Abstract: The numerical simulation of free surfaces flow has many applications in science and engineering, for instance in mold casting, glacier modeling, aluminum production, or bubbles simulation. We present a numerical framework for the simulation of three-dimensional two-phases flow with free surfaces, involving an incompressible liquid and a compressible gas. We use an implicit time splitting scheme to decouple the physical phenomena. It couples a method of characteristics for the solution of advection problems and an implicit finite element scheme for the solution of time dependent Stokes problems. A two-grids method that couples a structured grid of small cells and a finite element mesh of tetrahedrons is used. An interface tracking technique involving local adaptive mesh refinement around the interfaces is advocated to obtain a more accurate approximation of the interfaces and reduce numerical diffusion. Numerical experiments in a large variety of physical problems illustrate the efficiency and robustness of the approach. We present several (industrial and academic) applications ranging from mold casting, bubbles in aluminum electrolysis, glacier simulations or dam breaks.
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