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1.
S. P. Bautin 《Journal of Applied Mechanics and Technical Physics》2008,49(3):375-382
The Kuropatenko model is considered, as applied to a multicomponent medium where the number of the sought functions coincides
with the number of equations. The velocities of sound in a multicomponent medium at rest are determined. A formula of a polynomial
of power N whose positive roots are squared velocities of sound in a medium with N components is derived. For N = 2, the values
of two velocities of sound are determined in explicit form. It is demonstrated that the thus-found maximum value of the velocity
of sound in a two-component medium containing nitrogen and oxygen with volume concentrations corresponding to air differs
(in dimensionless form) from the velocity of sound in air by less than 0.3%. Numerical calculations predict the existence
of three velocities of sound in a three-component medium. If the velocity of sound in all N components is identical, it is
proved that the maximum velocity of sound in such a medium equals this velocity, and there is only one more velocity of sound
in the medium, which has a lower value.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 35–44, May–June, 2008. 相似文献
2.
Thermodynamic equilibrium, which involves mechanical, thermal, and chemical equilibria, in a multiphase porous medium, is defined and discussed, both at the microscopic level, and at the macroscopic one. Conditions are given for equilibrium in the presence of forces between the surface of the solid matrix and the fluid phases. The concept ofapproximate thermodynamic equilibrium is introduced and discussed, employing the definition of athermodynamic potential. This discussion serves as the basis for the methodology of determining the number of degrees of freedom in models of phenomena of transport (of mass, energy, and momentum) in porous media. Equilibrium and nonequilibrium cases are considered. The proposed expressions for the number of degrees of freedom in macroscopic transport models, represent the equivalent ofGibbs phase rule in thermodynamics. Based on balance considerations and thermodynamic relationships, it is shown that the number of degrees of freedom, NF, in a problem of transport in a deformable porous medium, involving NP fluid phases and NC components, under nonisothermal conditions, with equilibrium among all phases and components, is $${\text{NF = NC + NP + 4}}{\text{.}}$$ Under nonequilibrium conditions among the phases, the rule takes the form $${\text{NF = NC }} \times {\text{ NP + 2NP + NC + 4}}{\text{.}}$$ In both cases, when fluid phase velocities are determined by Darcy's law, NF is reduced by NP. When the solid matrix is nondeformable, NF is reduced by 3. The number of degrees of freedom is also determined for conditions of approximate chemical and thermal equilibria, and for conditions of equilibrium that prevail only among some of the phases present in the system. Examples of particular cases are presented to illustrate the proposed methodology. 相似文献
3.
Macroscopic modelling of transport phenomena in porous media. 2: Applications to mass,momentum and energy transport 总被引:1,自引:0,他引:1
In this second paper, the averaging rules presented in Part 1 are employed in order to develop a general macroscopic balance
equation and particular equations for mass, mass of a component, momentum and energy, all of a phase in a porous medium domain.
These balance equations involve averaged fluxes. Then macroscopic equations are developed for advective, dispersive and diffusive
fluxes, all in terms of averaged state variables of the system. These are combined with the macroscopic balance equations
to yield field equations that serve as the core of the mathematical models that describe the transport of extensive quantities
in a porous medium domain.
It is shown that the methodology of averaging leads to a better understanding of the effective stress concept employed in
dealing with transport phenomena in deformable porous media. 相似文献
4.
刘慈群 《应用数学和力学(英文版)》1988,9(6):521-252
The transient spherical flow behavior of a slightly compressible non-Newtonian, power-law fluids in porous media is studied.
A nonlinear partial differential equation of parabolic type is derived. The diffusivity equation for spherical flow is a special
case of the new equation. We obtain analytical, asymptotic and approximate solutions by using the methods of Laplace transform
and weighted mass conservation. The structures of asymptotic and approximate solutions are similar, which enriches the theory
of one-dimensional flow of non-Newtonian fluids through porous media. 相似文献
5.
The results of an experimental investigation and numerical simulation of heat exchange are given for sharp and blunt plates in a hypersonic air flow. The experiments were carried out in a Ludwig-type wind tunnel at hypersonic Mach numbers and a Reynolds number ReL which varied over the range from 0.24 106 to 1.31 106. The bluntness radius r was varied over the range from 0.008 mm (almost sharp plate) to 4 mm (the corresponding Reynolds numbers Rer from 15 to 4 104). The numerical simulation was carried out by solving the complete two-dimensional Navier-Stokes equations. The experimental data were correlated using the well-known viscous hypersonic interaction parameters.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 168–180. Original Russian Text Copyright © 2005 by Borovoi, Egorov, Skuratov and Struminskaya. 相似文献
6.
S. Langer S. A. Nazarov M. Specovius-Neugebauer 《Journal of Applied Mechanics and Technical Physics》2006,47(2):229-235
The concept of classes of algebraically equivalent anisotropic three-dimensional media is introduced: elastic fields in such
media are related by simple algebraic expressions. An explicit formula is obtained for a fundamental matrix with ten free
constants in the elastic modulus tensor (rather than for five free constants, as in the famous case of transverse isotropy).
A hypothesis is formulated and several questions are posed, which are related to the notion of algebraic equivalence under
discussion.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 95–102, March–April, 2006. 相似文献
7.
By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blowup phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘ small ‘ solution. 相似文献
8.
On the boundedness and periodicity of the solutions of a certain vector differential equation of third-order 总被引:1,自引:0,他引:1
Cemil Tune 《应用数学和力学(英文版)》1999,20(2):163-170
IntroductionWeshallbeconcernedherewiththird-ordersystemofnon-lineardifferentialequationsoftheformX F(X,X)X Ba H(X)=P(t,X,X,X),(l)whereX6R",R"denotestherealn-dimensionalEuclldeanspaceRxRx'xR(nfactors),R=(--ac,ac),Fisannxn-matrixfunction,Bisarealnxn-constantsymmetricmatrix,H:R"~R"1andp:RxR"xR"xR"~R".ThedotsindicatCdifferentiationwithrespeCttot.ThefunctionsF,HandParecontinuousforallvaluesoftheirrespeCtivearguments.Moreover,theexistenceandtheuniquenessofthesolutionsof(l)willbeassu… 相似文献
9.
Francesco Fedele Melissa McKay George F. Pinder Joseph F. Guarnaccia 《国际流体数值方法杂志》2004,44(12):1337-1354
The classical collocation method using Hermite polynomials is computationally expensive as the dimensionality of the problem increases. Because of the use of a C1‐continuous basis, the method generates two, four and eight unknowns per node for one, two and three‐dimensional problems, respectively. In this paper we propose a numerical strategy to reduce the nodal unknowns to a single degree of freedom at each node. The reduction of the unknowns is due to the use of Lagrangian polynomials to approximate the first‐order derivatives over the minimal compact stencil surrounding each node. For the solvability of the problem the reduction of the number of collocation equations is done by a nodal weighting strategy. We have applied the proposed approach to enhance the efficiency of a collocation‐based multiphase flow and transport simulator. Benchmark cases illustrate the higher performance of the new methodology when compared to classical Hermite collocation. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
10.
一种求解有限元问题结点平衡方程的快速方法 总被引:1,自引:0,他引:1
目前随着工程实际问题复杂程度的增加及分析的要求,特别是材料非线性分析的引入,尽管计算机的运算速度、内存、外存容量等不断提高,但并不能完全满足大规模计算的需要,更快、更节省存贮空间的算法一直是有限元法分析过程中的一项核心技术要求。本文针对一些结点及单元均规律化地排列的有限元问题,提出可以透过其相邻结点的关系记录结点平衡方程中系数矩阵的非零元素,无需再像等带宽存贮那样去记录带宽内大量的零元素。此方法可以大大地减少系数矩阵元素的存贮量,从而可以提高计算机读取数据的速度及改善利用迭代法求解的效率。 相似文献
11.
建立了考虑车-桥(线)纵向振动及其能量相互转化机制的竖平面内精细耦合运动方程.将车-桥(线)视为一个整体系统,车辆各剐体的纵向运动均作为独立的自由度,考虑到车-桥(线)纵向振动及其能量相互转化机制,车辆驱动或制动作用采用轮轨间的纵向相互作用力和轮对作用力矩模拟,桥梁、线路结构采用梁单元离散,线路与桥梁之间的钢轨基础采用竖向和纵向的均布弹簧阻尼连接,建立了竖平面内精细耦合运动方程,它可合理模拟车桥(线)间能量相互转化的过程.简支梁桥算例表明:车辆在桥上无驱动或制动运行过程中,不考虑轨道结构时车速先增加后减小,而考虑轨道结构时车速只有减小的趋势,轮对还发生了高频的纵向振动,且车体和轮对的纵向振动对轨道竖向不平顺较为敏感;此外,考虑轮轨滚动碾压作用和能量转化机制时,钢轨加速度响应略偏大.本文研究可为实际车辆动态变速运行的模拟和更精细空间耦合模型的建立提供研究基础. 相似文献
12.
This paper presents numerical examples for the moving grid finite element algorithm derived in Part Ito solve the non-linear coupled set of PDEs governing immiscible multiphase flow in porous media in one dimension. Examples include single- and double-front simulations for two- and three-phase flow regimes and incorporating a mass sink. The modelling approach is shown to achieve significant savings in computation time and memory allocation when compared with fixed grid solutions of equivalent accuracy. This work includes sensitivity analyses for the parameters which are incorporated in the grid adaptation method, including the curvature weights, artificial viscosity and artificial repulsive force. It is found that the curvature weights are exponential functions of the negative ratio of the square root of the domain length to the number of discrete nodes. These weighting parameters are also shown to depend upon the shape of the front. On the basis of the examined simulations, it is recommended that artificial viscosity be neglected in the solution of the coupled non-linear set of PDEs governing multiphase flow in porous media. Similarly, use of a repulsive force is found to be unnecessary in simulations involving the migration of two liquid phases. For multiphase flows incorporating a gas phase it is recommended to use a non-zero value for the repulslive force to avoid development of an ill-conditioned nodal distribution matrix. An equation to evaluate the repulsive force under these circumstances is suggested. 相似文献
13.
Amaury C. Alvarez Gustavo Hime Dan Marchesin Pavel G. Bedrikovetsky 《Transport in Porous Media》2007,70(1):43-62
Deep bed filtration of particle suspensions in porous media occurs during water injection into oil reservoirs, drilling fluid
invasion of reservoir production zones, fines migration in oil fields, industrial filtering, bacteria, viruses or contaminants
transport in groundwater etc. The basic features of the process are particle capture by the porous medium and consequent permeability
reduction. Models for deep bed filtration contain two quantities that represent rock and fluid properties: the filtration
function, which is the fraction of particles captured per unit particle path length, and formation damage function, which
is the ratio between reduced and initial permeabilities. These quantities cannot be measured directly in the laboratory or
in the field; therefore, they must be calculated indirectly by solving inverse problems. The practical petroleum and environmental
engineering purpose is to predict injectivity loss and particle penetration depth around wells. Reliable prediction requires
precise knowledge of these two coefficients. In this work we determine these quantities from pressure drop and effluent concentration
histories measured in one-dimensional laboratory experiments. The recovery method consists of optimizing deviation functionals
in appropriate subdomains; if necessary, a Tikhonov regularization term is added to the functional. The filtration function
is recovered by optimizing a non-linear functional with box constraints; this functional involves the effluent concentration
history. The permeability reduction is recovered likewise, taking into account the filtration function already found, and
the functional involves the pressure drop history. In both cases, the functionals are derived from least square formulations
of the deviation between experimental data and quantities predicted by the model. 相似文献
14.
丁协平 《应用数学和力学(英文版)》2005,26(12):1556-1563
By applying coincidence theorems in part (Ⅰ) for two families of set-valued mappings defined on product space of noncompact FC-spaces in preceding paper, some new existence theorems for system of vector equilibrium problems, system of inequalities and system of minimax theorems were established in FC-spaces. These results generalize some known results in recent literature. 相似文献
15.
The paper proposes a modification of the mixed variational principle from which stationarity conditions are derived in the
form of a mixed system of equations resolved for the first derivatives of the displacement and stress components acting in
a plane perpendicular to one of the coordinate axes. The variational principle allows decreasing the dimension of the problem
of elasticity thus reducing the system of equations to a canonical form. The modified mixed principle helps immediately obtain
a canonical system of equations for various applied theories. This possibility is demonstrated with the example of the Timoshenko
theory of plates
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 55–62, May 2007. 相似文献
16.
A mathematical model is developed for saturated flow of a Newtonian fluid in a thermoelastic, homogeneous, isotropic porous medium domain under nonisothermal conditions. The model contains mass, momentum and energy balance equations. Both the momentum and energy balance equations have been developed to include a Forchheimer term which represents the interaction at the solid-fluid interface at high Reynolds numbers. The evolution of these equations, following an abrupt change in both fluid pressure and temperature, is presented. Using a dimensional analysis, four evolution periods are distinguished. At the very first instant, pressure, effective stress, and matrix temperature are found to be disturbed with no attenuation. During this stage, the temporal rate of pressure change is linearly proportional to that of the fluid temperature. In the second time period, nonlinear waves are formed in terms of solid deformation, fluid density, and velocities of phases. The equation describing heat transfer becomes parabolic. During the third evolution stage, the inertial and the dissipative terms are of equal order of magnitude. However, during the fourth time period, the fluid's inertial terms subside, reducing the fluid's momentum balance equation to the form of Darcy's law. During this period, we note that the body and surface forces on the solid phase are balanced, while mechanical work and heat conduction of the phases are reduced. 相似文献
17.
V. Yu. Liapidevskii K. N. Gavrilova 《Journal of Applied Mechanics and Technical Physics》2008,49(1):34-45
The problem of a homogeneous heavy liquid flow over a local obstacle is considered in the long-wave approximation. The steady
and unsteady waves in the vicinity of the obstacle are described by second-order models of the shallow-water theory and their
hyperbolic approximations. The flow in the vicinity of the leading and trailing edges of bluff bodies (sills and steps) is
studied. The solution of the problem of the blocked zone upstream of the step is constructed.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 45–58, January–February, 2008. 相似文献
18.
Nonempty intersection theorems and system of generalized vector equilibrium problems in product G-convex spaces 总被引:1,自引:0,他引:1
丁协平 《应用数学和力学(英文版)》2004,25(6):618-626
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature. 相似文献
19.
For the system of multilayer dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources. 相似文献
20.
Dynamic systems described by nonlinear differential equations of the second order are studied. It is assumed that certain
preliminary information on the dissipative or elastic characteristics of systems is known. A new approach is demonstrated
to obtaining full information on unknown or partially known characteristics of a system from measurements of not only displacements
but also velocities and accelerations
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Published in Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 139–143, June 2005. 相似文献