Asymptotic Preserving and Multiscale Methods for Kinetic and Hyperbolic Problems

Some problems and simulation methods motivated by the modeling of particles laden flows

Thierry Goudon

INRIA Sophia Antipolis Research Centre
[SLIDES]

The mathematical modeling of particulate flows naturally lead to multi-scale problems. In turn, a wide variety of PDEs systems can be considered. Such systems can couple kinetic and hydrodynamic systems, or adopt a fully hydrodynamic viewpoint. Furthermore, in the incompressible framework the problem is complemented by constraint on a combination of fluid and particles velocities. To handle the difficulty we introduce a new family of schemes working on staggered grids, with a kinetic flavor in the design of the numerical fluxes.