Conservative scheme for the thermodiffusion Stefan problem

We suggest further development of the principle of conservation for problems with moving boundaries. Using the problem of phase transitions in binary compounds as an example, we demonstrate a technique for constructing divergence and nondivergence finite difference schemes guaranteeing that the energy and mass conservation laws hold in the discrete model. In a class of front tracking methods, we prove the equivalence of the approach based on the use of moving grids with that based on a dynamic change of variables which permits one to solve the problem on a fixed grid.     

Numerical investigation of roll convection stability

This study is devoted to the mathematical modeling of Rayleigh-Bénard convection in a rectangular cavity with rigid boundaries. The stability of the roll motion induced by an initial disturbance of special form is studied on the basis of two-dimensional and three-dimensional calculations. Different patterns of flow restructuring with respect to the wavenumber are analyzed on the Rayleigh number range Ra = 1708–7000 for the Prandtl numbers Pr = 1 and 0.71.     

Numerical study for diffusion processes in dissolution and growth of heterostructures formed by LPE. Part II. Effect of programmed temperature changes

The paper presents the numerical study of mass transfer in growth and dissolution of CdHgTe compounds in LPE systems that are subjected to temperature changes. Effect of solid-state diffusion on heterostructure formation is analyzed in the wide range of operating parameters.     

Unconditionally Stable Algorithm for Solving the Three-Dimensional Nonstationary Navier–Stokes Equations

We propose an unconditionally stable method for solving the three-dimensional nonstationary Navier–Stokes equations in the velocity–pressure variables. The method is based on a conservative finite-difference scheme and the simultaneous solution of the momentum and continuity equations at each time layer. The velocity and pressure fields are calculated by using a parallel algorithm for solving systems of linear equations by the Gauss method.     

Numerical study for diffusion processes in dissolution and growth of heterostructures formed by LPE. Part I. Isothermal conditions

The paper deals with computer simulation for growth and dissolution of ternary CdHgTe compounds in liquid-phase epitaxy (LPE) systems. The mathematical model accounts for the matter transport in both solid and liquid phases and the equilibrium phase diagram. The study displays the effect of solid-state diffusion on compositional grading at the substrate-layer boundary, on the formation of concentration distribution in both phases and on interface motion. The simulation has been done for isothermal conditions.     

Computer simulation of transient states in capillary zone electrophoresis and isotachophoresis.

Transient states in the evolution of electrophoretic systems comprising aqueous solutions of weak monovalent acids and bases are simulated. The mathematical model is based on the system of nonstationary partial differential equations, expressing the mass and charge conservation laws while assuming local chemical equilibrium. It was implemented using a high resolution finite-difference algorithm, which correctly predicted the behavior of the concentration, pH and conductivity fields at low computational expense. Both the regular and the irregular modes of separation in capillary zone electrophoresis and isotachophoresis are considered. It is shown that the results of separation, particularly zone order, strongly depend on pH distribution. Simulation data as well as simple analytical assessments may help to predict and correctly interpret the experimental results.