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About this book

This book presents best selected research papers presented at the Thirteenth International Conference on Applied Mathematics and Mechanics in the Aerospace Industry (AMMAI 2020), held from September 6 to September 13, 2020, at the Alushta Health and Educational Center (The Republic of Crimea). The book is dedicated to solving actual problems of applied mechanics using modern computer technology including smart paradigms. Physical and mathematical models, numerical methods, computational algorithms, and software complexes are discussed, which allow to carry out high-precision mathematical modeling in fluid, gas, and plasma mechanics, in general mechanics, deformable solid mechanics, in strength, destruction and safety of structures, etc. Technologies and software systems that provide effective solutions to the problems at various multi-scale levels are considered. Special attention is paid to the training of highly qualified specialists for the aviation and space industry. The book is recommended for specialists in the field of applied mathematics and mechanics, mathematical modeling, information technologies, and developers of modern applied software systems.

Table of Contents


Chapter 1. Applied Mathematics and Mechanics in Aerospace Industry

The chapter contains a brief description of chapters that contribute to the development and applications of computational methods and algorithms in different areas of gas, fluid, and plasma dynamics, solid mechanics, dynamic systems and optimal control, information technology. The first part presents the recent advances in computational fluid dynamics. The second part introduces numerical simulation of plasma and multiphase flows. The third part is devoted to computational solid mechanics, the fourth part provides a numerical study of dynamic systems and the fifth part focuses on information technology and artificial intelligence.
Margarita N. Favorskaya, Lakhmi C. Jain, Ilia S. Nikitin, Dmitry L. Reviznikov

Computational Fluid Dynamics


Chapter 2. Aspects of Meteoroids Flight in the Earth’s Atmosphere

We study the motion of meteoroids in the Earth’s atmosphere. It is shown that space bodies do not always fall on the Earth or explode and shatter into small fragments in the atmosphere. Instead, for certain aerodynamic characteristics and small angles of entry into the atmosphere, they may re-enter the outer space after traveling several thousand kilometres through the atmosphere.
Nina G. Syzranova, Viktor A. Andrushchenko

Chapter 3. Numerical Simulation of Flow Structure Near Descent Module in Mars Atmosphere

Based on the conservative numerical method of flux, a hypersonic flow of a viscous heat-conducting gas is simulated near the landing module in Martian atmosphere. Special attention is paid to the study of the structure of non-stationary flow on the side and bottom surfaces of the module. Flow parameters data in the indicated areas are given. Vortex flow patterns near the descent module reflecting the spatial non-stationary nature of the flow are presented. Numerical modeling is implemented on multiprocessor supercomputers of cluster architecture.
Alexander V. Babakov

Chapter 4. Mathematical Modeling of Wave Motions of Fluids

The study of wave movements of liquids is of interest both theoretically and practically. This can include flows with a free surface and flows with internal waves. For correct mathematical modeling of such flows, the finite-difference schemes of methods must have such properties as follows: high order of approximation, minimal scheme dissipation and dispersion, performance in a wide range of the Reynolds and the Froude numbers, and that is especially important the property of monotonicity. This chapter presents two approaches: splitting method for incompressible fluid flow (SMIF) method and compact accurately boundary adjusting high-resolution technique (CABARET) method, of course, whose finite-difference schemes have the properties listed above. A number of test tasks are considered and compared with theoretical, experimental data and calculations of other authors.
Valentin A. Gushchin, Vasilii G. Kondakov, Irina A. Smirnova

Chapter 5. Numerical Simulation of Taylor Vortex Flows Under the Periodicity Conditions

It is known from the experimental researches regarding the Taylor vortex flows between the rotating cylinders that a different number of pairs of the Taylor vortices can be formed within the one geometry. It means that different variants of the problem’s solution are allowable. The simulation method with periodic boundary conditions on the edges of the cylinder’s part was developed for the numerical research into the Taylor vortex flows. The results of the simulation of the flow for the various values of the periodicity sizes and different initial data are given.
Fedor A. Maksimov

Numerical Modeling of Plasma and Multiphase Flows


Chapter 6. The Investigation of the Evolution of Cluster Beam Development in the Nozzle-Skimmer System

The device skimmer is considered, which is intended to separate inert gas clusters with the aim of further collision them with a surface to increase its smoothness order. The condensation and the evaporation processes of Argon in the device are calculated. The modified method of moments (MM) is used for modeling. The droplet nucleation and growth rate coefficients were found by the semi-empirical model. Two-dimensional viscous axisymmetric case is considered. The moment equations are supplemented by the diffusion equation of a condensing gas. To solve the equations, the finite volume method is used. The Riemann problem is solved using the AUSM+ method.
Igor E. Ivanov, Vladislav S. Nazarov, Igor A. Kryukov

Chapter 7. Numerical Simulation of Generation, Distribution, and Impact of a High-Specific Energy Plasma Bunch on a Barrier

Physical and comprehensive numerical studies of the generation of plasma bunches with a high specific energy have been carried out with the use of a plasma gun. The parameters of the plasma bunch upon exit from the plasma accelerator and during propagation in the ionosphere (h > 200 km) to considerable distances (≈100 km) have been calculated. A special numerical algorithm is presented to determine the results of the impact of a rarefied high-velocity gas flow (∼5 × 107 cm/s) on the surface of crystalline and amorphous solid bodies. Based on the results, the electron concentration and the scale of the ionized region that formed during the passage of a high-speed toroidal plasma bunch through the rarefied air were estimated. When the bunch spreads at a height ∼120 km and a distance ∼50 km, the ionized area with transverse dimensions of ∼20 km has an electron concentration of ∼6 × 108 cm–3.
Evgeniy L. Stupitsky, Andrey A. Motorin, Darya S. Moiseeva

Chapter 8. Some Aspects on Pulsating Detonation Wave Numerical Simulation Using Detailed Chemical Kinetics Mechanism

The chapter is dedicated to the numerical study of pulsating gaseous detonation wave propagation. The mathematical model is based on the Euler equations written for the multicomponent gas and supplemented by the detailed chemical reactions model to describe the combustion of the hydrogen–air mixture. The Petersen and Hanson kinetics is applied as the detailed chemical model. The numerical algorithm is based on the finite volume approach, essentially non-oscillatory scheme, AUSM numerical flux and the Runge–Kutta method. The numerical investigation of pulsating detonation wave propagation with direct detonation initiation near the closed end of the channel is carried out. The peculiarities of high-frequency and high-amplitude pulsations modes are discussed.
Alexander I. Lopato

Chapter 9. A Godunov-Type Method for a Multi-temperature Plasma with Strong Shock Waves and a General Equation of State

A multi-temperature code for a multi-component gas dynamic is considered. The velocities of components with nonzero mass are assumed to be identical to each other. The gas dynamic part is the Godunov-type method based on the efficient approximate solution of the Riemann problem operating with all components of the homogeneous gas mixture. The method assumes the table equation of state (EOS), but the system of the hydrodynamic equations should be hyperbolic. This work contains the test of the method on a strong shock wave in hydrogen plasma, so-called Shafranov’s solution. By taking into account the radiation component, the chapter discusses the applicability of the two temperature models for the strong shock wave in the hydrogen with the large temperatures behind a shock wave without consideration of the radiation at a considered short timescale. General EOS for the mixture of protons, electrons, and radiation differs from an ideal gas low EOS for two components (protons and electrons) fully ionized hydrogen plasma.
Alexey G. Aksenov

Chapter 10. Thruster Rotation Angle Control During Contactless Removal of Space Debris Objects

The chapter deals with the issues of contactless removal of space debris objects, the orbit of which is changed by a high-velocity ion beam injected from the service spacecraft moving in the immediate vicinity of the debris object. We consider the issues of controlling the angles of rotation of electric propulsion thrusters to implement changes in the thrust components of electric propulsion system in the longitudinal and transverse directions required during the debris object transportation. Arrangement of thrusters is proposed taking into account the location of solar arrays and the difference in permissible angles of thruster deflection in different planes. We analyze possible options for the thruster rotation angles to provide the required values of the thrust projection onto the axes of the spacecraft-associated coordinate system. We propose an algorithm for controlling the thruster rotation angles to implement the required thrust projection values, which allows to control the sign of the momentum relative to the spacecraft longitudinal axis depending on the accumulated total momentum. The results of modeling the electric propulsion system operation during the space debris objects transportation are presented.
Vladimir A. Obukhov, Alexander I. Pokryshkin, Victoria V. Svotina

Chapter 11. Application of Low-Power Pulse Plasma Thrusters in Thrust Units of Small Spacecrafts

The chapter considers the current state of work on flight models of pulsed plasma propulsion systems. It is shown that the primary application area for propulsion systems based on an ablative pulsed plasma thruster is the station-keeping of small spacecraft with the power of supply system of up to 100 W and with an active lifetime in a range from 1 to 10 years in low Earth orbits with altitudes in a range from 400 to 700 km. It is also shown that ablative pulsed plasma thrusters can be efficiently used to solve the problems of accurate attitude control and angular stabilization of spacecraft.
Aleksander V. Bogatiy, Grigory A. Dyakonov, Roman V. Elnikov, Garri A. Popov

Computational Solid Mechanics


Chapter 12. Multi-mode Model and Calculation Method for Fatigue Damage Development

A multi-mode kinetic model of damage development under cyclic loading is proposed to describe the process of fatigue failure. To determine the coefficients of the kinetic equation of damage, the well-known criterion of multiaxial fatigue failure is used. A procedure is proposed for calculating the kinetic equation coefficients for various fatigue failure modes of the LCF-HCF and VHCF. A numerical method for calculating crack-like zones up to macrofracture is developed. The model parameters are determined from the condition of matching the experimental and calculated fatigue curve for a specimen of a certain geometry at a given load amplitude and cycle asymmetry coefficient. Using the obtained values, the results of experiments on specimens of a different geometry and asymmetry coefficients were reproduced and the model and calculation algorithm performance were confirmed.
Ilia S. Nikitin, Nikolay G. Burago, Alexander D. Nikitin, Boris A. Stratula

Chapter 13. Elastic Wave Propagation Modeling During Exploratory Drilling on Artificial Ice Island

This chapter is devoted to numerical modeling of elastic impacts on artificial ice islands arising as a result of drill impacts while drilling from the island, earthquakes, and pressure of structures located on the island, as well as collisions of the ice island with drifting ice layers. To solve this problem numerically, we use the grid-characteristic method with interpolation on regular rectangular and parallelepipedal meshes and unstructured triangular and tetrahedral ones. The grid-characteristic method most accurately describes the dynamic processes in exploration seismology problems, since it takes into account the nature of wave phenomena. The approach used makes it possible to construct correct computational algorithms at the boundaries and contact boundaries of the integrational domain. In the work, the process of propagation of elastic waves in the considered geological environment studies simulates the distribution of stresses and also studies the stability of the ice island to destruction using the Mises criterion.
Igor B. Petrov, Maksim V. Muratov, Fedor I. Sergeev

Chapter 14. Numerical Study on the Teeth Installation Parameters: Shift and Tilt Angle Effects

The chapter is dedicated to the study on the teeth installation parameters on the stress state of the prosthesis under typical chewing loads. The two main parameters are investigated: the role of the dentition installation line and the role of tilt angle of teeth blocks. The simple 3D models were developed and used for these calculations. The physically based boundary conditions are introduced. The results of the calculation show a higher sensitivity of the lower prosthesis basis to vary the parameters compared to the upper prosthesis basis. It is shown that external shift of teeth installation line leads to higher stress intensity compared to oral one. The tilt angle effect results in slightly lower stress intensity compared to the shift effect. The oral tilt angle effect leads to higher stress intensity compared to the external tilt angles.
Sergey D. Arutyunov, Dmitry I. Grachev, Grigoriy G. Bagdasaryan, Ilia S. Nikitin, Alexander D. Nikitin

Numerical Study of Dynamic Systems


Chapter 15. Astronomical and Geophysical Factors of the Perturbed Chandler Wobble of the Earth Pole

In the framework of the restricted three-body problem, a celestial–mechanical model of the steady-state Chandler wobble of the Earth pole is proposed. The contribution of the astronomical and geophysical disturbances to the observed Earth pole oscillations is discussed based on the processing of IERS observations of the Earth pole motion, NCEP/NCAR geophysical data of the atmospheric circulation, and NASA/JPL angular momentum of the ocean. The directions of the axes x′, y′ corresponding to 50° of west longitude and 40° of east longitude, respectively, are found in the projection, onto which its coordinates have the maximum and minimum intensities of perturbed oscillations. The Earth pole oscillatory process that is in-phase with the lunar orbit precessional motion is studied, and the contribution of moving media to this process is discussed.
Sergej S. Krylov, Vadim V. Perepelkin, Alexandra S. Filippova

Chapter 16. Application of Multi-agent Optimization Methods Based on the Use of Linear Regulators and Interpolation Search for a Single Class of Optimal Deterministic Control Systems

Two new multi-agent algorithms for controlling one class of deterministic systems are proposed: the hybrid multi-agent method of interpolation search and multi-agent method based on the use of linear regulators of agent movement control. Detailed descriptions of the strategies of these methods are given, and step-by-step algorithms for each multi-agent method are described. Since multi-agent algorithms are used to find optimal control of dynamic systems, step-by-step algorithms for finding optimal open-loop control using multi-agent methods are also given. Two approaches to the search for optimal open-loop control are considered: when control is sought in relay form with a certain number of switches and when control is sought in the form of an expansion in a system of basis functions. In this chapter, cosine curves were considered as basis functions. Based on the above algorithms, software has been formed that allows finding the optimal open-loop control. Recommended parameters are given for each multi-agent algorithm. To study the effectiveness of the above algorithms, a specially selected set of test problems for finding the optimal open-loop control is solved, where the model of the control object is described by an ordinary differential equation linear in bounded control. During the study, it was shown that the described algorithms successfully cope with the task and can find a solution close to the exact one.
Andrei V. Panteleev, Maria Magdalina S. Karane

Chapter 17. Modified Continuous-Time Particle Filter Algorithm Without Overflow Errors

The modification for the continuous-time particle filter algorithm is offered. The developed modification that is based on the well-known strategy such as modeling trajectories to numerically solve stochastic differential equations provides the lack of overflow errors during the calculation of particle weights. To implement such an idea practically particle weights should be expressed in terms of logarithms with an additional customization of exponents. The effectiveness of the modified algorithm is demonstrated when solving the tracking problem to find coordinates and velocities of an aircraft executing a maneuver in the horizontal plane.
Irina A. Kudryavtseva, Konstantin A. Rybakov

Chapter 18. Incomplete Pairwise Comparisons Method for Estimating the Impact Criteria for Hub Airports Network Optimization

This chapter proposes a solution to the problem of determining the contribution of airport rating criteria for assessing the integral risk of modernization. The purpose of modernization is to increase the throughput of the Moscow aviation hub. To solve this problem, the experts formed a list of criteria. To determine their contribution to the overall risk assessment, the method of pairwise comparisons was applied. However, due to the fact that the criteria being evaluated relate to different areas, and experts from different areas were involved, an interval system of evaluating alternatives based on Saaty’s scale was used. The results of expert evaluations were combined into a common matrix of interval evaluations of alternatives. To increase the consistency of the matrix, some elements were deleted. The method proposed to solve the problem allows us to obtain the alternatives’ weights for incomplete pairwise comparisons matrices of large dimension, as well as, alternative estimates in interval form, which is illustrated by an example. This method differs from most existing methods for solving the problem of incomplete pairwise comparisons by the ability to process incomplete pairwise comparisons matrices without restoring missing data. It can be applied to solve other decision problems, where most of the known methods based on the pairwise comparisons method are not applicable to solve a problem.
Nataliya M. Kuzmina, Alexandra N. Ridley

Chapter 19. Adaptive Interpolation, TT-Decomposition and Sparse Grids for Modeling Dynamic Systems with Interval Parameters

Problems with uncertainties arise in many practical fields and traditionally are formulated as dynamic systems with interval parameters. Often the complexity of existing methods is exponential in relation to the number of interval parameters. The adaptive interpolation algorithm and approaches directed to reducing the curse of dimensionality are considered. The main assumption on which these approaches are based is that not all interval parameters make a significant contribution to the solution of the problem. The use of tensor train decomposition and sparse grids allows us to take into account these features and expand the scope of the algorithm for the case of a large number of interval parameters. The effectiveness of the considered approaches is confirmed on several model problems.
Alexander Yu. Morozov, Dmitry L. Reviznikov

Chapter 20. Using Spectral Form of Mathematical Description to Represent Iterated Stratonovich Stochastic Integrals

In this chapter, it is suggested to apply the spectral form of mathematical description for the representation of the iterated Stratonovich stochastic integrals of an arbitrary multiplicity. Some invariant relations for expansion coefficients and the iterated Stratonovich stochastic integrals are obtained. An algorithm for modeling the iterated Stratonovich stochastic integrals is discussed.
Konstantin A. Rybakov

Information Technologies


Chapter 21. Fractal Analysis and Programming of Elastic Systems Using Container-Component Model

The analysis and design of distributed algorithms is one of the main reasons to use fractal programming. Its aims are to represent the distributed algorithm as an “elastic object” that transforms dynamically at runtime. The use of container-component model provides the following advantages: the ability to select automatically a distributed configuration, building a visual model of the elastic computing organization, and evaluating its effectiveness. Container-component model is integrated with the box-counting fractal analysis method and fractal control based on dynamic sampling of the workload. The example of fractal analysis and programming of the distributed gradient ascent algorithm is given.
Alexander S. Semenov

Chapter 22. On the Modeling of the University Education Processes in the Information Technology

The problem of training qualified professionals in the field of information technology is very acute. At the level of the ministry and universities, measures are being taken to stimulate teachers, but the result is poorly felt. The reason is an exaggerated assessment of scientific activity to the detriment of education. The model proposed in the work shows the inefficiency of this approach: it reduces the level of control influence in negative feedback and does not lead to the formation of a stable learning process. In addition, feedback from the student is not taken into account, and the teacher does not seek to raise his/her level. But for successful work in the rapidly changing field of information technology, it is impossible to achieve quality without this. Thus, the teacher needs to find time for self-training. It is natural to use software tools to support the educational process. Existing tools are difficult to use. In addition, the teacher for various reasons hardly understands them. Given the high entry threshold, the authors propose simple and accessible software tools that allow one to free up teacher time for effective student training. The proposed solution does not pretend to completeness, but it makes it possible to form control materials, conduct control measures of different levels, take into account the attendance of classes, the dynamics of the educational process, and maintain interaction with a group of students. It is natural to spend the free time to improve your own skills.
Vladimir N. Lukin, Lev N. Chernyshov

Chapter 23. Entity-Event Ontology Construction by Conceptualization of Mentions in Text Corpus

Knowledge-based systems constitute a powerful tool for tackling and navigating complex domains, but they have the potential to be employed more often in practical tasks if some obstacles are cleared. Creating and keeping knowledge bases up-to-date is a challenging problem without automatic extraction of knowledge from data sources like documents. One of the solutions is ontology learning, which enables automatic construction and population of ontologies used to store knowledge. This chapter proposes an automatic method for domain ontology construction based on extracting entities and events from texts. Also, it is stated that upper-level template ontologies used when analyzing text corpus are suitable for creating target instance ontologies that describe a specific domain. The task of instance ontology construction is formulated in the terms of reconstructing real-world events via analyzing their mentions in a text corpus and structuring them according to the template ontology. This method allows an automatic analysis of big volumes of textual data like posts from social networks, news, contracts, specifications, etc., by utilizing natural language understanding tools used to extract domain knowledge. We developed a system that collects texts from the Internet, analyzes them, builds an ontology, and presents it as a knowledge base. One of the current applications is in optimizing business processes in a domain of civil aviation: document management, sorting and navigating documents, text summarization, semantic enterprise search, and exploratory search. Furthermore, it is claimed that extracted knowledge can be used to construct informative features in machine learning tasks.
Michael C. Ridley

Chapter 24. 3D Object Classification, Visual Search from RGB-D Data

In this chapter, we consider the problem of creating a system for processing 3D models obtained using RGB-D sensors for the purpose of semiautomatic selection and classification of objects and their auto-completion based on visual search. We have proposed several heuristic preprocessing algorithms for selecting an object of interest on a scan that contains noise and extraneous objects. To implement the visual search algorithm, we obtained a modification of the ray casting 3D-shape feature extraction algorithm. To solve the classification problem, the possibility of using deep learning architectures based on convolution mechanisms on graphs is investigated. The information about the object class obtained during the classification stage is used for faster and more accurate auto-completion. The resulting system has been tested on real data.
Vadim L. Kondarattsev, Alexander Yu. Kryuchkov, Roman M. Chumak


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