Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces. The present work is devoted to the study on unsteady flows of two immiscible viscous fluids separated by free moving interface. Our goal is to elaborate a unified strategy for numerical modelling of two-fluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The proposed computational approach essentially relies on three basic components: the finite element method for spatial approximation, the operator-splitting for temporal discretization and the level-set method for interface representation. We show that the finite element implementation of the level-set approach brings some additional benefits as compared to the standard, finite difference level-set realizations. In particular, the use of finite elements permits to localize the interface precisely, without introducing any artificial parameters like the interface thickness; it also allows to maintain the second-order accuracy of the interface normal, curvature and mass conservation. The operator-splitting makes it possible to separate all major difficulties of the problem and enables us to implement the equal-order interpolation for the velocity and pressure. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh–Taylor instability are presented to validate the computational method.

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  1. Metivet, Thibaut; Sengers, Arnaud; Ismaïl, Mourad; Maitre, Emmanuel: Diffusion-redistanciation schemes for 2D and 3D constrained Willmore flow: application to the equilibrium shapes of vesicles (2021)
  2. Gao, Puyang: The finite element numerical investigation of free surface Newtonian and non-Newtonian fluid flows in the rectangular tanks (2020)
  3. Gu, Zhenghua; Yao, Yuan; Yu, Ching-Hao; An, Ruidong: Development of a volume of fluid method for computing interfacial incompressible fluid flows (2020)
  4. Li, Qiang; Dong, Fangmian; Li, Larry K. B.: An interface-sharpening method with adaptive mesh refinement for volume-of-fluid simulations of two-phase compressible flows (2020)
  5. Bezchlebová, Eva; Dolejší, Vít; Feistauer, Miloslav; Sváček, Petr: Numerical simulation of two-phase flow of immiscible fluids by the finite element, discontinuous Galerkin and level-set methods (2019)
  6. Ngo, Long Cu; Choi, Hyoung Gwon: Efficient direct re-initialization approach of a level set method for unstructured meshes (2017)
  7. Pino-Muñoz, Daniel; Bruchon, J.; Drapier, S.; Valdivieso, F.: Sintering at particle scale: an Eulerian computing framework to deal with strong topological and material discontinuities (2014)
  8. Muñoz, D. Pino; Bruchon, J.; Drapier, S.; Valdivieso, F.: A finite element-based level set method for fluid-elastic solid interaction with surface tension (2013)
  9. Turek, Stefan; Mierka, Otto; Hysing, Shuren; Kuzmin, Dmitri: Numerical study of a high order 3D FEM-level set approach for immiscible flow simulation (2013)
  10. Choi, Hyoung Gwon: A least-square weighted residual method for level set formulation (2012)
  11. Liao, Jian-Hui; Zhuang, Zhuo: A consistent projection-based SUPG/PSPG XFEM for incompressible two-phase flows (2012)
  12. Billaud, Marie; Gallice, Gérard; Nkonga, Boniface: A simple stabilized finite element method for solving two phase compressible-incompressible interface flows (2011)
  13. Levy, A.; Le Corre, S.; Chevaugeon, N.; Poitou, A.: A level set based approach for the finite element simulation of a forming process involving multiphysics coupling: ultrasonic welding of thermoplastic composites (2011)
  14. Idelsohn, Sergio R.; Mier-Torrecilla, Monica; Nigro, Norberto; Oñate, Eugenio: On the analysis of heterogeneous fluids with jumps in the viscosity using a discontinuous pressure field (2010)
  15. Villa, A.; Formaggia, L.: Implicit tracking for multi-fluid simulations (2010)
  16. Xing, Xianghua; Wei, Peng; Wang, Michael Yu: A finite element-based level set method for structural optimization (2010)
  17. Becker, Jürgen; Junk, Michael; Kehrwald, Dirk; Thömmes, Guido; Yang, Zhaoxia: A combined lattice BGK/level set method for immiscible two-phase flows (2009)
  18. Sheu, Tony W. H.; Yu, C. H.; Chiu, P. H.: Development of a dispersively accurate conservative level set scheme for capturing interface in two-phase flows (2009)
  19. Terashima, Hiroshi; Tryggvason, Grétar: A front-tracking/ghost-fluid method for fluid interfaces in compressible flows (2009)
  20. Thömmes, G.; Becker, J.; Junk, M.; Vaikuntam, A. K.; Kehrwald, D.; Klar, A.; Steiner, K.; Wiegmann, A.: A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method (2009)

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