Section: Research Program

Finite element and finite volume methods

Conservation Laws, Anti-Diffusive Schemes, Viscous Flows, Control, Turbulence, Finite element methods, Finite volume methods

Flow control techniques are widely used to improve the performances of planes or vehicles, or to drive some internal flows arising for example in combustion chambers. Indeed, they can sensibly reduce energy consumption, noise disturbances, or prevent the flow from undesirable behaviors. Passive as well as active control were performed on the "Ahmed body geometry", which can be considered as a first approximation of a vehicle profile. This work was carried out in collaboration with the EPI Inria MC2 team in Bordeaux (C.H. Bruneau, I. Mortazavi and D. Depeyras), as well as with Renault car industry (P. Gillieron). We combined active and passive control strategies in order to reach efficient results, especially concerning the drag coefficient, for two and three dimensional simulations [36] , [37] .

Numerical investigations are very useful to check the behavior of systems of equations modelling very complicate dynamics. In order to simulate the motion of mixtures of immiscible fluids having different densities, a recent contribution of the team was to develop an hybrid Finite Element / Finite Volume scheme for the resolution of the variable density 2D incompressible Navier-Stokes equations. The main points of this work were to ensure the consistency of the new method [41] as well as its stability for high density ratios [38] . Now, C. Calgaro and E. Creusé, in collaboration with T. Goudon (Inria-COFFEE), have in mind the following objectives :

• Develop and freely distribute a new version of the matlab code (http://math.univ-lille1.fr/~simpaf/SITE-NS2DDV/ equipped with a graphic interface and an accurate documentation) to promote new collaborations in the domain, allow some easy comparisons with concurrent codes on the same benchmark cases, and compare alternative numerical solution methods (for instance to compare updating LU factorizations, see [40] );

• To generalize the stability results obtained in [39] for the scalar transport equation to the full 2D Euler system, in particular very low density values (near vacuum);

• Complete the C++ code to treat more general hydrodynamic models (combustion theory, transport of pollutants). We plan to check the behavior of the equations (typically the Kazhikhov-Smagulov model of powder-snow avanlanches) in the regime when the current existence theory does not apply, and extend our kinetic asymptotic-based schemes to such problems.