Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.12
A. Voskobijnyk, V. Turick, O. Voskoboinyk, V. Voskoboinick
The paper presents the results of experimental studies of the space-time characteristics of the velocity and pressure field inside a hemispherical dimple on a flat surface. The features of the formation and development of vortex structures generated inside the dimple, as well as their interaction with the streamlined surface of the dimple and the boundary layer were established. Integral, spectral and correlation characteristics of the field of velocity, dynamic and wall pressure fluctuations were obtained. The velocities and directions of transfer of large-scale vortex structures and small-scale vortices inside the dimple were determined. The frequencies of rotations and ejections of large-scale vortices, the frequencies of oscillations of the vortex flow inside the dimple and self-oscillations of the vortex structures of the shear layer, their subharmonics and harmonics of higher orders were established.
{"title":"DIMPLE GENERATOR OF VORTEX STRUCTURES","authors":"A. Voskobijnyk, V. Turick, O. Voskoboinyk, V. Voskoboinick","doi":"10.17721/2706-9699.2021.1.12","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.12","url":null,"abstract":"The paper presents the results of experimental studies of the space-time characteristics of the velocity and pressure field inside a hemispherical dimple on a flat surface. The features of the formation and development of vortex structures generated inside the dimple, as well as their interaction with the streamlined surface of the dimple and the boundary layer were established. Integral, spectral and correlation characteristics of the field of velocity, dynamic and wall pressure fluctuations were obtained. The velocities and directions of transfer of large-scale vortex structures and small-scale vortices inside the dimple were determined. The frequencies of rotations and ejections of large-scale vortices, the frequencies of oscillations of the vortex flow inside the dimple and self-oscillations of the vortex structures of the shear layer, their subharmonics and harmonics of higher orders were established.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"03 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86270042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.2.03
S. Zub, I. Kyrychenko, V. S. Lyashko, I. Yaloveha
Paper provides a research of the mathematical model of a superconducting magnetic suspension in zero gravity. The model consists of a special configuration of the superconducting inductors and uniform magnetic field. The stabilization of suspension in dependence of angle between the magnetic field induction vector and the axis of the inductance coil that is a suspended «free» rigid body is researched. Analysis of the model on stability of equilibrium is carried out and the conditions of spatial magnetic well existence providing the contactless confinement of a rigid body in zero gravity are found.
{"title":"MATHEMATICAL MODEL OF A SUPERCONDUCTING MAGNETIC SUSPENSION IN ZERO GRAVITY","authors":"S. Zub, I. Kyrychenko, V. S. Lyashko, I. Yaloveha","doi":"10.17721/2706-9699.2021.2.03","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.2.03","url":null,"abstract":"Paper provides a research of the mathematical model of a superconducting magnetic suspension in zero gravity. The model consists of a special configuration of the superconducting inductors and uniform magnetic field. The stabilization of suspension in dependence of angle between the magnetic field induction vector and the axis of the inductance coil that is a suspended «free» rigid body is researched. Analysis of the model on stability of equilibrium is carried out and the conditions of spatial magnetic well existence providing the contactless confinement of a rigid body in zero gravity are found.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"74 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83988151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.15
S. Dovgiy, G. Bulanchuk, О. М. Bulanchuk
In this paper, a six-point finite-difference numerical scheme for calculating the Prandtl equation of a laminar boundary layer is proposed to determine the point of separation of flows with large Reynolds numbers when flowing around smooth bodies. The input data for this scheme are the results of modeling by the method of discrete vortices within the model of an ideal fluid. The velocity profile around the critical point is determined from the analytical solution. The resulting system of linear algebraic equations is solved by the run method. Because the coefficients of the system are nonlinear, the iteration method is used to find the solution. The thickness of the boundary layer is determined during the solution process. The point of separation and circulation of descending vortices is determined from the calculation of the boundary layer. Then at the point of separation the rise of several free vortices is modeled, the dynamics of which is modeled within the method of discrete vortices. The scheme was tested on the problem of the flow around the cylinder and showed good results in comparison with the experimental data and calculations of other authors.
{"title":"NUMERICAL SCHEME FOR CALCULATING THE BOUNDARY LAYER WHEN MODELING BY THE METHOD OF DISCRETE VORTICES","authors":"S. Dovgiy, G. Bulanchuk, О. М. Bulanchuk","doi":"10.17721/2706-9699.2021.1.15","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.15","url":null,"abstract":"In this paper, a six-point finite-difference numerical scheme for calculating the Prandtl equation of a laminar boundary layer is proposed to determine the point of separation of flows with large Reynolds numbers when flowing around smooth bodies. The input data for this scheme are the results of modeling by the method of discrete vortices within the model of an ideal fluid. The velocity profile around the critical point is determined from the analytical solution. The resulting system of linear algebraic equations is solved by the run method. Because the coefficients of the system are nonlinear, the iteration method is used to find the solution. The thickness of the boundary layer is determined during the solution process. The point of separation and circulation of descending vortices is determined from the calculation of the boundary layer. Then at the point of separation the rise of several free vortices is modeled, the dynamics of which is modeled within the method of discrete vortices. The scheme was tested on the problem of the flow around the cylinder and showed good results in comparison with the experimental data and calculations of other authors.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80603577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.2.08
P. Stetsyuk, V. Stovba, A. Suprun
A special form (B-form) of methods of Quasi-Newton type is discussed, which makes it easy to interpret these methods as gradient in appropriately transformed argument space. B-form of the Davidon–Fletcher–Powell method is given and compared with r-algorithms. To minimize smooth convex functions, a gradient method with space transformation is built, combining properties of both quasi-Newtonian methods and r-algorithms. Possible schemes of this type of methods for minimizing non-smooth convex functions are discussed.
{"title":"B-FORM OF THE DAVIDON–FLETCHER–POWELL METHOD","authors":"P. Stetsyuk, V. Stovba, A. Suprun","doi":"10.17721/2706-9699.2021.2.08","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.2.08","url":null,"abstract":"A special form (B-form) of methods of Quasi-Newton type is discussed, which makes it easy to interpret these methods as gradient in appropriately transformed argument space. B-form of the Davidon–Fletcher–Powell method is given and compared with r-algorithms. To minimize smooth convex functions, a gradient method with space transformation is built, combining properties of both quasi-Newtonian methods and r-algorithms. Possible schemes of this type of methods for minimizing non-smooth convex functions are discussed.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"11 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87173808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.02
S. Baranovsky
While the study of the interaction patterns of the immune system and the viruses detected in the body wide variety of models is used. Well-known infectious disease model by Marchuk which describes the most common mechanisms of immune defense, was obtained under the assumption that the environment of the "organism" is homogeneous and unlimited, in which all the active factors of the process are instantly mixed. The approach proposed by the authors to take into account the influence of spatially distributed diffusion "redistributions" on the nature of the infectious disease provides an opportunity to detect the reducing effect the model level of maximum antigen concentration at the infection epicenter due to their diffusion "erosion" in the disease development. In particular, in cases where the viral particles concentration at the initial time or the intensity of a concentrated source of viruses in any part of the body of infection exceeds a certain critical level of the immunological barrier such an effect of diffusion "redistribution" in a short time reduces supercritical concentrations of viral particles to values, in particular, already below the critical level and their further neutralization may be ensured by the existing level of own antibodies concentration or requires a more economical procedure of injection with a lower donor antibodies concentration. In this article the infectious disease mathematical model is generalized to take into account the curvature of the bounded environment in the conditions of spatial diffusion perturbations, convection and the presence of various concentrated influences. The corresponding singularly perturbed model problem with delay is reduced to a sequence of "solvable" problems without delay. The influence of "curvature" of a limited environment on the development of an infectious disease in the conditions of diffusion perturbations, convection and concentrated influences is illustrated.
{"title":"MODELING THE DYNAMICS OF AN INFECTIOUS DISEASE TAKING INTO ACCOUNT SPATIAL-DIFFUSE PERTURBATIONS, CONCENTRATED INFLUENCES AND ENVIRONMENT CURVATURE","authors":"S. Baranovsky","doi":"10.17721/2706-9699.2021.1.02","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.02","url":null,"abstract":"While the study of the interaction patterns of the immune system and the viruses detected in the body wide variety of models is used. Well-known infectious disease model by Marchuk which describes the most common mechanisms of immune defense, was obtained under the assumption that the environment of the \"organism\" is homogeneous and unlimited, in which all the active factors of the process are instantly mixed. The approach proposed by the authors to take into account the influence of spatially distributed diffusion \"redistributions\" on the nature of the infectious disease provides an opportunity to detect the reducing effect the model level of maximum antigen concentration at the infection epicenter due to their diffusion \"erosion\" in the disease development. In particular, in cases where the viral particles concentration at the initial time or the intensity of a concentrated source of viruses in any part of the body of infection exceeds a certain critical level of the immunological barrier such an effect of diffusion \"redistribution\" in a short time reduces supercritical concentrations of viral particles to values, in particular, already below the critical level and their further neutralization may be ensured by the existing level of own antibodies concentration or requires a more economical procedure of injection with a lower donor antibodies concentration. In this article the infectious disease mathematical model is generalized to take into account the curvature of the bounded environment in the conditions of spatial diffusion perturbations, convection and the presence of various concentrated influences. The corresponding singularly perturbed model problem with delay is reduced to a sequence of \"solvable\" problems without delay. The influence of \"curvature\" of a limited environment on the development of an infectious disease in the conditions of diffusion perturbations, convection and concentrated influences is illustrated.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77476321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.05
4. J. «VNIIAEN», Ukraine Sumy, Sumy State, S. Ukraine
Calculations of the centrifugal machines critical frequencies of the rotors are currently carried out on the basis of the finite element method using multi-functional software as same as ANSYS and other similar, that work with finite elements of the three-dimensional type, as well as some specialized computer programs working with the beam-type finite elements. Anyway, the finite element method is used. But in this case an user needs a lot of time for prepation of the initial data. Therefore, this article presents a calculation of the critical frequencies of the rotor of a centrifugal fuel pump of a liquid-propellant engine based on its discrete model. This calculation also includes an algorithm of results clarification. This model has been verificated by comparing the critical frequencies obtained in calculations based on the finite element beam model and discrete model with using the algorithm of results clarification and without it.
{"title":"CALCULATION OF THE CENTRIFULAL PUMP CRITICAL FREQUENCIES BASED ON ITS DISCRETE MATHEMATICAL MODEL","authors":"4. J. «VNIIAEN», Ukraine Sumy, Sumy State, S. Ukraine","doi":"10.17721/2706-9699.2021.1.05","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.05","url":null,"abstract":"Calculations of the centrifugal machines critical frequencies of the rotors are currently carried out on the basis of the finite element method using multi-functional software as same as ANSYS and other similar, that work with finite elements of the three-dimensional type, as well as some specialized computer programs working with the beam-type finite elements. Anyway, the finite element method is used. But in this case an user needs a lot of time for prepation of the initial data. Therefore, this article presents a calculation of the critical frequencies of the rotor of a centrifugal fuel pump of a liquid-propellant engine based on its discrete model. This calculation also includes an algorithm of results clarification. This model has been verificated by comparing the critical frequencies obtained in calculations based on the finite element beam model and discrete model with using the algorithm of results clarification and without it.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85177963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.08
G. Voropaiev, I. Zagumennyi, N. Rozumnyuk
The paper presents the numerical results on gas-dynamic processes in various elements of the impulse ejector, including pre-chamber, supersonic nozzle and mixing chamber, to determine optimal geometric parameters providing the given flow rate characteristics. At an extra-high pressure of the ejecting gas (>100 bar) it is impossible to create a nozzle design with continuously changing cross-sectional area and limited nozzle length. So, it is necessary to place a pre-chamber between the gas generator and the ejector nozzle for throttling full gas pressure. In order to optimize the pre-chamber parameters in the ejector with discrete holes of the gas generator and the operating pressure in the range of 400÷1000 bar, a series of calculations were performed to determine the pre-chamber parameters, ensuring stable operation of the supersonic annular nozzle at the high pressure of 35÷45 bar and the flow rate of 0.5÷0.6 kg/s. 3D numerical simulation of the gas flow into the pre-chamber through the gas generator holes shows the degree of the flow pattern non-uniformity in the pre-chamber at the ejector nozzle inlet is quite low. This justifies the numerical simulation of gas flow in the ejector in axisymmetric formulation and allows restricting the number of the gas generator holes without inducing significant non-uniformity in the azimuthal direction.
{"title":"MODELING OF GAS-DYNAMIC PROCESSES IN THE ELEMENTS OF IMPULSE EJECTOR","authors":"G. Voropaiev, I. Zagumennyi, N. Rozumnyuk","doi":"10.17721/2706-9699.2021.1.08","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.08","url":null,"abstract":"The paper presents the numerical results on gas-dynamic processes in various elements of the impulse ejector, including pre-chamber, supersonic nozzle and mixing chamber, to determine optimal geometric parameters providing the given flow rate characteristics. At an extra-high pressure of the ejecting gas (>100 bar) it is impossible to create a nozzle design with continuously changing cross-sectional area and limited nozzle length. So, it is necessary to place a pre-chamber between the gas generator and the ejector nozzle for throttling full gas pressure. In order to optimize the pre-chamber parameters in the ejector with discrete holes of the gas generator and the operating pressure in the range of 400÷1000 bar, a series of calculations were performed to determine the pre-chamber parameters, ensuring stable operation of the supersonic annular nozzle at the high pressure of 35÷45 bar and the flow rate of 0.5÷0.6 kg/s. 3D numerical simulation of the gas flow into the pre-chamber through the gas generator holes shows the degree of the flow pattern non-uniformity in the pre-chamber at the ejector nozzle inlet is quite low. This justifies the numerical simulation of gas flow in the ejector in axisymmetric formulation and allows restricting the number of the gas generator holes without inducing significant non-uniformity in the azimuthal direction.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"72 6 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87285077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.19
Shevchenko, National University, Kyiv of Kyiv, nastialuita, zhilina.1958
In this paper, problems of bi-level convex minimization in a Hilbert space are considered. The bi-level convex minimization problem is to minimize the first convex function on the set of minima of the second convex function. This setting has many applications, but the implicit constraints generated by the internal problem make it difficult to obtain optimality conditions and construct algorithms. Multilevel optimization problems are formulated in a similar way, the source of which is the operation research problems (optimization according to sequentially specified criteria or lexicographic optimization). Attention is focused on problem solving using two proximal methods. The main theoretical results are theorems on the convergence of methods in various situations. The first of the methods is obtained by combining the penalty function method and the proximal method. Strong convergence is proved in the case of strong convexity of the function of the exterior problem. In the general case, only weak convergence has been proved. The second, the so-called proximal-gradient method, is a combination of one of the variants of the fast proximal-gradient algorithm with the method of penalty functions. The rates of convergence of the proximal-gradient method and its weak convergence are proved.
{"title":"PROXIMAL ALGORITHMS FOR BI-LEVEL CONVEX OPTIMIZATION PROBLEMS","authors":"Shevchenko, National University, Kyiv of Kyiv, nastialuita, zhilina.1958","doi":"10.17721/2706-9699.2021.1.19","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.19","url":null,"abstract":"In this paper, problems of bi-level convex minimization in a Hilbert space are considered. The bi-level convex minimization problem is to minimize the first convex function on the set of minima of the second convex function. This setting has many applications, but the implicit constraints generated by the internal problem make it difficult to obtain optimality conditions and construct algorithms. Multilevel optimization problems are formulated in a similar way, the source of which is the operation research problems (optimization according to sequentially specified criteria or lexicographic optimization). Attention is focused on problem solving using two proximal methods. The main theoretical results are theorems on the convergence of methods in various situations. The first of the methods is obtained by combining the penalty function method and the proximal method. Strong convergence is proved in the case of strong convexity of the function of the exterior problem. In the general case, only weak convergence has been proved. The second, the so-called proximal-gradient method, is a combination of one of the variants of the fast proximal-gradient algorithm with the method of penalty functions. The rates of convergence of the proximal-gradient method and its weak convergence are proved.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"33 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83201020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.25
A. Sokhatsky
The main stages of the development of the discrete singularities’ method are described. Modern results on the numerical solution of boundary hypersingular integral equations by the methods of collocations and piecewise constant approximations are given. The modern going near planning of aerodynamic design outline of transport vehicles conditionally can be divided into three stages: engineering approaches are close, design on the basis of methods of discrete singularities, approaches that arе based on integration of complete and the Reynolds-averaged of Navier-Stokes equations. On the first stage various engineering approaches are used for forming of aerodynamic outline, going out a requirement specification and requirements of customer. Close geometrical and aerodynamic descriptions are determined in the first. An aerodynamic outline is formed in the first close. On the second stage it follows to use more difficult models of aerodynamics on the basis of various approaches that is built on the model of ideal liquid. Bearing properties are determined, power and moment characteristics for the corresponding outline of aircraft. The third stage is most difficult and expensive cost. On this stage it follows to use methods and models that are based on equations for turbulent flow. The second stage is in-process considered – as means of the previous planning of aerodynamic arrangement with the use of methods of discrete features. A non-stationary chart in that tearing away is designed from all sharp edge of wing is in-process used. This chart has the most general case of forming of process of flowing around of the bearing system of aircraft. However, complication of physical interpretation of forming of such processes in the conditions of ideal liquid remains problematic. The necessities of practice require expansion and deepening of theoretical approaches for the study of non-stationary. Application of model of ideal liquid for the calculation of the bearing system of a perspective transport vehicle allows to set forth aerodynamic task as task of Neumann for Laplace operator. The calculations of the bearing systems of difficult geometrical plane form are conducted. Dependences of carrying capacity and longitudinal moment are got depending on the corner of attack and distance to the ground clearance. A computational experiment confirmed that a method of discrete vorteces was one of important methods of computational aerodynamics. He is effective means for untiing of a number of aerodynamic tasks.
{"title":"METHOD OF DISCRETE FEATURES AS PLANNING MEANS IS AERODYNAMIC OUTLINES OF TRANSPORT VEHICLES","authors":"A. Sokhatsky","doi":"10.17721/2706-9699.2021.1.25","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.25","url":null,"abstract":"The main stages of the development of the discrete singularities’ method are described. Modern results on the numerical solution of boundary hypersingular integral equations by the methods of collocations and piecewise constant approximations are given. The modern going near planning of aerodynamic design outline of transport vehicles conditionally can be divided into three stages: engineering approaches are close, design on the basis of methods of discrete singularities, approaches that arе based on integration of complete and the Reynolds-averaged of Navier-Stokes equations. On the first stage various engineering approaches are used for forming of aerodynamic outline, going out a requirement specification and requirements of customer. Close geometrical and aerodynamic descriptions are determined in the first. An aerodynamic outline is formed in the first close. On the second stage it follows to use more difficult models of aerodynamics on the basis of various approaches that is built on the model of ideal liquid. Bearing properties are determined, power and moment characteristics for the corresponding outline of aircraft. The third stage is most difficult and expensive cost. On this stage it follows to use methods and models that are based on equations for turbulent flow. The second stage is in-process considered – as means of the previous planning of aerodynamic arrangement with the use of methods of discrete features. A non-stationary chart in that tearing away is designed from all sharp edge of wing is in-process used. This chart has the most general case of forming of process of flowing around of the bearing system of aircraft. However, complication of physical interpretation of forming of such processes in the conditions of ideal liquid remains problematic. The necessities of practice require expansion and deepening of theoretical approaches for the study of non-stationary. Application of model of ideal liquid for the calculation of the bearing system of a perspective transport vehicle allows to set forth aerodynamic task as task of Neumann for Laplace operator. The calculations of the bearing systems of difficult geometrical plane form are conducted. Dependences of carrying capacity and longitudinal moment are got depending on the corner of attack and distance to the ground clearance. A computational experiment confirmed that a method of discrete vorteces was one of important methods of computational aerodynamics. He is effective means for untiing of a number of aerodynamic tasks.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"32 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89142739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.17721/2706-9699.2020.2.02
S. Denisov, V. V. Semenov
The problems of optimization of linear distributed systems with generalized control and first-order methods for their solution are considered. The main focus is on proving the convergence of methods. It is assumed that the operator describing the model satisfies a priori estimates in negative norms. For control problems with convex and preconvex admissible sets, the convergence of several first-order algorithms with errors in iterative subproblems is proved.
{"title":"FIRST-ORDER METHODS FOR GENERALIZED OPTIMAL CONTROL PROBLEMS FOR SYSTEMS WITH DISTRIBUTED PARAMETERS","authors":"S. Denisov, V. V. Semenov","doi":"10.17721/2706-9699.2020.2.02","DOIUrl":"https://doi.org/10.17721/2706-9699.2020.2.02","url":null,"abstract":"The problems of optimization of linear distributed systems with generalized control and first-order methods for their solution are considered. The main focus is on proving the convergence of methods. It is assumed that the operator describing the model satisfies a priori estimates in negative norms. For control problems with convex and preconvex admissible sets, the convergence of several first-order algorithms with errors in iterative subproblems is proved.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90804170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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