Numerical Simulation of Three Dimensional Free Surface Flows with Bubbles

  • Alexandre Caboussat
  • Vincent Maronnier
  • Marco Picasso
  • Jacques Rappaz
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 35)


A numerical model is presented for the simulation of free surface flows. The unknowns are the volume fraction of liquid, the velocity and pressure in the liquid and the pressure in the bubbles of gas which can appear in the liquid flow.

The volume fraction of liquid satisfies an advection equation, the pressure in each bubble is uniformly constant in space but depends on time and is computed using the ideal gas law, the velocity and pressure in the liquid satisfy the incompressible Navier-Stokes equations, the gas pressure being imposed as a normal force on the liquid-gas interface.

The numerical method is similar to the one described in [12, 13], advection and diffusion phenomena being solved on two different grids. Numerical results in the frame of mould filling show that the effect of pressure in the bubbles of gas surrounded by the liquid cannot be neglected.


Finite Element Mesh Stokes Problem Coloration Algorithm Advection Problem Advection Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Alexandre Caboussat
    • 1
  • Vincent Maronnier
    • 2
  • Marco Picasso
    • 1
  • Jacques Rappaz
    • 1
  1. 1.Institut de MathématiquesEcole Polytechnique Fédérale de LausanneSwitzerland
  2. 2.Calcom SAParc ScientifiqueSwitzerland

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