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


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.