## Section: Application Domains

### Fluid mechanics

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

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 for example the one of air in standard conditions, or a more general one as in real gases and multiphase flows. 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
for the same physical models. Depending on the applications, the
physical models considered involve the Navier-Stokes equations, or the
non-linear or linearized 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, while maintaining
the desired accuracy.