• Fluid flows in moving domains

I worked on to the numerical stability of a time discretization scheme for fluids in moving domains, through the so called ALE (Arbitrary Eulerian Lagrangian) formulation. The difficulty comes from those integrals, which are integrated over the moving domain at a given time-step. It can be shown that adding a suitable consistent term we can get a stable energy inequality without fulfilling any Geometric Conservation Laws, that were so far necessary to establish an energy balance for the fluid equations on a moving domain.

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