Application of Regularized Equations for Dynamics of Heterogeneous Binary Mixtures for Modeling Water–Vapor Phase Transitions

Mathematical Models and Computer Simulations. 2025. Vol. 17. No. 3. P. 352–364.

Zlotnik A., Lomonosov T.

A system of four balance differential equations is used to describe dynamics of heteroge neous compressible binary mixtures with stiffened gas equations of state for the mixture’s components, including gas and liquid ones. The main points are its quasi-homogeneous form, which arises as a result of eliminating volume fractions of components from the collection of sought functions and the construction of a quadratic equation for the common pressure of components, as well as its subsequent regularization of the quasi-gasdynamic type. We present a description of the phase transition in the limit of instantaneous relaxation to thermodynamic equilibrium between components, whose imple mentation is reduced to solving nonlinear equations for the saturation temperature and pressure. In general, this approach is implemented by an explicit finite-difference scheme, which is two-level in time and symmetric three-point conservative in space, without limiters and with splitting with respect to physical processes (in the one-dimensional case). Using this scheme, test computations with the water–vapor phase transition are carried out.

Keywords: quasi-gasdynamic regularization, gas dynamics, heterogeneous binary mixture, water-vapor phase transition, explicit in time and symmetric conservative in space finite-difference scheme

Publication based on the results of: Decision-Making in Socio-Economic, Political and Financial Spheres (2025)