Emilie Marchandise

Title ( download pdf here)

Simulation of three-dimensional two-phase flows: coupling of a stabilized finite element method with a discontinuous level set approach.

Abstract

The subject of this thesis is the development of an accurate, general and robust numerical method capable of predicting the flow behavior of two-phase immiscible fluids, separated by a well defined interface. In the quest of an accurate and robust numerical method for the modeling of two-phase flows, one has to keep in mind the intrinsic properties and difficulties associated with the problem:

those flows are mostly three-dimensional,
some flows are steady, others unsteady,
the interface might encounter a lot of topology changes (like merger or break-up),
large jumps of density and viscosity might exist across the interface (e.g. ratio of density of 1/1000 for water and air),
surface tension forces may play a very important role in the interface dynamics; hence, the influence of this force should be accurately evaluated and incorporated into the model,
mass conservation is of primary importance.

All these issues are addressed in this thesis, and special techniques are proposed for their treatment, which enables to construct the desired computational method. The chosen computational method combines a pressure stabilized finite element method for the Navier Stokes equations with a discontinuous Galerkin (DG) method for the level set equation. Such a combination of those two numerical methods results in a simple and effective algorithm that allows to simulate diverse flow regimes presenting large density and viscosity ratios (ratio up to 1/1000).

Presentation ( download presentation here)