Abstract
The paper considers flow modeling of two-phase heterogeneous medium. Each phase of the medium is considered as continuum, which is described by the compressible Euler equations. The phases are separated by the contact surface (interface) and are not mixed on the molecular level. Examples of such medium are: mixtures of solid particles and gas (in dense or dilute concentration of particles), liquids with small bubbles, solid porous materials filled with gas or liquid. The phase can be of connected structure (dense particles, porous solid, gas between dilute particles, etc.) or of non-connected structure (separated inclusions as gas bubbles, dilute particles, closed pores in solid, etc.). The connectivity of the phase is closely related to the propagation of acoustic perturbations. An attempt was made to consider all the cases of the phase connectivity in the framework of a unique approach. The paper presents an approach that couples the models designed for different cases of phase connectivity to the generalized hyperbolic and thermodynamically consistent form. The proposed model is applicable for simulating flows with change of the phase connectivity, e.g. dense-to-dilute two-phase flows. The model is verified on several problems of gas–solid granular medium flows. In numerical simulations the Godunov method with the HLLEM flux approximation on arbitrary moving Euler grids is used.
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