| Abstract: |
| Continuum models of two-phase flow have been employed to investigate a wide variety of physical phenomena, ranging from gas-liquid flows to detonation waves in granular energetic materials. Typically, the set of governing equations consists of mass, momentum and energy balance for each phase, and an equation for the evolution of volume fraction of either phase. The set is closed by providing an equation of state for each phase and by specifying the inter-phase interaction terms. Examination of the time scales associated with mechanisms of phase interaction shows that in many applications, pressures and velocities equilibrate rapidly, thereby leading to a reduced, 5-equation model. Such a reduction is incomplete in that it only provides an outer solution in the sense of matched asymptotic expansions. Closure can be achieved in one of two ways, either by examining thin inner layers that are just the partly dispersed shocks of the full model, or by providing a suitable regularization of the reduced model. In this work we discuss both approaches, with an eye on the sensitivity of the closure to choices of the relevant parameters. |
|