A New Approach for a Multiphase Flow Problem

Abstract

We consider in this paper a method to study a multiphase flow problem. Multiphase flows are probably the flows of most interest, that encompasses a broad range of engineering disciplines and a multitude of different analytical and numerical approaches. As a matter of fact, these kinds of flows are particularly hard to numerically model because of some features, such as complex physics, free boundaries, phase changes, large density ratios,
etc.. One of the most important features is free boundaries and there are many ways to track them at the numerical point of view : level set methods, volume of fluid methods, meshless particle methods, etc. In fact we study the dynamics of the interface between two immiscible fluids and track the free boundary. The simplicity of the front tracking method presented here is compensated by numerous drawbacks and numerical artefacts: loss of material mass, boundary diffusion and inaccuracy on the free boundary position. To improve the front tracking, we make use of an advanced computational method, the highorder accuracy level sets method. Two applications are considered and numerical results are presented.