## 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
[10] . We are also interested in the control of flows by active devices
[16] . These questions naturally lead to investigate tools of numerical analysis like e.g.
*a posteriori* estimators
[17] or linear algebra problems
[14] . In
[27] 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.