Eulerian models with particle pressure for air-particle flows

Abstract

Abstract A hierarchy of Eulerian models for air-particle flows is derived when the particle density is assumed to be constant. The first starting model is a weakly hyperbolic zero-pressure system of conservation laws for the particulate phase. Adding a particle pressure gradient, we obtain a strictly hyperbolic system. The second starting model is a conditionally hyperbolic single-pressure system written in non-conservative form. Considering two pressures and rewriting pressure gradients, we get a hyperbolic two-pressure system in conservative form. Particle pressure modeling and a way of writing the pressure gradients to keep the models in conservative form are discussed. Numerical results are presented.