The article describes variants for computing the series 1 + 1 + 1 + ... performed by different authors. Many of the variants give different sums. On this basis, these methods are concluded to be incorrect. In opposition to them, a description of the approach that can be recognized as a method of summing this and other divergent series is given. This approach allows extending the range of applicability of computing devices up to infinity.

The paper suggests a modification of boundary elements numerical method, which uses displacement discontinuity method in 3D space. The advantage of this method is in essential decrease of computational elements number in 3D space because only the surface of a fracture is placed on final elements simulating the discontinuity of elastic medium. Thus the dimension of the problem is decreased. The method proved to be effective for hydraulic fractures modeling and their interaction with natural faults in host rock formations.

A system of differential equations for determining the pressure, saturation, and concentration of components in the simulation of three-phase multicomponent flow of oil, gas, and water is considered. A method for determining the concentration of components in phases is described by solving the initial system of equations for the material balance of a mixture using the Newton – Raphson method. An example of the use of this method for modeling the water- alternating-gas injection is given.

The article describes the linear kinetic model of the glass transition of PVC plastic compounds. Dependences of some physico-mechanical and dielectric properties of PVC plastic compounds on the plastic content and temperature are obtained. Experimental and calculation data for PVC samples with different contents of plasticizer are presented; those were obtained during thermal aging and dosed saturation of PVC resin with a plasticizer.

The article considers a mathematical modeling of viscous incompressible fluid flows in channels with transverse dimensions alternating with time. The modeling consists of: construction of a mathematical model; numerical algorithm; carrying out computational experiments to study the dependence of flow characteristics on the vibration mode of edges of a channel.

The mathematical modeling of flows described by Liouville, Boltzmann, Smoluchowski equations and generalized systems of conservation laws are described in the paper. These balance equations (continuity) are the fundamental relationships that determine the statistical solutions of dynamical systems modeling the interaction of particles by long-range potentials and local collisions. The nonlinear dynamics of the flows described by these equations leads to the appearance of singularities for hydrodynamic parameters interpreted as the appearance of a front-type structure stable at macroscopic scales. The mechanisms of the appearance of the structures and computational aspects of their localization are considered.

The article considers a process of heat propagation from a heated gallery of production wells to an oil reservoir. A one-dimensional diffusion-convection equation for a region with an unknown moving boundary is proposed to describe this process. For the correct formulation of the problem, an auxiliary condition is set for the temperature at the gallery of wells. By changing variables, the problem is transformed into a coefficient inverse problem. Further, the time derivative is discretized and explicit-implicit schemes are used to approximate the operators of the problem. To solve the resulting differential-difference problem, a special representation is proposed. As a result, at each discrete value of the time variable, the differential-difference problem splits into two direct boundary-value problems and a linear algebraic equation with respect to the approximate value of the sought-for coefficient. The Thomas algorithm is used for the numerical solution of the obtained direct boundary value problems. Numerical experiments were performed on the basis of the proposed numerical algorithm.

Seismic prospecting is the routine method of locating oil and gas fields. In view of the discovery of non-traditional reservoirs, an important task is the development of new procedures for processing field data. The development of high-performance computing systems allows simulating seismic wave propagation processes in heterogeneous geological environments to prepare synthetic- seismograms with high precision. The article presents the use of the grid-characteristic method on hexahedral grids, which describes correctly the curved boundaries between geological layers and explicitly identifies fractured inclusions. The problem of waves’ propagation from an earthquake source occurring in the shelf area is solved; a complete three-dimensional picture of the process is obtained. A study of the passage of seismic waves through a fractured medium with a variation in the fracture parameters is undertaken. The kinematic and dynamic anisotropy of the signal recorded on the day surface is estimated.

In this work the results of extracting the system of channels and pores from the data processing of the X-ray tomography of the core sample are presented. Based on the developed pores structure numerical 3-D simulations of viscous incompressible fluid flow in this system and evaluating of porosity and permeability of this structure is performed.

The article describes visualization methods of hydrodynamic models. Main purpose of seam examination is to predict its status and to find ways of increasing final oil recovery. Modeling of the oil reservoir allows increasing accuracy of reservoir properties and geological structure of the seam during history matching, as well as choosing the best strategy of reservoir management. Geometry of the modelled oil seam (called grid) is represented via the finite number of elements or cells that determine size and volume of the oil reservoir. The more elements used for reservoir volume approximation, the more detailed are the simulation results. However, increasing the accuracy of modeling leads to bigger amount of computation and higher memory usage, therefore final geometry is a compromise between computational complexity and accuracy.

Geometry elements may be presented in various forms that influence the modeling accuracy. One of the simplest ways is to present cells of the grid as uniform cubes. The article presents a method of creating cell geometry for reservoir hydrodynamic models with the use of “corner points” that allows achieving better accuracy.

The article is devoted to the description of the mathematical apparatus and testing techniques, designed to quantify network protocols and interpolation methods, which can be used to transfer and transform information about processes in real-time systems.

The article describes problems of mathematical modeling of three-phase filtration in conditions of thermal gas treatment for an advanced recovery method. Brief description of stratum in the Bazhenov formation is given. Basic mechanisms of the thermal gas treatment during enhanced oil recovery are considered. The main features of the applied technology during injection of the water-air mixture in the wet in-situ combustion process are discussed.

The article considers the problem of the process modeling of catalytic oil cracking. The model represents a system of homogeneous differential equations of order one with constant coefficients. An approach to algorithmic presentation of an analytical solution of similar systems of differential equations in modeling problems of the oil refining process is proposed.

Educational process of the present-day world is impossible without using leading digital technologies. These technologies are able to facilitate and accelerate the transfer of information. This paper shows features of virtual and augmented reality and their possible contribution to the teaching students of the landscape architecture program and to their future professional field. The article discusses core principles of virtual and augmented reality, open source software for 3D modeling and AR-applications.

The article considers an alternative approach to the decision making on the selection of downhole equipment. It is based on a retrospective analysis of the operating methods of a well in order to obtain the actual supply characteristics of the well and the performance of a pump on a real liquid.

The article considers aspects of teaching preschool children and primary school pupils to programming with the help of the non-textual programming system PiktoMir. The solution for the general methodological task of teaching preschool children and primary school pupils to the basics of algorithmics is proposed.

The article considers an analysis of existing models and algorithms that are or can be applied for simulating, forecasting and supporting decision-making in fighting forest fires. The analysis is based on a large number of domestic and foreign scientific publications. The structure of a complex information analysis computer system for fighting forest fires is proposed. A classification of problems that can be solved by such system, as well as by corresponding models and algorithms, is proposed.

The development strategy of the digital economy in the Russian Federation provides global changes in all spheres of life, both for the state and society. New challenges of modern times set new tasks to accelerate the rates of development of production, technology and education. The pace of digitalization of education and the breadth of implementation of the digital educational environment must meet the goals and objectives of modern educational processes. The article considers the challenges facing modern education, examines the technology of implementation and development of digital processes in education. A comprehensive approach to the construction of individual tracks of students is proposed.

In this paper the adaptive architecture of a multifunctional computer simulator is considered. This simulator solves the problem of analytical and simulation modeling of the technological process, training and analysis of the training efficiency of the human operator. The mathematical model of the components of the simulated system is adjusted taking into account the selected operating mode of the simulator that provides a balance of time parameters for the computer simulator. This task is especially relevant in the modeling of parallel dissimilar processes occurring in automated control systems. A feature of the proposed mathematical model of the human-machine system is the possibility of its adaptation by means of an artificial neural network (ANN). The ANN provides an identification of the control object and the results of the operator's actions. As an example of constructing an analytical model, a dynamic model for heating the coolant is given. The paper proposes the approach to constructing a simulator in which an evaluation of the effectiveness of the human-machine system is carried out. Numerical indicators of resource consumption are used. Such evaluation can be represented by a diagram form (quality indicators and the dynamics of some operators’ participation). The availability of such performance indicators allows improving the efficiency of the computer simulator. The paper presents a classification and principles of multifunctional computer simulator development for personnel training.

The article considers the problem of determining the efficiency of oil wells. A choice and a brief description of performance indicators of injection wells are presented. These indicators have the indirect effect on the main feature of an oil well – the production rate. The correlation between highlighted characteristics is established; therefore the factor analysis to combine them into the independent groups (factors) is carried out. The regression equation for determining and predicting the efficiency of wells is applied to describe the relation between obtained factors and the production rate. Software package STATISTICA is used for the multivariate analysis of the initial data.

The paper considers some approaches to modeling the occurrence and spread of landscape peat fires and their connection with new monitoring methods. A brief overview of remote monitoring methods is given. The potential for their use not only for discovery of started fire, but also for the purposes of areas detection where current meteorological and other conditions could possibly contribute to peat fires is described. Such places should become objects of additional efforts to prevent or detect early of peat fires.

Features of the functioning of automated process control systems for water quality control in water circulation systems of industrial enterprises are singled out. Based on the general system of vulnerability assessment, an algorithm for assessing the threats to information security of the automated process control system for water quality control in water circulation systems is proposed. An estimate of the level of the most common threats to information security upon the criteria of the research group Positive Technologies is derived. It is shown that the threat of malicious code execution is the most dangerous for the normal functioning of this system.