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Development Trefftz Method for Problems of Nonhomogeneous Media 非均质介质问题的特雷弗兹法发展
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602534
D. B. Volkov-Bogorodskiy
{"title":"Development Trefftz Method for Problems of Nonhomogeneous Media","authors":"D. B. Volkov-Bogorodskiy","doi":"10.1134/s1995080224602534","DOIUrl":"https://doi.org/10.1134/s1995080224602534","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A new scheme for solving problems in the mechanics of structurally nonhomogeneous media is proposed. This scheme is based on dividing of the initial domain into system of subdomain-blocks similar to finite elements and on approximation of the solution in each block by a systems of functions that exactly satisfy the equation and do not assume unlike the finite element method continuity at the block boundaries. This scheme is based on the Papkovich–Neuber analytical representation through the auxiliary potentials, which makes it possible to construct the complete approximation systems in nonhomogeneous media that analytically satisfy the initial equations and contact conditions on the boundaries of inhomogeneities. Also this scheme is based on the generalization of a direct Trefftz method in the system of subdomain-blocks, which approximates the solution in discontinuous energy space. It is shown that generalized Trefftz method has the ability simultaneously with minimizing of the energy functional to stitch together all the necessary quantities at the block boundaries. They are displacements, surface forces and for gradient elasticity models also derivatives and cohesion moments. This ability is achieved solely due to the analytical representation of the used functions. This analytical representation opens up the possibility of construction of finite element approximations for complex nonhomogeneous media on unstructured meshes and inconsistent shape functions, that analytically accurately reproduce the stress state at the vicinity of inclusions and can be considered as a new technology of finite element approximations.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217034","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}
引用次数: 0
Unsteady Contact Interaction of Liquid and Solid Bodies 液体和固体物体的非稳态接触相互作用
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602558
G. V. Fedotenkov, A. A. Orekhov, L. N. Rabinskiy
{"title":"Unsteady Contact Interaction of Liquid and Solid Bodies","authors":"G. V. Fedotenkov, A. A. Orekhov, L. N. Rabinskiy","doi":"10.1134/s1995080224602558","DOIUrl":"https://doi.org/10.1134/s1995080224602558","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The processes of unsteady contact interaction of liquids described by different mathematical models with solid deformable bodies are considered. Closed mathematical formulations of unsteady contact problems in the case of various models of liquids and linear-elastic bodies are developed. The analytical solution of the nonstationary problem of interaction between an acoustic fluid and a deformable solid body is obtained. The time integral Laplace transform is used to construct the solution. The distributions of displacements and stresses in the solid body, as well as pressure and velocity fields in the fluid during unsteady contact interaction are analyzed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216978","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}
引用次数: 0
Stationary Modes of Compressible Fluid Flow in a Thermodynamically Consistent Coupled Model 热力学一致耦合模型中可压缩流体流动的静态模式
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602492
N. N. Nazarenko, A. G. Knyazeva
{"title":"Stationary Modes of Compressible Fluid Flow in a Thermodynamically Consistent Coupled Model","authors":"N. N. Nazarenko, A. G. Knyazeva","doi":"10.1134/s1995080224602492","DOIUrl":"https://doi.org/10.1134/s1995080224602492","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Processes of fluid flow in porous media are encountered in various spheres of human activity. The structure of porous media is extremely diverse, and the gases, liquids, mixtures, suspensions, suspensions, etc. moving in them are significantly different in terms of transport and rheological properties. The models used by different authors to describe fluid flows in porous media are also different. In this paper, classical models of filtration theory are supplemented with thermodynamically consistent constitutive relations that take into account the phenomenon of barodiffusion and an example of a coupled two-dimensional model that takes into account the pressure change associated with the redistribution of impurities due to different transport phenomena is presented. Different flow regimes in a flat layer with asymmetric inlet and outlet are demonstrated.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217036","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}
引用次数: 0
Mathematical Modeling of Non-isothermal Flow of Two-phase Media in Curved Channels 弯曲通道中两相介质非等温流动的数学建模
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602200
R. I. Ibyatov, F. G. Akhmadiev
{"title":"Mathematical Modeling of Non-isothermal Flow of Two-phase Media in Curved Channels","authors":"R. I. Ibyatov, F. G. Akhmadiev","doi":"10.1134/s1995080224602200","DOIUrl":"https://doi.org/10.1134/s1995080224602200","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The mathematical modeling of the non-isothermal flow of two-phase media in curved channels and pipes of complex geometric shapes is considered. Simplified equations of motion of a two-phase medium, taking into account the flow characteristics, written in an orthogonal coordinate system associated with the flow region, are solved by the method of equal flow surfaces. An algorithm for calculating the flow is constructed for the implementation of a computational experiment. This takes into account changes in the physical characteristics of the two-phase medium depending on temperature. Numerical calculations have been performed for channels of parabolic and conical shapes, taking into account changes in the effective viscosity of the medium from temperature, the initial section of the flow, and the influence of the centrifugal force field. Based on the conducted computational experiment, various flow regimes and the influence of various parameters on the hydrodynamic situation in the flow region are studied.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217080","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}
引用次数: 0
Numerical Solution of the Inverse Problem of Non-stationary Filtration of Bingham Non-Newtonian Fluid to a Horizontal Well 宾汉非牛顿流体对水平井非静态过滤反问题的数值求解
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602224
M. Kh. Khairullin, E. R. Badertdinova
{"title":"Numerical Solution of the Inverse Problem of Non-stationary Filtration of Bingham Non-Newtonian Fluid to a Horizontal Well","authors":"M. Kh. Khairullin, E. R. Badertdinova","doi":"10.1134/s1995080224602224","DOIUrl":"https://doi.org/10.1134/s1995080224602224","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Unsteady filtration of a Bingham non-Newtonian fluid to a horizontal well is considered. The experimental results show that when such liquids flow in porous media at low pressure gradients, deviations from the linear Darcy law appear. A feature of the movement of Bingham non-Newtonian fluids in a porous medium is the fact that filtration becomes noticeable only after the pressure gradient reaches a certain critical value—the limiting pressure gradient. The formulation of the inverse coefficient problem for determining filtration parameters during the flow of Bingham non-Newtonian fluid to a horizontal well is given. Pressure change curves measured at the well are used as initial information. To numerically solve the inverse coefficient problem, a computational algorithm based on regularization methods is proposed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217086","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}
引用次数: 0
One Problem for the Bessel Equation with a Spectral Parameter in the Boundary Condition 贝塞尔方程的一个问题，边界条件中有一个频谱参数
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s199508022460242x
N. Kapustin, A. Kholomeeva
{"title":"One Problem for the Bessel Equation with a Spectral Parameter in the Boundary Condition","authors":"N. Kapustin, A. Kholomeeva","doi":"10.1134/s199508022460242x","DOIUrl":"https://doi.org/10.1134/s199508022460242x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we consider the spectral problem for the\u0000semi-integer Bessel equation with a boundary condition containing\u0000the square of the spectral parameter and a complex physical\u0000parameter. The system of eigenfunctions of the problem and the\u0000characteristic equation for the eigenvalues are derived. The\u0000equation for multiple roots of the characteristic equation is\u0000derived. The results on the basis properties (Riesz basis) of the\u0000system of eigenfunctions at different values of the parameter are\u0000obtained. For each case a biorthogonally conjugate system is\u0000constructed. At the end of the paper there is an example for the\u0000order of Bessel functions equal to <span>(1/2)</span>.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216983","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}
引用次数: 0
Dynamics of a Wheel with a Deformable Periphery 外围可变形车轮的动力学特性
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602510
V. G. Vil’ke, I. F. Kozhevnikov
{"title":"Dynamics of a Wheel with a Deformable Periphery","authors":"V. G. Vil’ke, I. F. Kozhevnikov","doi":"10.1134/s1995080224602510","DOIUrl":"https://doi.org/10.1134/s1995080224602510","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider a model of a wheel consisting of a disc and a continuous set of rods joined to the disc. The rods are replaced by a continuous set of masses at free ends, joined by springs and dampers (the longitudinal and transverse stiffness of the tread rods) to the wheel disc. The viscous friction acts at the contact points of the rods with the road. The equations of motion of the wheel in the vertical plane are obtained, taking into account the impact phenomena at the boundary points of the contact area. The shape of the deformed periphery, the contact area, the frequencies of rods vibrations in steady-state regime are found. The value of external forces power required to existence of a steady-state regime is determined when wheel translational motion speed and its angular velocity are constant. The wheel vibrations in the vertical plane about the equilibrium position of the loaded wheel are also studied.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217030","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}
引用次数: 0
Interaction of Two Gas Bubbles Rising One after Another in a Liquid 液体中相继上升的两个气泡的相互作用
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602285
I. V. Morenko
{"title":"Interaction of Two Gas Bubbles Rising One after Another in a Liquid","authors":"I. V. Morenko","doi":"10.1134/s1995080224602285","DOIUrl":"https://doi.org/10.1134/s1995080224602285","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The dynamics of two gas bubbles rising in a stagnant viscous liquid is studied. The mathematical model is based on the laws of conservation of mass, momentum and energy, taking into account the compressibility of media. The gas is assumed to be calorically perfect. To trace the gas–liquid interface, the volume of fluid method is used. The solution to the problem is carried out using the finite volume method. The evolution of the bubble shape during the process of ascent and hydrodynamic interaction is shown. The change in the bubble shapes occurs under the influence of buoyancy force, drag force, viscous force, inertia force, and surface tension force. The results of the test calculations are in good agreement with the known data of other authors. The mechanism of coalescence of bubbles is described in the case of their movement one after another, when one bubble falls into the region of the hydrodynamic wake of another. Dependencies of bubble volume and temperature change on time are established.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217091","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}
引用次数: 0
Mathematical Modeling of Anisotropic Thermal Protection with a High Degree of Longitudinal Anisotropy 具有高度纵向各向异性的各向异性热保护数学模型
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s199508022460256x
V. F. Formalev, B. A. Garibyan
{"title":"Mathematical Modeling of Anisotropic Thermal Protection with a High Degree of Longitudinal Anisotropy","authors":"V. F. Formalev, B. A. Garibyan","doi":"10.1134/s199508022460256x","DOIUrl":"https://doi.org/10.1134/s199508022460256x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this work, based on a new analytical solution to the third initial-boundary value problem of thermal conductivity in an anisotropic strip, an effective method for thermal protection of high-speed aircraft is proposed by channeling heat flows from the central part of the strip to its periphery using an anisotropic material with a high degree of longitudinal anisotropy (longitudinal to transverse thermal conductivity coefficient ratio not less than twenty).</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216980","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}
引用次数: 0
Solution of the Biharmonic Problem with the Steklov-type and Farwig Boundary Conditions 利用斯特克洛夫型和 Farwig 边界条件求解双谐波问题
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602479
Giovanni Migliaccio, Hovik A. Matevossian
{"title":"Solution of the Biharmonic Problem with the Steklov-type and Farwig Boundary Conditions","authors":"Giovanni Migliaccio, Hovik A. Matevossian","doi":"10.1134/s1995080224602479","DOIUrl":"https://doi.org/10.1134/s1995080224602479","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we consider a biharmonic problem with Steklov-type boundary conditions on one part of the boundary and with the Farwig condition on the other part. For this problem, questions of uniqueness of solutions are studied, and in the case of non-uniqueness, provided that the weighted Dirichlet integral is bounded, the exact number of linear independent solutions to the problem under consideration is established. Using the variational principle, uniqueness (non-uniqueness) theorems are obtained, as well as exact formulas for calculating the dimension of the space of solutions depending on the value of the parameter included in the weighted Dirichlet integral.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217032","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}
引用次数: 0
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