Lobachevskii Journal of Mathematics最新文献

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Mathematical Modeling of Water Vapor Injection into a Saturated Porous Medium 水蒸气注入饱和多孔介质的数学建模

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602236

M. K. Khasanov, S. L. Borodin, M. V. Stolpovsky

Abstract

A mathematical model of the process of water vapor injection into a porous reservoir containing methane is proposed, taking into account vapor condensation in the porous medium. A self-similar solution of this problem is constructed and an algorithm for its numerical solution is developed. Calculations were carried out, which showed good agreement between the self-similar and numerical solutions at a sufficiently low reservoir permeabilities. It is noted that for high-permeability reservoirs, in order to obtain adequate results, it is necessary to carry out longer-term calculations using the proposed numerical algorithm. Based on the analysis of the numerical experiment results, it is shown that when vapor is injected into a reservoir containing methane, five characteristic regions can be formed, namely: region with superheated vapor; with vapor and water in state of phase equilibrium; with methane, vapor and water in state of phase equilibrium; with methane and vapor; and region that contains only methane. Also the results of numerical experiments on the effect of vapor injection pressure and temperature on a reservoir heating are presented.

摘要考虑到多孔介质中的水汽凝结，提出了向含甲烷的多孔储层注入水汽过程的数学模型。构建了该问题的自相似解，并开发了数值解算法。计算结果表明，在储层渗透率足够低的情况下，自相似解与数值解之间具有良好的一致性。需要指出的是，对于高渗透率储层，为了获得充分的结果，有必要使用所提出的数值算法进行长期计算。基于数值实验结果的分析表明，向含有甲烷的储层注入蒸汽时，可形成五个特征区域，即：过热蒸汽区域；处于相平衡状态的蒸汽和水；处于相平衡状态的甲烷、蒸汽和水；甲烷和蒸汽；以及仅含有甲烷的区域。此外，还介绍了蒸汽注入压力和温度对储层加热影响的数值实验结果。

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引用次数: 0

Refined Analysis of Shear Stress Distribution in Tapered Rods Accounting for Gradient Effects 考虑梯度效应的锥形杆剪应力分布精细分析

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602522

A. V. Volkov, K. S. Golubkin, Y. O. Solyaev

Abstract

In this article, we propose to apply the strain gradient elasticity theory for the refined stress analysis in the tapered rods with variable cross section. Corresponding statement of the higher-order boundary value problem with extended set of boundary conditions is derived based on the variational approach. Considering an example for the cylindrical/conical rod loaded by self-equilibrated body and end forces, we provide the comparison between the stress distributions that can be obtained within the classical 3D elasticity, classical 1D rod theory and the established 1D rod theory with the strain gradient effects. It is shown that the last one allows to obtain the smoothed solution for the shear stresses that can be fitted to 3D elasticity solution under appropriate choice of additional length scale parameter of gradient theory. In contrast, solution of classical rod theory cannot be fitted exactly to 3D elasticity solution and contains unavoidable discontinuities of shear stresses.

摘要本文提出应用应变梯度弹性理论对变截面锥形杆进行精细应力分析。基于变分法，推导出了具有扩展边界条件集的高阶边界值问题的相应表述。考虑到圆柱形/圆锥形杆在自平衡体力和端力作用下的载荷实例，我们对经典三维弹性理论、经典一维杆理论和具有应变梯度效应的既定一维杆理论所能获得的应力分布进行了比较。结果表明，在适当选择梯度理论的附加长度尺度参数的情况下，最后一种方法可以获得与三维弹性解相匹配的剪应力平滑解。与此相反，经典杆理论的解无法与三维弹性解精确拟合，并且包含不可避免的剪应力不连续性。

引用次数: 0

On Sums of Special Functions 论特殊函数之和

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602418

Yu. A. Brychkov

Abstract

Sums of the form (sum_{k=0}^{n}frac{prod_{i=1}^{p}left(a_{i}right)_{k}}{prod_{j=1}^{q}left(b_{j}right)_{k}}w^{k}{}F_{k}(z)) are considered(,) where (F_{k}(z)) are special functions of hypergeometric type. Such sums involving Bessel, Struve, incomplete gamma functions, and Laguerre, Hermite, Jacobi, Legendre, and Chebyshev polynomials can be represented in terms of the Kampé de Fériet and generalized Horn hypergeometric functions of two variables.

AbstractSums of the form （(sum_{k=0}^{n}frac{prod_{i=1}^{p}left(a_{i}right)_{k}}{prod_{j=1}^{q}left(b_{j}right)_{k}}w^{k}{}F_{k}(z)）被认为是（、其中 (F_{k}(z)) 是超几何类型的特殊函数。涉及贝塞尔函数、斯特鲁夫函数、不完全伽马函数、拉盖尔多项式、赫米特多项式、雅可比多项式、勒让德多项式和切比雪夫多项式的这类和可以用两个变量的坎佩-德-费里特函数和广义霍恩超几何函数来表示。

引用次数: 0

Stress-strain State Analysis of Porous Elasto-plastic Size-dependent Plates Subjected to Hygro-Mechanical Loads Using the Variational Iterations Method 使用变量迭代法分析受水文机械荷载作用的多孔弹塑性尺寸相关板的应力应变状态

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224600948

A. D. Tebyakin, T. V. Yakovleva, A. V. Krysko

Abstract

In this study, for the first time, a mathematical model of the stress-strain state of porous elasto-plastic size-dependent plates is constructed, taking into account hygro-mechanical loads. An original algorithm is proposed and developed. It uses the highly accurate Variational Iteration Method (VIM) or the Extended Kantorovich Method (EKM). This algorithm is applied to study stress-strain state of porous metallic Kirchhoff’s plates, taking into account elasto-plastic deformations, medium moisture and porosity. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. The developed algorithm includes two nested one-to-one iteration procedures: the Variational Iteration Method and Birger’s method of variable elasticity parameter (MVEP). For each of these iterative methods there are theorems proving their convergence. Elasto-plastic deformations are considered using the deformation theory of plasticity. The proposed mathematical model and the developed algorithm provide high accuracy and computational speed in comparison to the results obtained by grid, variational and finite element methods. The effect of three porosity patterns and moisture accounting on the stress-strain state depending on the value of the size-dependent parameter is analysed.

摘要在本研究中，首次构建了多孔弹塑性尺寸相关板应力-应变状态的数学模型，并考虑了水文机械载荷。提出并开发了一种独创的算法。它采用了高精度的变异迭代法（VIM）或扩展康托洛维奇法（EKM）。考虑到弹塑性变形、介质湿度和孔隙率，该算法被用于研究多孔金属基尔霍夫板的应力应变状态。修正耦合应力理论（MCST）用于考虑尺寸效应。所开发的算法包括两个嵌套的一对一迭代程序：变量迭代法和伯杰弹性参数可变法（MVEP）。每种迭代法都有定理证明其收敛性。弹塑性变形是利用塑性变形理论来考虑的。与网格法、变分法和有限元法得出的结果相比，所提出的数学模型和所开发的算法精度高、计算速度快。分析了取决于尺寸参数值的三种孔隙率模式和水分含量对应力应变状态的影响。

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引用次数: 0

Acoustics of a Viscoelastic Liquid with Perfluorocarbon Droplets in the Presence of Phase Transitions 带有全氟碳化物液滴的粘弹性液体在相变情况下的声学特性

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602169

D. A. Gubaidullin, D. D. Gubaidullina, Yu. V. Fedorov

Abstract

In this work, a modified Rayleigh–Lamb equation which takes into account the radial oscillations of a perfluorocarbon droplet with a vapor bubble in the center in a viscoelastic liquid has been derived. The viscoelasticity of the carrier medium has been taken into account based on the Zener rheological model. For small inclusion oscillations, the problem of heat and mass transfer between vapor, liquid phase and carrier liquid has been solved. The energy equation has been found. Based on the obtained equations of radial oscillations of the inclusion, energy and the well-known wave equation for a bubbly liquid, the dispersion relation has been determined. For a mixture of polydimethylsiloxane with droplets of octafluoropropane C({}_{3})F({}_{8}) and vapor bubbles in the center, the dependencies of the phase velocity and attenuation coefficient on the perturbation frequency have been plotted. The influence of the shear modulus and relaxation time of the elastic carrier liquid on the dynamics of acoustic waves has been illustrated.

摘要在这项工作中，推导出了一个修正的 Rayleigh-Lamb 方程，该方程考虑到了在粘弹性液体中中心带有气泡的全氟化碳液滴的径向振荡。载体介质的粘弹性已根据齐纳流变模型考虑在内。对于小的包含振荡，解决了蒸汽、液相和载液之间的传热和传质问题。能量方程已经求出。根据所得到的夹杂物径向振荡方程、能量方程和著名的气泡液体波方程，确定了分散关系。对于中心含有八氟丙烷液滴和气泡的聚二甲基硅氧烷混合物，绘制了相速度和衰减系数对扰动频率的依赖关系图。说明了弹性载液的剪切模量和弛豫时间对声波动力学的影响。

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引用次数: 0

Pressure Diffusion Waves in a Porous Medium Saturated by Three Phase Fluid 三相流体饱和多孔介质中的压力扩散波

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602339

R. V. Sadovnikov

Abstract

Pressure diffusion waves in a porous medium saturated with three phase fluid are considered. The influence of frequency and saturations of phases are investigated on the governing relations for phase velocity, attenuation coefficient, wavelength, diffusion coefficient and penetration depth.

摘要考虑了三相流体饱和多孔介质中的压力扩散波。研究了频率和各相饱和度对相速度、衰减系数、波长、扩散系数和穿透深度的支配关系的影响。

引用次数: 0

The Temperature Effect on the Stress-strain State of Inelastic Torispherical Heads under Internal Pressure 温度对内压下非弹性球形封头应力应变状态的影响

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602273

V. E. Moiseeva, Z. V. Skvortsova

Abstract

The effect of a temperature change on nonlinear axisymmetric straining of the clamped torispherical shell under internal pressure is investigated. The solution is based on the Kirchhoff–Love hypothesis, taking into account geometric and material nonlinearities. The stress-strain state is examined at cryogenic or elevated temperatures with the temperature-dependent material’s characteristics. The analysis has been performed numerically using a combination of linearization and S.K. Godunov’s orthogonal sweep methods. Shells made of alloys with various mechanical and thermophysical properties are considered. The effect of the alloy’s properties on the nature of the stress-strain state dependence of the torispherical heads on temperature is discussed.

摘要研究了温度变化对内压下夹紧环球壳非线性轴对称应变的影响。解法基于基尔霍夫-洛夫假设，并考虑了几何和材料非线性因素。应力-应变状态是在低温或高温条件下根据与温度相关的材料特性进行研究的。分析采用线性化和 S.K. 戈杜诺夫正交扫描方法相结合的数值方法进行。研究考虑了由具有各种机械和热物理性质的合金制成的壳体。讨论了合金特性对环球形封头的应力-应变状态随温度变化的性质的影响。

引用次数: 0

Research of Thermal Explosion Conditions in Nonlinear Heat Conduction Problems with a Nonlinear Heat Source 带非线性热源的非线性热传导问题中的热爆炸条件研究

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602443

V. A. Kudinov, K. V. Trubitsyn, K. V. Kolotilkina, S. V. Zaytsev, T. E. Gavrilova

Abstract

Using an additional sought function (ASF) and additional boundary conditions (ABCs), an analytical solution of the nonlinear heat conduction problem for a symmetric plate with a nonlinear heat source has been obtained. ASF characterizes the temperature change over time at the center of the plate. Its usage enables the solution reduction of the original partial differential equation to the integration of a temporal ordinary differential equation (ODE). From its solution, exact eigenvalues are found, determined by classical methods from solving the Sturm–Liouville boundary value problem specified in the spatial coordinate domain. Hence, this study considers another direction of their determination, based on solving the temporal ODE with respect to ASF. ABCs are formulated in such a way that their fulfillment by the sought solution is equivalent to satisfying the original differential equation at the boundary points. It leads to its fulfillment within the considered domain, bypassing the direct integration process over the spatial variable and confining it only to the execution of the heat balance integral—the averaged original differential equation.

摘要利用附加求函数 (ASF) 和附加边界条件 (ABC)，获得了带有非线性热源的对称板非线性热传导问题的解析解。ASF 描述了板中心温度随时间的变化。使用 ASF 可以将原始偏微分方程简化为时间常微分方程（ODE）的积分。通过求解空间坐标域中指定的 Sturm-Liouville 边界值问题的经典方法，可以找到精确的特征值。因此，本研究考虑了确定特征值的另一个方向，即在求解与 ASF 有关的时间 ODE 的基础上确定特征值。在制定 ABC 时，所寻求的解决方案满足 ABC 等价于满足边界点上的原始微分方程。这将导致在所考虑的域内满足其要求，绕过空间变量的直接积分过程，而只限于执行热平衡积分--平均原始微分方程。

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引用次数: 0

Evolution of Acoustic Streaming Inside and Around the Open Tube Resonator 开放管谐振器内部和周围声流的演变

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602327

P. P. Osipov, D. A. Gubaidullin, A. A. Abdyushev

Abstract

Using the numerical integration of the equations of ideal gas dynamics, written in a conservative form in a cylindrical coordinate system, the velocity and pressure fields inside and around the tube of an open resonator are investigated at the first resonant frequency. The patterns of streamlines of instantaneous and cycle-averaged velocities, as well as the evolution of intense secondary streaming near the open end of the tube are analyzed. An intense secondary streaming inside and around the tube resonator is developed, forming toroidal vortex inside and strong jet outside the tube along the axis. Comparison of simulation results with experimental data of other authors shows good agreement.

摘要利用在圆柱坐标系中以保守形式书写的理想气体动力学方程的数值积分，研究了第一共振频率下开放式谐振器管内和周围的速度场和压力场。分析了瞬时速度和周期平均速度的流线模式，以及管子开口端附近强烈二次流的演变。在管道谐振腔内部和周围形成了强烈的次级流，沿轴线在管道内部形成了环形涡流，在管道外部形成了强烈的射流。模拟结果与其他学者的实验数据进行了比较，结果显示两者吻合良好。

引用次数: 0

The Use of Artificial Neural Networks to Determine the Aerodynamic Forces and Moments Acting on an Aircraft in a Vortex Wake 利用人工神经网络确定飞机在涡流中的空气动力和力矩

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602364

Yu. N. Sviridenko

Abstract

The article proposes a method based on the use of artificial neural networks to determine what additional forces and moments act on an aircraft in a vortex wake of another aircraft in real time. The method is based on neural-network approximating additional forces and moments acting on the aircraft. These are caused by the influence of individual vortex segments. To generate a set of data for training neural networks, the method of hydrodynamic singularities has been used. Estimates of the accuracy and speed of the proposed method have been carried out.

摘要本文提出了一种基于人工神经网络的方法，用于实时确定在另一架飞机的涡流尾流中作用在飞机上的附加力和力矩。该方法基于神经网络近似作用在飞机上的附加力和力矩。这些都是由单个涡流段的影响造成的。为了生成一组用于训练神经网络的数据，使用了流体力学奇点法。对拟议方法的准确性和速度进行了评估。

引用次数: 0

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