共查询到20条相似文献,搜索用时 31 毫秒
1.
V. Sh. Shagapov M. K. Khasanov N. G. Musakaev 《Journal of Applied Mechanics and Technical Physics》2008,49(3):462-472
Specific features of formation of gas hydrates due to injection of a gas into a porous medium initially filled by a gas and
water are considered. Self-similar solutions of an axisymmetric problem, which describe the distributions of the basic parameters
in the reservoir, are constructed. The existence of solutions is demonstrated, which predict gas hydrate formation both on
the frontal surface and in the volume zone.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 137–150, May–June, 2008. 相似文献
2.
S. V. Khabirov 《Journal of Applied Mechanics and Technical Physics》2007,48(5):641-648
All partially invariant solutions in terms of the group of extensions for a model of radial motions of an ideal gas are found.
The solutions are obtained by the method of separation of variables in an equation containing functions of one variable but
different functions of different independent variables. The solutions predict different continuous unsteady convergence or
expansion of the gas under the action of a piston with a point sink or source. If the sink or source affects all particles
simultaneously, a collapse or an explosion occurs.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 26–34, September–October, 2007. 相似文献
3.
V. V. Bublik 《Journal of Applied Mechanics and Technical Physics》1999,40(5):820-823
All invariant solutions of rank 1 of the two-dimensional equations of motion of a heat-conducting perfect gas with a polytropic
equation of state are described. A sufficient condition for reducibility of regular, partially invariant solutions of rank
1 and defect 1 to invariant solutions is given.
Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated
from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 51–54, September–October, 1999. 相似文献
4.
V. V. Bublik 《Journal of Applied Mechanics and Technical Physics》2006,47(6):790-799
A system of the Navier-Stokes equations of two-dimensional motion of a viscous heat-conducting perfect gas with a polytropic
equation of state is considered. Regular, partially invariant solutions of rank 1 and defect 1 are studied. A sufficient condition
of their reducibility to invariant solutions of rank 1 is proved. All solutions of this class with a linear dependence of
the velocity-vector components on spatial coordinates are examined. New examples of solutions that are not reducible to invariant
solutions are obtained.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 23–33, November–December, 2006. 相似文献
5.
N. V. Khusnutdinova 《Journal of Applied Mechanics and Technical Physics》2008,49(4):548-552
A problem is considered for the system describing gas flows with plate boundary layer separation in Mises variables in boundary-layer
theory. The existence of generalized solutions of the problem is proved.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 36–41, July–August, 2008. 相似文献
6.
Self-similar problem of decomposition of gas hydrates in a porous medium upon depression and heating
R. I. Nigmatulin V. Sh. Shagapov V. R. Syrtlanov 《Journal of Applied Mechanics and Technical Physics》1998,39(3):421-427
We consider the specifics of decomposition of gas hydrates under thermal and depressive action on a porous medium completely
filled with a solid hydrate in the initial condition. The existence of volumetric-expansion zones, in which the hydrate coexists
in equilibrium with water and gas, is shown to be possible in high-permeable porous media. The self-similar problems of hydrate
decomposition upon depression and heating are studied. Ii is shown that there are solutions according to which hydrate decomposition
can occur both on the surface of phase transitions and in the volumetric region. We note that, in the first case, decomposition
is possible without heat supply to a medium and even with heat removal.
Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences, Tyumen' 625000. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 111–118, May–June, 1998. 相似文献
7.
O. V. Voinov 《Journal of Applied Mechanics and Technical Physics》2007,48(3):385-392
The motion of thin films of a viscous incompressible liquid in a gas under the action of capillary forces is studied. The
surface tension depends on the surfactant concentration, and the liquid is nonvolatile. The motion is described by the well-known
model of quasi-steady-state viscous film flow. The linear-wave solutions are compared with the solution using the Navier-Stokes
equations. Situations are studied where a solution close to the inviscid two-dimensional solutions exists and in the case
of long wavelength, the occurrence of sound waves in the film due to the Gibbs surface elasticity is possible. The behavior
of the exact solutions near the region of applicability of asymptotic equations is studied, and nonmonotonic dependences of
the wave characteristics on wavenumber are obtained.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 103–111, May–June, 2007. 相似文献
8.
G. N. Dudin 《Fluid Dynamics》2000,35(1):101-107
The flow formed as a result of gas injection through the permeable surface of a triangular plate is investigated in the regime
of strong viscous-inviscid interaction between the hypersonic flow and the laminar boundary layer. The features of the flow
past strongly cooled surfaces with the formation of supercritical and subcritical flow regions in the boundary layer are studied.
The injected gas distribution ensuring the existence of self-similar solutions in the supercritical flow regions is obtained.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 125–133, January–February,
2000.
The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-01391). 相似文献
9.
Michael Struwe 《Journal of Mathematical Fluid Mechanics》2007,9(2):235-242
We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result
of Zhou [28]. 相似文献
10.
V. Sh. Shagapov I. G. Khusainov R. M. Khafizov 《Journal of Applied Mechanics and Technical Physics》2006,47(1):91-98
The pressure testing of a hole in porous and permeable rock by gas injection is considered. An integral equation for the hole
pressure relaxation is obtained whose numerical and analytical solutions describe the dependence of the relaxation time of
hole pressure on the reservoir properties of the surrounding porous rock as well as on the initial gas content and the initial
pressure gradient in the hole.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 109–118, January–February, 2006. 相似文献
11.
We obtain a criterion for solutions of a linear discrete Volterra system with operator coefficients to be bounded or summable
to a power p.
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Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 184–187, April–June, 2007. 相似文献
12.
Mohammadhossein Heidari Sureshjani Shahab Gerami Mohammad Ali Emadi 《Transport in Porous Media》2012,93(1):147-169
One of the widely used methods for modeling matrix–fracture fluid exchange in naturally fractured reservoirs is dual porosity
approach. In this type of modeling, matrix blocks are regarded as sources/sinks in the fracture network medium. The rate of
fluid transfer from matrix blocks into fracture medium may be modeled using shape factor concept (Warren and Root, SPEJ 3:245–255,
1963); or the rate–time solution is directly derived for the specific matrix geometry (de Swaan, SPEJ 16:117–122, 1976). Numerous works have been conducted to study matrix–fracture fluid exchange for slightly compressible fluids (e.g. oil).
However, little attention has been taken to systems containing gas (compressible fluid). The objective of this work is to
develop explicit rate–time solutions for matrix–fracture fluid transfer in systems containing single phase gas. For this purpose,
the governing equation describing flow of gas from matrix block into fracture system is linearized using pseudopressure and
pseudotime functions. Then, the governing equation is solved under specific boundary conditions to obtain an implicit relation
between rate and time. Since rate calculations using such an implicit relation need iterations, which may be computationally
inconvenient, an explicit rate–time relation is developed with the aid of material balance equation and several specific assumptions.
Also, expressions are derived for average pseudopressure in matrix block. Furthermore, simplified solutions (originated from
the complex general solutions) are introduced applicable in infinite and finite acting flow periods in matrix. Based on the
derived solutions, expressions are developed for shape factor. An important observation is that the shape factor for gas systems
is the same as that of oil bearing matrix blocks. Subsequently, a multiplier is introduced which relates rate to matrix pressure
instead of matrix pseudopressure. Finally, the introduced equations are verified using a numerical simulator. 相似文献
13.
We establish a rigorous demonstration of the hydrodynamic convergence of the Boltzmann equation towards a Navier–Stokes–Fourier system under the presence of long-range interactions. This convergence is obtained by letting the Knudsen number tend to zero and has been known to hold, at least formally, for decades. It is only more recently that a fully rigorous mathematical derivation of this hydrodynamic limit was discovered. However, these results failed to encompass almost all physically relevant collision kernels due to a cutoff assumption, which requires that the cross sections be integrable. Indeed, as soon as long-range intermolecular forces are present, non-integrable collision kernels have to be considered because of the enormous number of grazing collisions in the gas. In this long-range setting, the Boltzmann operator becomes a singular integral operator and the known rigorous proofs of hydrodynamic convergence simply do not carry over to that case. In fact, the DiPerna–Lions renormalized solutions do not even make sense in this situation and the relevant global solutions to the Boltzmann equation are the so-called renormalized solutions with a defect measure developed by Alexandre and Villani. Our work overcomes the new mathematical difficulties coming from the consideration of long-range interactions by proving the hydrodynamic convergence of the Alexandre–Villani solutions towards the Leray solutions. 相似文献
14.
We give sufficient conditions for the extendability of solutions of a nonlinear difference equation “to the left” in a Banach
space.
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Translated from Neliniini Kolyvannya, Vol. 10, No. 3, pp. 298–302, July–September, 2007. 相似文献
15.
O. I. Kocherha 《Nonlinear Oscillations》2007,10(2):246-256
We prove the asymptotic character of a solution of the Cauchy problem for a singularly perturbed linear system of differential
equations with degenerate matrix of the coefficients of derivatives in the case where the limit matrix pencil is regular and
has multiple “finite” and “infinite” elementary divisors. We establish conditions under which the constructed formal solutions
are asymptotic expansions of the corresponding exact solutions.
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Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 247–257, April–June, 2007. 相似文献
16.
L. V. Ovsyannikov 《Journal of Applied Mechanics and Technical Physics》1999,40(2):191-197
The notion of a “simple” solution of a system of differential equations that admit a local Lie group G of transformations
of the basic space is considered as an invariant H-solution of type (0, 0) with respect to the subgroup HυG. Such solutions
are attractive since they are described by explicit formulas that provide a clear physical interpretation for them. For gas-dynamic
equations with a polytropic gas law, all simple solutions that are not related to special forms of gas flow are listed. Examples
of simple solutions are given and the collapse phenomenon, which has been previously studied for barochronic flows, is described.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 5–12, March–April, 1999. 相似文献
17.
B. N. Elemesova 《Journal of Applied Mechanics and Technical Physics》1999,40(1):28-35
The plane-parallel unsteady-state shear gas flow in a narrow channel of constant cross section is considered. The existence
theorem of solutions in the form of simple waves of a set of equations of motion is proved for a class of isentropic flows
with a monotone velocity profile over the channel depth. The exact solution described by incomplete beta-functions is found
for a polytropic equation of state in a class of isentropic flows.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 36–43, January–February, 1999. 相似文献
18.
N. V. Plotnikova 《Nonlinear Oscillations》2006,9(3):375-390
We construct an approximation of a bundle of solutions of a linear impulsive differential inclusion using a system of linear
impulsive differential equations with Hukuhara derivative.
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Translated from Neliniini Kolyvannya, Vol. 9, No. 3, pp. 386–400, July–September, 2006. 相似文献
19.
N. I. Blashchak 《Nonlinear Oscillations》2005,8(2):152-156
We obtain sufficient conditions for the existence of periodic solutions of a system of nonlinear functional partial differential
equations.
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Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 154–158, April–June, 2005. 相似文献
20.
D. V. Parshin A. P. Chupakhin 《Journal of Applied Mechanics and Technical Physics》2006,47(6):773-784
The nonbarochronic regular partially invariant submodel of the equations of gas dynamics is studied. The submodel reduces
to an implicit ordinary differential equation of the first order for an auxiliary function X = X(x). The physical quantities
(velocity, density, and pressure) are expressed in terms of the function X. The properties of the solutions of the equation
are investigated and interpreted physically in terms of gas motion. The existence of a shock-wave solution is proved. The
properties of the shock adiabat are studied. It is shown that the results obtained are new and differ significantly from the
results for the case of no constant force.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 3–16, November–December, 2006. 相似文献