## Section: Application Domains

### Fluid mechanics

Participants : Rémi Abgrall [ Corresponding member ] , Marc Duruflé, Mario Ricchiuto.

The numerical simulation of steady and unsteady flows is still a
challenge since efficient schemes and efficient implementations are
needed. The accuracy of schemes is still a problem nowadays. This
challenge is even higher if large size problems are considered, and if
the meshes are not regular. The schemes developed in for fluid
mechanics problems use `Scotch` , `HIPS` and `PaStiX` when the type of
problems and the CPU requirements make this useful.

#### Steady transonic and supersonic flows

One of our application fields is the one of steady subsonic, transonic and supersonic flow problems when the equation of state is the one of standard air. This class of physical problems corresponds to “standard” aerodynamics and the models are those of the Euler equations and the Navier Stokes ones, possibly with turbulent effects. Here we consider the residual distribution and SUPG schemes.

#### Unsteady transonic flows

Another field of application is the one of *unsteady* problems
with the same physics, or in the case of the linearized Euler
equations. The schemes we develop are the Residual distribution
schemes
5.2 and Discontinuous Galerkin schemes
5.7 . Specific modifications, with respect to their
steady counter parts, are done in order to reduce dramatically the
computational time.