Volume 11, Nº 4 (2019)

This paper proposes a new approach for solving problems of vortex structures’ interaction with a free surface. The second-order accuracy finite-difference scheme based on the well-known CABARET scheme is suggested for incompressible viscous fluid with a free surface. The CABARET method in the case of an incompressible medium additionally solves the problem of the velocity field’s solenoidation. Solving such a problem implies solving a system of linear equations with respect to the pressure variable and then taking the pressure gradient into account when calculating equations of motion. Solving the system of linear equations is a separate related problem that is not included in the description of the CABARET method, and this paper presents only the problem statement without specifying a specific method for solving the system.

In this paper, we describe the stages and results of investigating the features of oil-saturated fractured zones through the analysis of the spatial dynamic wave patterns obtained by supercomputer-aided modeling with the grid-characteristic method. Full-wave modeling is employed in geophysics to construct synthetic seismograms and to solve inverse problems. In this paper, we demonstrate that the analysis of spatial dynamic wave patterns allows us to make conclusions that can later be useful in geophysical surveys. Compared to methods for analysis and interpretation of seismograms, the proposed approach to wave pattern analysis facilitates the investigation of the dynamics of waves of different types, while also being more accurate than the ray-tracing method and geometric approximation. Three types of fractured clusters—solid, intermittent, and chess—are considered. As a result of the investigation, some characteristic regularities are discovered, e.g., the dependence of the seismic wave scattering angle on the source frequency and the geometric arrangement of the fractures in the cluster, and the source frequency dependence of the trajectory and velocity of the point at which the longitudinal head wave separates from the S-wave. These regularities can subsequently be adapted to optimize the seismic prospecting of hydrocarbons and the investigation of fractured zones, e.g., to select the optimal equipment and method for seismic survey. In addition, we discuss the importance of analyzing the spatial dynamic wave patterns when designing and testing numerical methods, as well as interface and boundary conditions, including the absorbing ones. Moreover, we propose an approach to construct a nonlinear scale that enables the simultaneous analysis of the spatial dynamic wave processes whose amplitudes differ by more than two orders of magnitude.

The processes of charge transfer in semiconductors are considered. A model is constructed based on the quantum kinetic equations for the distribution functions of conduction electrons and holes of the valence band in the phase space of coordinates and quasi-momenta. Scattering of charge carriers is modeled by the statistical particle method. The basic processes of electron scattering by lattice defects are considered. The calculations of the electron drift velocity in pure and doped silicon are presented.

Two different data assimilation methods are compared: the author’s method of the generalized Kalman filter (GKF) proposed earlier and the standard ensemble objective interpolation (EnOI) method, which is a particular case of the ensemble Kalman filter (EnKF) scheme. The methods are compared with respect to different criteria, in particular, the criterion of the forecasting error minimum and a posteriori error minimum over a given time interval. The Archiving, Validating and Interpolating Satellite Oceanography Data (AVISO), i.e., the altimetry data, was used as the observation data; the Hybrid Circulation Ocean Model (HYCOM) model was used as a basic numerical model of ocean circulation. It has been shown that the GKF method has a number of advantages over the EnOI method in particular, it provides the better temporal forecast error. In addition, the results of numerical experiments with different data assimilation methods are analyzed and their results are compared with the control experiment, i.e., the HYCOM model without data assimilation. The computation results are also compared with independent observations. The conclusion is made that the studied assimilation methods can be applied to forecast the state of the ocean.

The article investigates the questions of calculating the dynamics of quantum gases on the basis of the stochastic interpretation of Schrödinger equation. A comparison of several appropriate methods for solve of equations of quantum mechanics – based on the method of simulating the dynamics of quantum particles as a Brownian motion, using an analytical solution of the equations of quantum hydrodynamics and directly the Schrödinger equation. An example of modeling the gas flow of quantum particles with allowance for the temperature and electric fields and friction forces is considered. The influence of the form factor of the initial distribution of the gas density, temperature, and parameters of the computational method is studied.

We propose a description and explanation of a heuristic approach that can be used in applied dynamic economic models containing agent optimization problems. Solving such problems, we can obtain a system containing differential and algebraic equations, inequalities, and complementary slackness conditions. These conditions significantly complicate the analysis of such models even at the calibration stage. We show that the natural assumption about the alternation of regimes defined by the method of the resolution of the complementary slackness conditions allows us to pass to relations that are more regular and convenient from the point of view of the model’s calibration.

The present study aims to develop a hybrid scheme using trigonometric cubic B-spline basis functions with differential quadrature method for solving nonlinear Schrödinger equation in both one and two dimensions. This method reduces the nonlinear equation into a set of ordinary differential equations which can be further solved by the modified form of Ruge–Kutta method. This proposed method has been applied to this equation using two different approaches and also has been tested for proficiency on seven numerical examples. The obtained numerical results found to be synonymous when related with the exact solution. The obtained numerical results are also in good agreement with the results available in the literature. Comparison of numerical and the exact solution is depicted in the form of figures and tables.