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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.


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