Surface tension problems solved with the particle finite element method using large time-steps

•Improvements of PFEM-2 to solve surface tension dominant problems.•Lagrangian convection with particles allows large time-steps.•A FEM approach of the S-CLSVOF method is used to improve the curvature calculation.•Stability analysis of the semi-implicit CSF formulation is presented.•A preliminary simulation of a primary atomization of a liquid jet is done. In previous works [S. R. Idelsohn, J. Marti, P. Becker, E. Oñate, Analysis of multifluid flows with large time steps using the particle finite element method, International Journal for Numerical Methods in Fluids 75 (9) (2014) 621–644. doi:10.1002/fld.3908. URL http://dx.doi.org/10.1002/fld.3908, Juan M. Gimenez and Leo M. González, An extended validation of the last generation of particle finite element method for free surface flows, J Comput Phys 284 (0) (2015) 186–205. doi:http://dx.doi.org/10.1016/j.jcp.2014.12.025. URL http://www.sciencedirect.com/science/article/pii/S0021999114008420 ], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology which uses X-IVS [S. Idelsohn, N. Nigro, A. Limache, E. Oñate, Large time-step explicit integration method for solving problems with dominant convection, Comp Methods in Appl Mech Eng 217–220 (2012) 168–185.] to treat convection terms allowing large time-steps was validated for problems where the gravity forces and/or the inertial forces dominate the flow. Although that is the target range of problems to solve with PFEM-2, most of real problems that fall in these categories also includes other flow regimes in certain regions of the domain. Maybe the most common secondary regime is when the surface tension dominates, as an example when drops or bubbles are released from the main flow, and this feature must be taken into account in any complete numerical strategy. Attending to that, in this work the treatment of the surface tension to PFEM-2 is included. An implicit CSF methodology is employed together with a coupling between the marker function with a Level Set function to obtain a smooth representation of the normal of the interface which allows an accurate curvature calculation. Examples for curvature calculation and isolated bubbles and drops are presented where the accuracy and the computational efficiency are analyzed and contrasted with other numerical methodologies. Finally, a simulation of a jet atomization is analyzed. This case presents the above mentioned f