A Review of the Relaxation Models for Phase Transition Flows Centered on the Topological Aspects of the Nonequilibrium Mass Transfer Modelling

The first part of this work is a brief (application-oriented) review of the different classes of multiphase flow models. The review starts with the most generic approaches and descends to the class of Homogeneous Relaxation Models (HRM) of two-phase flow. Subsequently, this work presents a detailed review of the developed relaxation equations describing nonequilibrium mass transfer in two-phase flows. Some of the reviewed equations (in particular, the closure equations of HRMs) have quite simple mathematical structures but there are indications that they should be, in a specific way, more complex. Consequently, the main aim of this article is to bring attention to this problem and expose its nature and practical importance. The analyses conducted in this study reveal that relaxation closure equations formulated as advection equations may disrupt the phase space structure of the model, whereas equations formulated as phasic mass conservation do not pose such an issue. This distinction arises from the presence of a greater number of gradients in the conservation equations (a minimum of two, compared to potentially just one in an advection equation), rendering the conservation equations mathematically more complex.