共查询到20条相似文献,搜索用时 750 毫秒
1.
Fully developed forced convection inside a circular tube filled with saturated porous medium and with uniform heat flux at
the wall is investigated on the basis of a Brinkman–Forchheimer model. The matched asymptotic expansion method is applied
at small Darcy numbers. For large Darcy numbers, the solution for the Brinkman–Forchheimer momentum equation is found in terms
of an asymptotic expansion. Once the velocity distribution is determined, the energy equation is solved using the same asymptotic
technique. The results for the two limiting cases of clear fluid and Darcy flow conditions show good agreement with those
available in the literature. 相似文献
2.
We tackle the issue of the inviscid limit of the incompressible Navier–Stokes equations when the Navier slip-with-friction
conditions are prescribed on impermeable boundaries. We justify an asymptotic expansion which involves a weak amplitude boundary
layer, with the same thickness as in Prandtl’s theory and a linear behavior. This analysis holds for general regular domains,
in both dimensions two and three. 相似文献
3.
O. E. Omel'chenko 《Nonlinear Oscillations》2005,8(3):329-350
Using the method of boundary functions, for a quasilinear parabolic equation with small diffusion coefficient we construct
an asymptotic expansion of a periodic solution with internal transition layer. Sufficient conditions for the existence of
this solution are obtained.
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Translated from Neliniini Kolyvannya, Vol. 8, No. 3, pp. 329–350, July–September, 2005. 相似文献
4.
Sebastian Bönisch Vincent Heuveline Peter Wittwer 《Journal of Mathematical Fluid Mechanics》2008,10(1):45-70
We consider the problem of solving numerically the stationary incompressible Navier–Stokes equations in an exterior domain
in two dimensions. For numerical purposes we truncate the domain to a finite sub-domain, which leads to the problem of finding
so called “artificial boundary conditions” to replace the boundary conditions at infinity. To solve this problem we construct
– by combining results from dynamical systems theory with matched asymptotic expansion techniques based on the old ideas of
Goldstein and Van Dyke – a smooth divergence free vector field depending explicitly on drag and lift and describing the solution
to second and dominant third order, asymptotically at large distances from the body. The resulting expression appears to be
new, even on a formal level. This improves the method introduced by the authors in a previous paper and generalizes it to
non-symmetric flows. The numerical scheme determines the boundary conditions and the forces on the body in a self-consistent
way as an integral part of the solution process. When compared with our previous paper where first order asymptotic expressions
were used on the boundary, the inclusion of second and third order asymptotic terms further reduces the computational cost
for determining lift and drag to a given precision by typically another order of magnitude.
Peter Wittwer: Supported in part by the Fonds National Suisse. 相似文献
5.
For a second-order symmetric uniformly elliptic differential operator with rapidly oscillating coefficients, we study the
asymptotic behavior of solutions of a mixed inhomogeneous boundary-value problem and a spectral Neumann problem in a thin
perforated domain with rapidly varying thickness. We obtain asymptotic estimates for the differences between solutions of
the original problems and the corresponding homogenized problems. These results were announced in Dopovidi Akademii Nauk Ukrainy, No. 10, 15–19 (1991). The new results obtained in the present paper are related to the construction of an asymptotic expansion
of a solution of a mixed homogeneous boundary-value problem under additional assumptions of symmetry for the coefficients
of the operator and for the thin perforated domain. 相似文献
6.
We study the low Mach number asymptotic limit for solutions to the full Navier–Stokes–Fourier system, supplemented with ill-prepared
data and considered on an arbitrary time interval. Convergencetowards the incompressible Navier–Stokes equations is shown. 相似文献
7.
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
8.
Yu. E. Ivanova V. E. Ragozina 《Journal of Applied Mechanics and Technical Physics》2006,47(6):892-898
The method of matched asymptotic expansions was employed to obtain approximate solutions to the one-dimensional boundary-value
problems of nonlinear dynamic elasticity theory of impact loading on the surface of a cylindrical cavity of an incompressible
medium that causes antiplane motion or torsion of the medium. The expansion of the solution in the near-front region is based
on solutions of evolution equations different from the equations for quasi-simple waves.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 144–151, November–December, 2006. 相似文献
9.
We consider a kinetic model for a system of two species of particles interacting through a long range repulsive potential
and a reservoir at given temperature. The model is described by a set of two coupled Vlasov–Fokker–Plank equations. The important
front solution, which represents the phase boundary, is a stationary solution on the real line with given asymptotic values
at infinity. We prove the asymptotic stability of the front for small symmetric perturbations. 相似文献
10.
A. E. Bukatov 《Fluid Dynamics》1994,29(4):549-555
The nonlinear interaction of periodic traveling waves of the first and second harmonics in a constant-depth uniform fluid
covered with broken ice is considered. Uniform asymptotic expansions up to third-order values for the velocity potential of
the fluid and the elevation of the basin surface are found by means of the multivariable expansion procedure. The dependence
of the wave perturbations on the thickness of the ice and the interacting-harmonic characteristics is analyzed.
Sevastopol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 136–143, July–August,
1994. 相似文献
11.
B. M. Zhirnov 《International Applied Mechanics》2000,36(7):969-977
A technique is proposed to study and design a mechanical self-oscillating system in the quasiharmonic-oscillation regime.
The technique is based on the polynomial approximation of the force due to dry sliding friction by a finite number of terms
in the Taylor-series expansion with allowance for energy dissipation in accordance with Pisarenko's hypothesis and the first
“improved” asymptotic approximation.
Transport University, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 137–144, July, 2000. 相似文献
12.
It is known that a transform of Liouville type allows one to pass from an equation of the Korteweg–de Vries (K–dV) hierarchy
to a corresponding equation of the Camassa–Holm (CH) hierarchy (Beals et al., Adv Math 154:229–257, 2000; McKean, Commun Pure
Appl Math 56(7):998–1015, 2003). We give a systematic development of the correspondence between these hierarchies by using
the coefficients of asymptotic expansions of certain Green’s functions. We illustrate our procedure with some examples. 相似文献
13.
Zh. L. Mal’tseva 《Journal of Applied Mechanics and Technical Physics》1999,40(5):824-830
Solitary waves on an interface between two fluids are considered. A uniform asymptotic expansion is constructed for internal
solitary waves with flat crests (of the plateau type) that degenerate into a bore in the limit. It is shown that, in this
case, in contrast to a Korteweg-de Vries wave, the wave amplitude is of the same order of smallness as the longwave approximation
parameter.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 55–61, September–October, 1999. 相似文献
14.
V. M. Khar’kov 《Nonlinear Oscillations》2008,11(4):571-584
We obtain asymptotic representations for one class of solutions of a second-order differential equation with nonlinearity
close to an exponential.
Translated from Neliniini Kolyvannya, Vol. 11, No. 4, pp. 541–553, October–December, 2008. 相似文献
15.
We construct asymptotic solutions of a singularly perturbed linear system of differential equations with irregular singular
point. We consider the case where the main matrix has a multiple eigenvalue associated with one or several elementary divisors
of the same multiplicity. We establish that, in the case of multiple elementary divisors, the corresponding asymptotic expansions
can be constructed in the form of double series in fractional powers of the parameter and the ratio of the independent variable
to the parameter.
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Translated from Neliniini Kolyvannya, Vol. 11, No. 1, pp. 128–144, January–March, 2007. 相似文献
16.
We consider the asymptotic limit for the complete Navier–Stokes–Fourier system as both Mach and Froude numbers tend to zero.
The limit is investigated in the context of weak variational solutions on an arbitrary large time interval and for the ill-prepared
initial data. The convergence to the Oberbeck–Boussinesq system is shown.
相似文献
17.
A. P. Krenevych 《Nonlinear Oscillations》2006,9(2):207-214
We investigate the problem of the asymptotic equivalence of systems of nonlinear ordinary and stochastic equations in mean
square and with probability one.
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Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 213–220, April–June, 2006. 相似文献
18.
We study applications of asymptotic methods of nonlinear mechanics and the method of Fokker-Planck-Kolmogorov equations to
stochastic oscillations in quasilinear oscillating systems with random perturbations.
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Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 510–518, October–December, 2007. 相似文献
19.
Mousa Jaber Abu-Elshour 《Nonlinear Oscillations》2008,11(2):242-254
We find asymptotic representations for certain classes of solutions of nonautonomous second-order differential equations that
are close, in a certain sense, to linear equations.
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Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 230–241, April–June, 2008. 相似文献
20.
P. F. Samusenko 《Nonlinear Oscillations》2008,11(3):427-441
We obtain an asymptotic solution of the Cauchy problem for a singularly perturbed degenerate system of differential equations
in the case of a singular limit pencil of matrices.
Translated from Neliniini Kolyvannya, Vol. 11, No. 3, pp. 408–420, July–September, 2008. 相似文献