The article considers the important problem of modeling nonlinear wave processes in a microwave generator with magnetic insulation. For its numerical analysis, a new computer model is proposed, comprising Maxwell’s equations and the equations of motion of relativistic charged particles, their joint integration by the grid method and the cloud particle method, and a parallel software implementation. In numerical experiments, the spatiotemporal characteristics of relativistic electron beams and plasma, as well as the parameters of the generator’s output radiation, were obtained. The analysis of the results confirmed the correctness of the numerical approach developed.

The work discusses a web laboratory designed for a supercomputer modeling of spraying processes. The main problems it solves are the unification of interaction with various remote supercomputers and the automation of computational experiments through an interactive graphical user web interface. The work describes the architecture and the main technology stack used to build the laboratory, and also provides the results of embedding a specific application.

The article considers the methodology of mathematical modeling of the process of hydrocarbon fluid isomerization in a catalytic reactor used for the synthesis of organic fuels. A model for calculating the parameters of fluid flow in a mixed medium "open space – porous body" has been developed, taking into account the properties of the porous material and the main chemical transformations characterizing hydroisomerization. The model includes the Navier-Stokes equations regularized on the basis of the quasi-hydrodynamic approach, averaged over a representative elementary volume, and a system of convection-diffusion equations for calculating the evolution of the concentrations of raw materials and the reaction product. In the spatially two-dimensional case, a numerical algorithm for solving the problem has been developed; its software implementation has been performed. Trial calculations of the model problem have been carried out, which have shown the correctness of the developed numerical approach and the operability of the created software code.

Spraying the nanoparticles on a substrate is an actual and promising technology in many industries. The theoretical study of this process in various conditions is often implemented using computer modeling. In this work, a comprehensive methodology for modeling spraying processes is presented. The methodology is based on direct atomic-molecular calculations. Parallel technologies are used for the computer implementation of the methodology, which allow obtaining results with a given level of resolution and accuracy. Various aspects of the developed technology and computation results are discussed on the example of the interaction of nanoparticles with a substrate consisting of nickel atoms.

Problem of modeling the interaction of metal nanoclusters in very large-scale integrated circuits (VLSIC) interconnects is considered in the context of improving manufacturing technologies for promising microelectronics instruments and devices. This problem is relevant when analyzing the performance and durability of VLSIC, the main components of which are obtained using epitaxy, sputtering and lithography methods. At the current stage of development, a feature of such technologies is the transition of the VLSIC element base to the nanometer range, which significantly increases the quality requirements for all their components.The work presents a supercomputer technology for atomistic modeling, which is proposed to be applied to the numerical analysis of the degradation problem for ultra-thin interconnects of VLSIC elements. It includes the construction of a mathematical model, its parallel numerical implementation and test calculations. The result of the work is a numerical analysis of the interaction processes between copper and tantalum nanoclusters, which are typical components of interconnects. The data obtained as a result of the analysis are consistent with theoretical ideas about the processes occurring in such microsystems.

The aim of this work is modeling processes of field electron emission in strong electromagnetic fields. This problem is relevant for many technical and medical applications. At present time, electrical devices that combine a large value of field, a powerful relativistic effect and an ultra-short time interval of action are in demand. They find their application in the treatment of the surfaces with inorganic, organic and mixed structures. Modeling of such devices encounters certain difficulties due to the complexity of the mathematical description of the emission processes. In this paper, an approach using the method of large smoothed particles in combination with grid calculation of fields based on Maxwell's equations is proposed. The study was carried out within the framework of the problem of calculating the field emission of electrons from the surface of axisymmetric metal cathodes on Cartesian and unstructured curved meshes. To implement the approach, a complex mathematical model, a parallel numerical algorithm and its software realization have been developed. The elaborated software is focused on the use of multiprocessor computing systems with a central architecture. Test calculations confirmed the correctness of the proposed approach and the high efficiency of its software implementation.

The work presents a digital platform for supercomputer modeling the problems of spraying the particles on substrates. The purpose of this work is to discuss the general architecture, technology stack and implementation features of the platform's user interface. The platform is based on web technologies for access and management of calculations, which allow implementing a user system for conducting a full cycle of a computational experiment, including the configuration of applied applications, their launch on remote computing resources, monitoring the completion of tasks, analysis and interactive visualization of results. User interaction with computing resources is implemented through the graphical interface that does not require the client computer to have any additional software, except actual version of a modern web browser. An important advantage of the platform is the ability to make large-scale computer research in a multi-user mode that is based on the natural principles of building client-server applications. The presented digital web platform was successfully tested on computing clusters of the KIAM RAS in solving a number of the topical mathematical problems of nanotechnology. Also, with its help, for the last 3 years, group training of MIPT students in modern information technologies has been carried out.

Данная работа посвящена развитию численного подхода к моделированию стадии «тонкой» фильтрации водной среды, следующей за прохождением механических фильтров. На этом этапе очистки водная среда подвергается электромагнитному или тепловому воздействию. Для анализа процессов очистки предлагаются математические модели течения жидкости с учетом тепловых эффектов, эволюции концентрации загрязнителя в условиях развитых конвекционно-диффузионных процессов и при наличии квазистатического электрического поля. Для описания течения водной среды, содержащей частицы твердых мелкодисперсных примесей, используется квазигидродинамическая модель, дополненная уравнениями конвекциидиффузии-реакции. Численная реализация модели в случае трехмерной декартовой геометрии основана на методе конечных объемов на нерегулярных тетраэдральных и призматических сетках и ориентирована на применение параллельных вычислений. В качестве примеров использования разработанной компьютерной технологии моделирования рассмотрены задачи электромагнитной очистки водной среды и загрязнения теплоэлектронагревательного (ТЭН) элемента. В первой задаче рассчитана зависимость концентрации загрязнителя от времени, которая демонстрирует эффект очистки и позволяет оценить ее степень в зависимости от параметров электрического поля. Во второй задаче исследовался процесс образования накипи и последующей регенерации ТЭНа. Проведенные расчеты показывают, как происходит загрязнение ТЭНа и как при воздействии соляной кислоты происходит его очистка. Эти данные позволяют уточнить параметры перспективных установок замкнутого цикла, в которых чередуются циклы нагрева среды и регенерации нагревательных элементов.

This paper studies the development of a numerical approach to model the stage of fine filtration of an aquatic environment, after the water passes through mechanical filters. At this stage of purification, the aquatic environment is subject to electromagnetic or thermal effects. For the analysis of cleaning processes, mathematical models of the fluid’s flow are proposed, taking into account thermal effects and the evolution of the pollutant’s concentration, taking into consideration the developed convection-diffusion processes in the presence of a quasi-static electric field. To describe the flow of an aqueous medium containing particles of solid fine impurities, a quasi-hydrodynamic model, supplemented by the equations of convection-diffusion-reaction, is used. The numerical implementation of the model in the case of three-dimensional Cartesian geometry is based on the finite volume method on irregular tetrahedral and prismatic meshes and is focused on the use of parallel computing. The problems of electromagnetic cleaning of the aquatic environment and pollution of the electric heating element are considered are considered as examples of the use of the developed technology of computer modeling. In the first problem, the dependence of the pollutant’s concentration on time is calculated. It demonstrates the cleaning effect and allows us to estimate the degree of cleaning depending on the parameters of the electric field. In the second problem, the process of scale formation and subsequent regeneration of the heating element is studied. The calculations performed show how the heating element is contaminated and how it is cleaned under the effect of hydrochloric acid. These data make it possible to refine the parameters of promising closed-cycle plants, in which cycles of medium heating and regeneration of heating elements alternate.

The paper discusses the problem of computer simulation of electron emission processes in strong electromagnetic fields. In this work, a numerical method for calculating electron emission from the surface of a metal cathode for the axial symmetric geometry of a technical system is proposed. For modelling, the particle method and grid calculations of electromagnetic fields based on Maxwell's equations are applied. The approach uses the representation of large smoothed Gaussian particles and implements calculations of the electromagnetic fields on Cartesian spatial grids. The software realization is directed towards on parallel computing. The calculation of the emission process in a coaxial cylindrical diode with magnetic self-insulation with the use of developed technique was carried out. The process is considered for two situations: with and without the longitudinal plasma layer. The calculations show that the presence of plasma leads to an increase in the emission current. This result is consistent with the results of experiments.

The problem of calculating the processes of electron emission from metal surfaces in strong electromagnetic fields is considered with allowance for relativistic effects. One of the methods of simulation in these processes is the particle method combined with grid calculation of fields on the basis of Maxwell’s equations. Similar techniques have been developed since the 1960s to the present. However, existing approaches have certain limitations. In this work, for an axisymmetric geometry of the generating system, a new numerical technique simulating the processes of electron emission from metal cathode surfaces is presented. The technique uses the representation of large smoothed Gaussian particles and implements the calculation of electromagnetic fields on Cartesian spatial grids. The software implementation is oriented to parallel computing. The aim of numerical experiments was to determine the parameters of electron emission. Diode and triode cylindrical systems were chosen as test problems. In numerical calculations, the spatiotemporal characteristics of relativistic electron beams generated by emission processes are obtained, including the reproduction of the Child–Langmuir current. The numerical technique developed has confirmed its correctness and efficiency.

The paper is devoted to the development and computer implementation of a numerical method for modeling the interaction of metal nanoclusters with a substrate at the mesoscopic level. This research as a whole is relevant in connection with the development of nanotechnologies for obtaining extremely thin metal coatings by various spraying methods. From a practical point of view, its relevance is determined by the lack of adequate mathematical models at the mesoscopic level to describe processes in the submicron size range. This work presents the mathematical model of a metallic medium consisting of spherical nanoclusters and a parallel numerical algorithm for its implementation. The model includes Maxwell's equations of electrodynamics to describe the evolution of the electromagnetic field, as well as the averaged equations of Newtonian dynamics to describe the motion of individual nanoclusters and the electron gas surrounding them. The numerical algorithm is based on the method of grids and the integration of the equations of motion of the particles. The algorithm is parallelized with respect to both space and particles. We devised a set of parallel programs and carried out preliminary model calculations. Nickel is used as the material for the nanoclusters and the substrate. The conducted numerical experiments show the efficiency of the proposed computer model.

This paper discusses formation of calcium carbonate precipitation on electric heaters and removal of scale from them. This problem is relevant at the moment in the context of energy saving and the duration of the life cycle of electric heaters. To solve the problem, an approach based on mathematical modeling of the formation of solid deposits on heating elements is proposed. In this approach, the system of quasi-hydrodynamics equations is used as a model, supplemented by the equations of convection–diffusion-reaction. The numerical implementation of the model for a three-dimensional geometry is based on the grid method and parallel computing. The developed numerical technique allows us to analyze the influence of calcium carbonate precipitated on the surface of heaters on electricity consumption. The process of cleaning electric heaters with hydrochloric acid is also considered. The paper provides estimates of the efficiency of electric heating devices with scale and without scale after cleaning.

The work is devoted to the development of multiscale approaches for modeling the processes of supersonic cold gas dynamic spraying of nanoparticles on the substrates. Modeling of gas dynamic spraying processes involves solving two practical problems: a) controlled transportation of nanoclusters to the spraying place in the general gas flow; b) analysis of the interaction of nanoclusters with the substrate surface in its boundary layer. A combination of these problems is considered, which is implemented on the basis of a multiscale calculation of a two-phase flow of a gaseous medium with the inclusion of finely dispersed solid metal particles. The work proposes a new multiscale computing technology that combines macroscopic, microscopic and mesoscopic descriptions of the physical processes under study at the model level. Within its framework, two two-scale approaches are used, taking into account, respectively, macro- and micro- and macro- and mesolevels of spatial detail. The macroscopic components of the final mathematical model are based on modified quasigasdynamic equations for analyzing the flow of a two-phase multicomponent gaseous medium, as well as Maxwell’s equations near the substrate surface for calculating the effect of electromagnetic fields on the solid phase. Newton’s dynamics equations are used to describe processes on micro- and mesoscopic scales. In the first case, these are the equations of molecular dynamics, written taking into account the pressure forces in the gas phase and mechanical stresses in the solid phase. In the second case, these are the equations of particle dynamics, taking into account mainly the Lorentz force. For the numerical implementation of the macroscopic components of the model, the grid method of finite volumes is used; for the micromodel, the Verlet scheme is used; for the mesomodel, a symmetric scheme is used that approximates the equations of Newton’s electrodynamics. The aims of the work were a physically substantiated formulation of all model components and preliminary calculations of the motion of a nickel nanocluster accelerated by a supersonic nitrogen flow near a nickel substrate.

Modern approaches used in the design of high-performance hardware and software platforms for collective usage are considered. A web-system architecture has been proposed. Its main goal is to significantly simplify the use of software designed for mathematical computer modeling of physical processes of a complex nature on supercomputer devices. The technological stack has been developed, on the basis of which the digital web-platform prototype of has been developed. With the help of the developed platform, a number of tasks related to the purification of water and air from harmful impurities containing metal salts have been solved.

The work is devoted to the development of a multiscale approach for modeling multiphase liquid and gas flows in a porous medium. The problem of reprocessing organic fuels, including natural gas, has been chosen as an application. One of the important stages of such reprocessing is the purification of hydrocarbon raw materials from accompanying impurities (metal particles, solid organic compounds, etc.) in chemisorbers. To model treatment processes in such technical systems, a multiscale mathematical model is proposed that combines macroscopic and microscopic descriptions of multiphase fluid flows in a treatment system. The first part of the model refers to macroscopic scales and includes equations of gas and/or hydrodynamics for describing the multiphase multicomponent fluid flows, supplemented by convection-diffusion-reaction (CDR) equations for impurity concentrations. The second part of the model refers to microscopic scales and describes the processes in the boundary layers of the treatment system and in the pores. It is based on the equations of molecular dynamics and analytical chemistry. Both parts are conjugated within the method of splitting by physical processes. The work considers the problem of natural gas purification from hydrogen sulfide by passing contaminated fluid through a porous material. In it, the first part of the model is represented by quasistationary Navier–Stokes equations averaged over the volume. For their numerical implementation, an implicit grid algorithm implemented by Newton’s method is proposed. The CDR equations are solved according to an implicit time scheme. The second part of the model is represented by the dependencies of the permeability tensor components on porosity and impurity concentrations. The separate parts of the model have been calibrated in numerical experiments. In particular, model calculations of flows in a scrubber with a porous plug have been carried out. The calculations are performed using the FEniCS computing platform.

Modeling the processes of formation and removal of limescale formed in water treatment systems is considered to develop closed-loop technologies. Solid deposits that form over time on the surfaces of heat exchangers damage the heating elements of cleaning systems and neutralize their cleaning function. Various approaches are used to remove sedimentary fractions, but the most effective of them are based on mathematical modeling. In the work, a computational experiment is carried out, reproducing the main stages of water purification from solid impurities. For this purpose, the process of formation of solid deposits on a heating element of complex geometry was studied. The flow modelling is based on the quasi-hydrodynamic model supplemented with convection–diffusion–reaction equations. The performed three-dimensional calculations show the evolution of the heating element contamination, leading to a drop in the efficiency of its heat transfer and a decrease in the quality of cleaning. In addition, the process of restoring the characteristics of the heating element when pumping hydrochloric acid through the system is investigated in the calculations. The results illustrate the reduction of the sedimentary layer on the heating element and the restoration of its cleaning function.

The paper proposes a complex mathematical model designed to analyze the processes taking place in electromagnetic water filters and heat exchangers in terms of scale formation and removal. The formed mathematical model includes models of fluid flow taking into account thermal effects, the evolution of pollutant concentration with the reflection of convection-diffusion processes and electrostatic effects to take into account filtration effects. The software implementation of the computational algorithm for three-dimensional geometry is based on the finite volume grid method and parallel computing. The results of model calculations were obtained for the problem of electromagnetic water cleaning and the problem of scale contamination of the heat exchanger using the developed software package.

The work considers the construction of a modern digital platform for supercomputer modeling the problems of particles deposition on substrates. The web-based approach is proposed that makes it possible to form the unified user system for carrying out the full cycle of numerical calculation, including the configuration of applied applications, their launch on remote computing resources, monitoring of the task, analysis of the results, and interactive visualization. At the same time, the interaction with supercomputers and clusters is implemented through a graphical interface that does not require to have additional software, except for a web browser. Another advantage is the possibility of conducting a multi-user computational experiment, arising from the natural principles of building client-server platforms, in which specialists from different fields can access up-to-date data obtained during modeling. The digital web platform has been tested on KIAM clusters, and it is also used for group training of MIPT students in modern information technologies. This work is devoted to the discussion of the general architecture, the technological stack and the resulting user interface.

The problem of numerical modelling water purification from iron impurities is considered. The cleaning task is relevant for many industrial applications, including the development of new cleaning methods and devices for the preparation of ultrapure water. The performed mathematical study is associated with the calculations of the water flow and the transfer of contaminants in the treatment system for real geometry. In the work, a new numerical approach to solving the problem is proposed; the corresponding calculated data are obtained. The analysis of the results showed that they have a good agreement with the calculation results of the ANSYS CFD package.