On a two-dimensional model for computations of two-phase flows

In the preprint a critical review of the methodologies for calculating of two phase flows at the scale of local equilibrium is presented and a two-dimensional model for calculating of two phase flows is suggested. A closed model of the governing equations for a model medium with EOS of Van der Waals type is presented. The described calculation schematics is based on the DNS approach and is intended for the usage with the supercomputers (with the prospects of achieving of exaflops performance). The model is based on the concept of single-velocity continuum, where the phases differ by the density level. Also the model includes the EOS of Van der Waals type with the possibility to have the phase transition. Such EOS allows performing the uniform calculations and including into the consideration various non-equilibrium processes. The Euler equations with heat conduction effects form the hydrodynamic background.