## Section: New Results

### Computational Fluid Dynamics

We develop an original hybrid FV/FE(Finite Volume/Finite Element) method to compute (2D)
variable density viscous flows. The code allows to simulate complex phenomena like e. g. Rayleigh-Taylor instabilities or falling droplet with a very high density ratio [42] , [32] . We are also interested in the control of flows by active devices on the backward facing step as well as on the Ahmed body configuration [14] , [27] . These questions naturally lead to investigate tools of numerical analysis like e.g. *a posteriori* estimators [50] , [30] or linear algebra problems [46] .
In [41] C. Calgaro *et al.* address the problem of computing preconditioners for
solving linear systems of equations with a sequence of slowly varying matrices.
This problem arises in many important applications, for example in computational fluid dynamics, when
the equations change only slightly possibly in some parts of the domain.
In such situations, the papers discusses a number of techniques for computing incremental ILU factorizations.