A conservative approximation to compressible two-phase flow models in the stiff mechanical relaxation limit

In this article, we present and analyze a conservative approximation to reduced one-pressure one-velocity models for compressible two-phase flows that contain non-conservative products. This approximation is valid when certain material properties of the two phases are considerably different from each other. Although it cannot be applied to arbitrary mixtures, it is applicable to many heterogeneous mixtures of technological interest. Herein, we derive the Rankine–Hugoniot relations and Riemann invariants for the homogeneous part of the proposed model and develop an exact Riemann solver for it. Further, we investigate the structure of the steady two-phase detonation waves, with inert or reactive solid particles, admitted by the proposed model. Comparisons with the corresponding gaseous detonations are also made. Moreover, we derive a lower limit for the propagation speed of steady two-phase detonations in the case of reactive particles. At the limiting case of very dilute mixtures, this minimum speed tends to the Chapman–Jouguet velocity of gaseous detonations. Finally, we report on numerical simulations of the transmission of a purely gaseous detonation to heterogeneous mixtures containing inert or reactive solid particles. The effect of the solid particles on the structure of the resulting two-phase detonation is discussed in detail.