A hybrid kinetic-fluid relaxation scheme for particle-fluid flows

Résumé de l'exposé

We present a novel numerical method for the treatment of particle-fluid flows, in which a dispersed phase, composed of mesoscopic particles, interacts with a continuous fluid phase. It is well known that the kinetic description of such flows is very accurate in the dilute regime but suffers from robustness issues when the volumic fraction of particles increases. It is therefore common, in practical simulations, to perform a relaxation towards an eulerian two-phase mixture (typically a 4 or 5 equation model) when dense, highly collisional regimes are reached. In this presentation, we derive such a model by doing a modal decomposition of the density function (PDF) of the particles into a “kinetic” and an “eulerian” mode, according to some physically sound criterion, and taking the hydrodynamic limit of the latter. This gives rise to a coupled Vlasov-Euler system which contains a non-conservative mixing operator, representing the flux of particles going from the kinetic to the fluid sub-space of the phase space. This approach is related to so-called “hybrid” or “micro-macro” methods, which were initially developed in the context of rarefied gas dynamics and plasma transport. Numerically, this involves coupling a Lagrangian PIC solver with a finite-volume Euler solver through a relaxation scheme which aims at integrating the mixing source terms and enforcing thermodynamic equilibrium. The method is analyzed and illustrated on a test case: the interaction of a shock with a dense cloud of water particles, with addition of a simple break-up kernel as a driver of mixing.

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