Advances in the simulation of multi-fluid flows with the particle finite element method. Application to bubble dynamics

• Published in: International journal for numerical methods in fluids Vol. 67; no. 11; pp. 1516 - 1539
• Main Authors: Mier-Torrecilla, M., Idelsohn, S. R., Oñate, E.
• Format: Journal Article Publication
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 20.12.2011; Wiley
• Subjects: Bubble dynamics; Bubbles; Computational methods in fluid dynamics; Computer simulation; Dinàmica de fluids; Drops and bubbles; Exact sciences and technology; Finite element method; Fluid dynamics; Fluid flow; Fundamental areas of phenomenology (including applications); Lagrangian simulation; Mathematical analysis; Mathematical models; Multi-fluid flows; Nonhomogeneous flows; Numerical analysis; Particle Finite Element Method (PFEM); Physics; Pressure segregation; Simulació per ordinador; Surface tension; Geometrical shape; Computational fluid dynamics; Refinement method; Bubble ascent; Digital simulation; multi-fluid flows; bubble dynamics; Finite element method; Lagrangian simulation; Bubbles; Particle Finite Element Method (PFEM); Dynamics; pressure segregation; Modelling; Surface tension; Mesh generation
• ISSN: 0271-2091; 1097-0363; 1097-0363
• DOI: 10.1002/fld.2429

In this work, we extend the Particle Finite Element Method (PFEM) to multi‐fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking interfaces. We develop a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables. The scheme is based on decoupling the velocity and pressure variables through a pressure segregation method that takes into account the interface conditions. The interface is defined to be aligned with the moving mesh, so that it remains sharp along time, and pressure degrees of freedom are duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity. Furthermore, the mesh is refined in the vicinity of the interface to improve the accuracy and the efficiency of the computations. We apply the resulting scheme to the benchmark problem of a two‐dimensional bubble rising in a liquid column presented in Hysing et al. (International Journal for Numerical Methods in Fluids 2009; 60: 1259–1288), and propose two breakup and coalescence problems to assess the ability of a multi‐fluid code to model topology changes. Copyright © 2010 John Wiley & Sons, Ltd.