The supercomputer modeling the processes of creating metal composite materials using the supersonic cold gas-dynamic spraying the nanoclusters on a substrate is considered. The general relevance of the research is related to the development of technology for manufacturing nanoscale interconnections of electrical circuits that supply elements of very large-scale integrated circuits (VLSI). The relevance of this specific study is associated with the need to develop a mathematical apparatus and program tools for modeling all stages of composite creation technology. In this work, the final stage of the process is considered, where individual metal nanoclusters interact with each other and with the substrate. These processes are studied at the atomic-molecular level using molecular dynamics (MD) models. The integration of the MD equations is based on the velocity Verlet scheme using thermo- and barostats. Parallel algorithms are constructed on the basis of spatial decomposition of the computational domain and the methods for dynamic balancing the computing load. The program implementation is focused on the use of MPI and OpenMP technologies. The novelty of this study is associated with the development of a new approach to the calculations of different-material metallic systems based on applying the embedded atom model potential. As an example, the problem of copper and nickel nanoclusters interaction during the manufacture of the corresponding nanocomposite is chosen. Such nanocomposite is often used as an interconnection for elements of modern VLSI. Obtained results confirm the correctness of the developed computational procedure and the possibility of supercomputer modeling of metal composite nanostructures.

The problem of multiscale computer modeling the processes of supersonic cold gas-dynamic spraying (SCGDS) the nanoparticles onto a substrate is considered. The problem relevance is related to the development of technologies for the manufacture of micro- and nanostructures used in modern microelectronics. In this work, a multiscale approach is used. As its basic mathematical models, the quasi-gasdynamic equations system supplemented by Newton’s equations system, which describes the dynamics of individual particles, and the molecular dynamics method are used. To solve gas-dynamic equations, a classical grid approach based on the finite volume method is used. The particle method is implemented by integrating equations using the symmetric Adams scheme. To implement the molecular dynamics equations, the Verlet scheme is used. When combining these models, many problems arise related to matching the different scales, stability to small disturbances introduced by different scales, and the efficiency of calculations parallelization. This work attempts to study the above problems. Matching the different scales is realized using splitting the general algorithm by physical processes and scales and observing the conservatism principles at the level of the modeled medium macroparameters. Stability to small disturbances is ensured by matching the spatial and time steps of the applied numerical schemes. The efficiency of parallelization is ensured by a combination of the Schwartz domain decomposition method and the algorithms for computers dynamic load balancing. Testing and refinement of parameters and procedures for transition between different levels components of a SCGDS multiscale model confirms the correctness of the proposed approach.

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.

A mathematical model is developed and numerical modeling is performed to solve a scientific and industrial problem in the field of studying mass transfer processes in the “fracture set - matrix” system in a carbonate reservoir. The model is presented in a two-dimensional formulation, which is characterized by the presence of two subsystems with different sets of filtration parameters. The IMPES (implicit in pressure and explicit in saturation) and IMPIS (implicit in pressure and saturation) integration methods are used to numerically solve the system. An implicit finite-difference scheme is constructed for equations regarding pressure, when solving it, the saturations are set as fixed. Based on the solution of this scheme, the pressure in the fracture system and matrix is determined, and then the system is solved with respect to saturations. The explicit and implicit finite-difference schemes are considered to determine saturations. For a task on an industrial scale, significant resources are required to solve it. A parallel algorithm is proposed to speed up calculations with involves decomposing the computational domain into a lattice of domains of equal cardinality. Block-parallel processing is used when solving the implicit scheme. A series of computational experiments are performed to test the approach for both IMPES and IMPIS methods. Based on the obtained calculations, a comparative analysis of explicit and implicit methods for calculating equations for saturations is carried out. The calculation results confirm the effectiveness of the proposed fully implicit parallel algorithm.

The work is devoted to modeling the processes of spraying the nanoparticles transported by supersonic cold gas flow on substrates. This problem is relevant for the implementation of many nanotechnologies, for example, for the production of ultra-high resolution video systems, nanolithography technologies, etc. Experimental work in this area is based on theoretical analysis and mathematical modeling methods. Both the spraying process itself and the possibilities of controlling the quality of the resulting surface are studied. For this, a multiscale approach is often used combining models of continuum mechanics and particle models. Such combination makes it possible to describe the macroscopic properties of the gas flow carrying nanoparticles and its interaction with the substrate at the level of individual atoms and molecules. In this work, two scale levels are used. The macroscopic model is based on the equations of quasigasdynamics, the microscopic model is based on the equations of molecular dynamics. These two descriptions are used both separately and together. To analyze the full cycle of the spraying process, an original set of algorithms for pairing these models is proposed. The approach was tested on the example of spraying the nickel nanoclusters on a substrate of the same material and showed its efficiency.

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 work presents a parallel realization of a non-isothermal mathematical model of the process of heat and mass transfer of a two-phase fluid in a fractured-pore medium using a dual porosity model. Based on the algorithm of splitting by physical processes, a time-weighted difference scheme is constructed to ensure correctness and consistency of fluxes between the system of natural fractures and pore part of the reservoir. An implicit finite-difference scheme on a spatial grid is proposed for numerical solution of such a problem. The equation system is linearized by the chord method and solved by the method of matrix sweep. Computing the sweep coefficients for an algebraic problem requires large computational costs. To speed up the calculations, the matrix sweep is parallelized with the coefficients of the equations, which are matrices and vectors.

The process of two-phase filtration in a carbonate formation of fractured-pore type is considered. A mathematical model in a spatially two-dimensional formulation is proposed, a numerical method for solution and a parallel algorithm for its implementation are developed. The mathematical model is based on the Buckley-Leverett approach. The reservoir takes into account the exchange of fluids between low-permeability pores and natural fracturing, specified within the framework of the dual porosity model. The numerical algorithm is based on the use of the finite difference method and the splitting scheme by physical processes. To speed up calculations, a parallel algorithm based on two-dimensional domain decomposition is used. Numerical experiments were carried out, which showed that the developed algorithm is highly efficient and allows one to calculate the necessary characteristics of the modeled physical process.

Настоящая работа посвящена развитию многомасштабного подхода к расчету течений газа вблизи твердых поверхностей с учетом микроскопических эффектов. В рамках этого направления исследований рассматривается проблема постановки граничных условий на поверхности твердого тела с учетом данных эффектов, предварительно рассчитанных на атомно-молекулярном уровне. Основная цель работы состоит в формулировке макроскопических граничных уравнений, учитывающих процессы на поверхности обтекаемого газом твердого тела. В качестве основы макроскопической модели используется система квазигазодинамических (КГД) уравнений в объеме и уравнение теплопроводности в приповерхностном слое обтекаемого тела. Система дополняется реальными уравнениями состояния газа и зависимостями кинетических коэффициентов КГД уравнений от температуры и давления, полученными на основе молекулярно-динамических расчетов. Для апробации предложенных граничных уравнений рассмотрена задача об обтекании затупленного тела потоком газа. В качестве газа выбран сухой воздух. В качестве покрытия тела выбран никель. Расчеты проводились для двух значений скорости входного потока. Они подтвердили качественную корректность разработанной граничной модели и всей технологии моделирования.

This paper studies the development of a multiscale approach to calculate the gas flows near solid surfaces taking into account microscopic effects. In this line of research, the problem of setting boundary conditions on the surface of a solid body is considered, taking into account the effects preliminarily calculated at the atomic-molecular level. The main aim of this paper is to formulate macroscopic boundary equations that take into account the processes on the surface of a solid body around which there is a flow of gas. The macroscopic model is based on a system of quasi-gasdynamic (QGD) equations in the volume and the thermal conductivity equation in the near-surface layer of the streamlined body. The system is supplemented with real gas state equations and dependencies of the kinetic coefficients of the QGD equations on temperature and pressure, obtained on the basis of molecular dynamics calculations. To test the proposed boundary equations, the problem of the gas flow around a blunt body is considered. Dry air is selected as the gas. Nickel is chosen as the body coating. Calculations are carried out for two values of the inlet velocity. They confirm the qualitative correctness of the developed boundary model and the entire modeling technology.

This work considers the isothermal process of incompressible viscous fluid filtration in an oil-saturated, fractured-porous reservoir. A study of the pressure and water saturation distribution process is carried out for a case in which a production well is put into operation. For this problem, i.e., a mathematical model in a two-dimensional formulation, a numerical method and a parallel algorithm are proposed. The mathematical model of two-phase filtration is written in accordance with the classical laws of continuum mechanics and Darcy’s law and also includes a function of fluid exchange between low-permeability pores and high-permeability natural fractures within the framework of the Warren–Root model. The numerical solution is based on the finite-difference method and a splitting scheme of physical processes and spatial coordinates. For a split system with respect to piezoconductivity, an implicit finite-difference scheme with fixed saturations is constructed, and with respect to saturation transfer, explicit and implicit difference schemes are constructed. For parallel implementation of the developed numerical approach, a method based on geometric parallelism is selected. Testing of the developed method is performed using the example of calculating liquid mass transfer for a wide range of parameters. To verify the model, the obtained calculated pressure curves are compared with field data recorded by a deep-well measuring device. The results allow for estimation of the distribution of reservoir pressure and water saturation depending on the permeability of the fracture set and the pore part. The obtained results allow for monitoring of well operations, reducing unexpected accident risks and optimizing the development system in order to increase oil production in fractured-porous reservoirs. Computational experiments confirm the efficiency of the developed numerical algorithm and its parallel implementation.

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.

The work is devoted to numerical modeling of the processes of heat and mass transfer of a two-phase fluid in the environment of a production well, which is necessary for monitoring the development of fractured-porous reservoirs. This work proposes an efficient approach to constructing a solution to the problem. To solve the problem, a model of the “double medium” type is used, where the pore part of the reservoir is considered as the first medium, and the system of natural fractures is considered as the second medium. For the resulting mathematical model, the difference schemes with time weights are constructed based on the algorithm of splitting by physical processes, which ensure the correctness and consistency of fluxes in the fracture system and the pore reservoir. In the numerical solution, the approximations of differential operators obtained in the framework of the finite difference method are used. For the parallel implementation of the developed numerical approach, the domain decomposition method and the matrix sweep algorithm are chosen. The program implementation is made using the MPI standard. Computational experiments are carried out, the results of which confirm the effectiveness of the developed numerical algorithm and its parallel implementation. In numerical experiments, the distributions of pressure and temperature near an operating production well are obtained, on the basis of which it is possible to adjust the operation of wells in order to increase production.

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 concerns the efficiency of an exponential difference scheme for solving non-linear degenerate parabolic equations which models flow in saturated/unsaturated porous media. The discretization is based on backward Euler time approximation and quasilinearization of the obtained elliptic equation. Then the linear diffusion-convection problem is approximated by exponential finite difference scheme [20, 21]. The performance of the proposed scheme in the case of piecewise constant and degenerate absolute permeability is illustrated by various numerical tests.