COMPARISON OF COMPUTER IMPLEMENTATIONS OF EQUILIBRIUM AND CONTINUOUS METHODS FOR MODELING MULTI-PHASE MEDIA ON THE EXAMPLE OF A ONE-DIMENSIONAL UNSTATIONARY GAS SUSPENSION FLOW
Authors:   Institute of Mechanics and Engineering – Subdivision of the Federal State Budgetary Institution of Science “Kazan Scientific Center of the Russian Academy of Sciences”, Kazan, Russia, Tukmakov D.A. 
Published: August 2023

The work is devoted to the problems of mathematical modeling of hydrodynamic processes in inhomogeneous media. The purpose of the study is to compare the techniques for modeling the flows of inhomogeneous media. The continuum and equilibrium methods of modeling the dynamics of a gas suspension – a gas with dispersed inclusions – were compared. Comparisons were made between calculations carried out by an equilibrium mathematical model of the dynamics of gas suspensions with numerical implementations of continual mathematical models of the dynamics of gas suspensions with an ideal and viscous heat-conducting carrier medium. Various parameters of the simulated processes obtained by various mathe¬matical models were compared. Materials and methods. The paper presents two methods for modeling the dynamics of multiphase media. In the equilibrium method, an inhomogeneous medium is described as an ideal gas with the calculation of the correction coefficients of gas-dynamic functions, in the continuum modeling method for particles, the concept of “average density” is introduced; thus, for both the carrier phase – gas and the dispersed phase, a system of equations is solved consisting of the density conservation equation, for of the dispersed phase, the “average density” conservation equation, the momentum conservation equations of the mixture components, and the energy conservation equations of the gas and dispersed phase. The systems of equations of motion of single-phase and two-phase media were integrated by a numerical finite-difference method of the second order of accuracy. To suppress numerical oscillations at each time step, the method of nonlinear correction of the grid function was used. The software package for mo¬deling the dynamics of a gas suspension consisted of several components: a subroutine for setting the boundary conditions, a subroutine for the formation of a finite-difference partition of a physical domain, and the main program for calculating the dynamics of an inhomogeneous medium. Results. The discontinuity decay process in a homogeneous gas and in a gas suspension was modeled. Numerical calculations of pressure discontinuity decay in a homogeneous gas and numerical calculations of discontinuity decay in a gas suspension, obtained by the equilibrium modeling technique, were compared with analytical solutions known from the literature. It is determined that the highest propagation velocity of a disturbance in a gas suspension is observed in an equilibrium model, a lower propagation velocity in a continuum model with an ideal medium, and the lowest velocity is observed in a gas suspension with a viscous heat-conducting medium. It was found that for flows with different initial pressure discontinuity intensities, the presence of a dispersed phase in the mixture has a different effect. Conclusions. The regularities obtained demonstrate the features of each of the methods for modeling the dynamics of gases, which can be used in the development of computer models of the dynamics of multiphase media.