A marker-and-cell approach to free surface 2-D multiphase flows

F. L. P. Santos, V. G. Ferreira, M. F. Tomé, A. Castelo, N. Mangiavacchi, S. McKee

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the Navier-Stokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient.

Original languageEnglish
Pages (from-to)1543-1557
Number of pages15
JournalInternational Journal for Numerical Methods in Fluids
Issue number12
Early online date11 Jan 2012
Publication statusPublished - 30 Dec 2012


  • finite difference
  • free surface flows
  • marker-and-cell
  • multiphase flows
  • numerical simulation
  • surface tension

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