Multifluid Flows: A Kinetic Approach

Florent Berthelin (1, 2) , Thierry Goudon (1, 2) , Sebastian Minjeaud (2, 3)

1 COFFEE - COmplex Flows For Energy and Environment
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 CASTOR - Control, Analysis and Simulations for TOkamak Research

We propose a numerical scheme for the simulation of fluid-particles flows with two incompressible phases. The numerical strategy is based on a finite volume discretization on staggered grids, with a flavor of kinetic schemes in the definition of the numerical fluxes. We particularly pay attention to the difficulties related to the volume conservation constraint and to the presence of a close-packing term which imposes a threshold on the volume fraction of the disperse phase. We are able to identify stability conditions on the time step to preserve this threshold and the energy dissipation of the original model. The numerical scheme is validated with the simulation of sedimentation flows.

Domaines: Analyse numérique [math.NA]

Florent Berthelin, Thierry Goudon, Sebastian Minjeaud. Multifluid Flows: A Kinetic Approach. Journal of Scientific Computing, 2016, 66 (2), pp.792--824. ⟨10.1007/s10915-015-0044-1⟩. ⟨hal-01158016⟩