Том 10, № 4 (2018)

A single velocity model of one-component media for calculating two-phase flows is presented. The model is based on conservation laws with minimal additional assumptions. The model and numerical method are intended for the direct numerical simulation (DNS) of complex two-phase flows with high-performance computing systems (exascale computing). The closed set of governing equations is written for nonaveraged parameters (so-called microparameters) and for a medium with a complex equation of state. It is assumed that each point of the flow is completely characterized by a single density, single velocity, and single internal energy. The diffused interface model is used for describing an interphase boundary. A method for generating the relationship between thermodynamic functions and all possible values of density and internal energy is presented. The real functions for the pure phases are used. The hydrodynamic basis of the model consists of Navier-Stokes equations or Euler equations that take heat conductivity processes into consideration. The reliability of the model is tested on a 1D problem for real water, in particular, on the Stefan problem and on the problem on the formation and coalescence of bubbles.

The developed mathematical model simulates the thermomechanical effects which accompany electron scattering in a barrier. The generation of a space charge and an electromagnetic field is taken into account. For the ionized substance of the barrier and an electromagnetic field, Euler equations with the Lorentz force and Joule heating and Maxwell equations with a convective current are considered. Equations are constructed for the density of the Lorentz force acting on the ionized substance and for its Joule heating in the electromagnetic field. Conservative difference analogs of the quantities responsible for the interaction of the electromagnetic field with the ionized substance are developed.

The principles and methods of adapting an unstructured mesh to the distribution of ocean depths for long-wave models of tsunamis are described. It is shown that, in order to adequately reproduce tsunamis within the long-wave theory, the perturbation introduced in the model has to be smoothed or filtered to eliminate short-period components subject to phase dispersion. An explicit formula to calculate the cutoff period for a filter is proposed. The relative numerical efficiency of using unstructured meshes adapted to the distribution of ocean depths compared to regular meshes is estimated. It is shown that using unstructured meshes can ensure an increase in numerical efficiency by up to several thousand factors.

The conductivity of excitations in short chains of optical cavities containing two-level atoms capable of exchanging photons is considered. The Jaynes–Cummings–Hubbard (JCH) model is used taking into account the dephasing noise effect. Two counterintuitive quantum effects are reproduced for this model: the increase in conductivity by the dephasing noise (DAT effect) and the quantum bottleneck effect, which is a paradoxical slump in conductivity with the enhancement of the excitation transfer to the runoff. Using numerical simulation, we reveal an interesting relationship between those two effects. In particular, we found that the dephasing assisted transport (DAT) effect occurs only at the nonoptimal values of the runoff and inflow, i.e., in conditions where the conductivity is limited by the quantum bottleneck effect.

Highly accurate specialized quadrature formulas are constructed for directly computing the Fermi−Dirac functions of the half-integer index. It is shown that the dependence of the error on the number of nodes is not power-law but exponential. The properties of such formulas are investigated. It is demonstrated that the factor of the convergence exponent is determined by the distance to the nearest pole of the integrand. This provides a very fast convergence of the quadratures. Simple approximations of the Fermi−Dirac functions of the integer and half-integer indices with an accuracy better than 1% are constructed; these approximations are convenient for physical estimates. In passing, asymptotic representations for Bernoulli numbers are found.

Based on the previously developed closed mathematical model, the dynamics of a small horizontal axis wind turbine are studied. The procedure for identifying the aerodynamic torque is proposed for the case when the electromechanical interaction is nonlinear in a current. Elements of the system for the comparative analysis of different wind turbines are developed. The results of simulating the behavior of the device are compared with the available experimental data. It is shown that good agreement takes place. The behavior of the system under a changing wind is studied.

This paper considers a flow of rarefied gas with a specular-diffuse reflection of gas molecules from a model of a rectangular cross section of channel walls in the free regime. We assume that the channel maintains a constant pressure gradient. Mass and heat flows are obtained as a function of the tangential momentum’s accommodation coefficient and the ratio between the linear dimensions of the channel’s cross section. Similar results presented in the literature are compared.

The specific hydrodynamic properties of flows occurring under the heat convection of fluid with anomalous thermoviscosity in a closed square cavity are studied. The mathematical model is based on the equations of the dynamics of a continuous medium in the Oberbeck-Boussinesq approximation with a nonmonotonic viscosity dependence of the temperature. The finite volume method and SIMPLE algorithm based on multiprocessor technology are used for simulation. The dependence of the anomaly parameters on the character of the convective flow of the liquid is considered. The influence of the viscous barrier on the flow structure is determined for a number of problem parameters.