-phase flow benchmarks are solved using both the conventional and proposed CSF models, and the results are compared with each other and with the available literature. The results indicate that the modified model can efficiently increase the force evaluation accuracy in the pressure field at the interface. For instance, the relative error in pressure calculation using the proposed and conventional CSF models is 0.05% and 3.5%, respectively, when compared to the analytical solution, with both models having the same particle resolutions for the droplet deformation problem. In predicting the critical surface tension for hydrodynamic instabilities, such as the Rayleigh-Taylor instability, the M-CSF methodology exhibits much better alignment with existing theories, showing less than 5% deviation, while conventionally used CSF models can deviate up to 15% for the same problem. These findings confirm the superiority of the proposed methodology in evaluating interfacial forces, even in complex hydrodynamic instabilities.