A front-tracking method for the simulating of 3D multi-fluid flows with free surfaces

F.S. De Sousa, N. Mangiavacchi, L.G. Nonato, A. Castelo, M.F. Tomé, V.G. Ferreira, J.A. Cuminato, S. McKee

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102 Citations (Scopus)


A method for simulating incompressible, imiscible, unsteady, Newtonian, multi-fluid flows with free surfaces is described. A sharp interface separates fluids of different density and viscosity. Surface and interfacial tensions are also considered and the required curvature is geometrically approximated at the fronts by a least squares quadratic fitting. To remove small undulations at the fronts, a mass-conserving filter is employed. The numerical method employed to solve the Navier-Stokes equations is based on the GENSMAC-3D front-tracking method. The velocity field is computed using a finite-difference scheme on an Eulerian grid. The free-surface and the interfaces are represented by an unstructured Lagrangian grid moving through an Eulerian grid. The method was validated by comparing the numerical results with analytical results for a number of simple problems. Complex numerical simulations show the capability and emphasize the robustness of this new method.
Original languageEnglish
Pages (from-to)469-499
Number of pages30
JournalJournal of Computational Physics
Issue number2
Publication statusPublished - 10 Aug 2004


  • front-tracking method
  • multi-fluid flows
  • numerical simulation
  • surface tension
  • free surface flows
  • finite-difference method


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