共查询到20条相似文献,搜索用时 218 毫秒
1.
江福汝 《应用数学和力学(英文版)》1981,2(5):505-518
In this paper, the defect of the traditionary boundary layer methods (including the method of matched asymptotic expansions and the method of Visik-Lyusternik) is noted, from those methods we can not construct the asymptotic expansion of boundary layer term substantially. So the method of multiple scales is proposed for constructing the asymptotic expansion of boundary layer term, the reasonable result is obtained. Furthermore, we compare this method with the method used by Levinson, and find that both methods give the same asymptotic expansion of boundary layer term, but our method is simpler.Again, we apply this method to study some known works on singular perturbations. The limitations of those works have been noted, and the asymptotic expansion of solution is constructed in general condition. 相似文献
2.
The cases of large Reynolds number and small expansion ratio for the asym- metric laminar flow through a two-dimensional porous expanding channel are considered. The Navier-Stokes equations are reduced to a nonlinear fourth-order ordinary differential equation by introducing a time and space similar transformation. A singular perturbation method is used for the large suction Reynolds case to obtain an asymptotic solution by matching outer and inner solutions. For the case of small expansion ratios, we are able to obtain asymptotic solutions by double parameter expansion in either a small Reynolds number or a small asymmetric parameter. The asymptotic solutions indicate that the Reynolds number and expansion ratio play an important role in the flow behavior. Nu- merical methods are also designed to confirm the correctness of the present asymptotic solutions. 相似文献
3.
The effect of heat generation on the flow characteristics of the fully developed forced convection through a porous duct is investigated analytically on the basis of Brinkman?CForchheimer model. The duct is bounded by two isoflux plates. For solving momentum equation a regular asymptotic expansion method is used for hyper-porous materials and a matched asymptotic expansion method is used for low-porous materials. This solution permits a uniform solution for the energy equation to find the temperature distribution as well as Nusselt number. A numerical solution is found here to check the accuracy of the asymptotic one. 相似文献
4.
徐钧涛 《应用数学和力学(英文版)》1988,9(7):681-692
In this paper, the method of two-variables expansion is used to construct boundary layer terms of asymptotic solution of the
boundary-value problem for a second-order DDE. The n-order formal asymptotic solution is obtained and the error is estimated.
Thus the existence of uniformly valid asymptotic solution is proved. 相似文献
5.
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
6.
We examine the problem of swirling-jet development in an infinite space filled with the same fluid. The fourth term of the asymptotic expansion of the tangential-velocity component is obtained. The constant appearing in the solution is obtained semlempirically. Results are presented of calculations of the velocities and pressure in swirling jets and of experimental studies.Swirling jet flows play an important role in the process of combustion intensification and stabilization and are widely used in engineering.The formulation and first solution of the problem of swirling-jet development in an infinite space filled with the same fluid at rest were accomplished by Loitsyanskii [1], who found the first two terms of the asymptotic expansion of the solution of the boundary-layer equations. The third and fourth terms of the asymptotic expansion of the axial-velocity component were found in [2], which made it possible to study the effect of jet swirl on the axial-velocity-component profile.In the present study we obtain the fourth term of the asymptotic expansion of the tangential-velocity component and present results of experimental studies on swirling jets.The authors wish to thank L. G. Loitsyanskii for valuable comments. 相似文献
7.
Warren B. Gordon 《Wave Motion》1982,4(4):349-369
The one dimensional Klein-Gordon equation with spatially varying coefficients and with amplitude modulated high frequency signaling data is analyzed. A formal uniformly valid asymptotic expansion of the solution across a space-time shadow boundary is obtained with the help of two families of rays. These rays may also give rise to shadow regions. The asymptotic expansion involves three functions, a Fresnel function and two successive Bessel functions of integer order. 相似文献
8.
9.
Mariana Silva Moshe Matalon Daniel A. Tortorelli 《International Journal of Solids and Structures》2010,47(22-23):3053-3066
The topological derivative provides the variation of a response functional when an infinitesimal hole of a particular shape is introduced into the domain. In this work, we compute higher order topological derivatives for elasticity problems, so that we are able to obtain better estimates of the response when holes of finite sizes are introduced in the domain. A critical element of our algorithm involves the asymptotic approximation for the stress on the hole boundary when the hole size approaches zero; it consists of a composite expansion that is based on the responses of elasticity problems on the domain without the hole and on a domain consisting of a hole in an infinite space. We present a simple example in which the higher order topological derivatives of the total potential energy are obtained analytically and by using the proposed asymptotic expansion. We also use the finite element method to verify the topological asymptotic expansion when the analytical solution is unknown. 相似文献
10.
The multiple-scale expansionmethod is used for constructing a uniformly applicable asymptotic approximation of the solution of the linearized Boltzmann equation for small Knudsen numbers. The asymptotic expansion is constructed for the particular example of a sound wave generated by a plane oscillation source and dissipating in a half-space. The simplicity of the problem makes it possible clearly to demonstrate the appearance of secular terms in the expansion and the introduction of multiple scales opens the way to eliminating them. 相似文献
11.
The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton–Maclaurin expansion. Several basic theorems on the renormalization method are proven. Some interesting applications are given, including asymptotic solutions of quantum anharmonic oscillator and discrete boundary layer, the reductions and invariant manifolds of some discrete dynamics systems. Furthermore, the homotopy renormalization method based on the Newton–Maclaurin expansion is proposed and applied to those difference equations including no a small parameter. In addition, some subtle problems on the renormalization method are discussed. 相似文献
12.
Susan N. Brown 《Applied Scientific Research》1968,19(1):111-119
Summary A further term is found in the asymptotic expansion suggested by Stewartson for the eigenvalues arising in perturbations about the Blasius solution. The method employed is that of matched asymptotic expansions, and good agreement is obtained with the numerical results of Libby. 相似文献
13.
The pth moment Lyapunov exponent of a two-codimension bifurcation system excited parametrically by a real noise is investigated. By a linear stochastic transformation, the differential operator of the system is obtained. In order to evaluate the asymptotic expansion of the moment Lyapunov exponent, via a perturbation method, a ralevant eigenvalue problem is obtained. The eigenvalue problem is then solved by a Fourier cosine series expansion, and an infinite matrix is thus obtained, whose leading eigenvalue is the second-order of the asymptotic expansion of the moment Lyapunov exponent. Finally, the convergence of procedure is numerically illustrated, and the effects of the system and the noise parameters on the moment Lyapunov exponent are discussed. 相似文献
14.
In this paper, problems of buckling of an annular thin plate under the action of in-plane pressure and transverse load are studied by using the method of multiple scales. We obtain N-order uniformly valid asymptotic expansion of the solution. In the latter part of this paper we discuss a particular example, and calculate the critical value of in-plane pressure. We see that the asymptotic expansion obtained by the multiple scales is completely consistent with that of the exact solution. 相似文献
15.
A single asymptotic derivation of three classical nonlinear plate theories is presented in a setting which preserves the frame-invariance properties of three-dimensional finite elasticity. By a successive scaling of the external loading on the three-dimensional body, the nonlinear membrane theory, the nonlinear inextensional theory and the von Kármán equations are derived as the leading-order terms in the asymptotic expansion of finite elasticity. The governing equations of the nonlinear inextensional theory are of particular interest where 1) plane-strain kinematics and plane-stress constitutive equations are derived simultaneously from the asymptotic analysis, 2) the theory can be phrased as a minimization problem over the space of isometric deformations of a surface, and 3) the local equilibrium equations are identical to those arising in the one-director Cosserat shell model. Furthermore, it can be concluded that with a regular, single-scale asymptotic expansion it is not possible to obtain a system of plate equations in which finite membrane strain and finite bending strain occur simultaneously in the leading-order term of an asymptotic analysis. 相似文献
16.
This paper provides an asymptotic expansion for the mean integrated squared error (MISE) of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators. However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent. 相似文献
17.
《International Journal of Solids and Structures》2003,40(9):2057-2068
Shear horizontal waves, in the form of transient perturbations, are considered at the interface between two different viscoelastic solids. The admissibility of these interfacial waves is studied via the asymptotic expansion of the Laplace transform of the viscoelastic kernel. The compatibility condition is reduced to a set of algebraic systems which can be solved iteratively to the desired order in the asymptotic expansion. Two classes of solutions are found which correspond to transient waves decaying away from the interface and attenuated along the propagation direction. Numerical examples are given to illustrate the results. 相似文献
18.
L. I. Karandjulov 《Nonlinear Oscillations》2008,11(1):44-54
We construct an asymptotic expansion of a solution for singularly perturbed linear systems of ordinary differential equations
of the Noether type in the critical case. We successively determine all terms of the asymptotic expansion by the method of
boundary functions and pseudoinverse matrices.
__________
Translated from Neliniini Kolyvannya, Vol. 11, No. 1, pp. 45–54, January–March, 2007. 相似文献
19.
L. I. Karandjulov 《Nonlinear Oscillations》2004,7(2):154-167
For linear singularly perturbed systems of ordinary differential equations, we construct an asymptotic expansion of a solution by using the method of boundary functions. Using pseudoinverse matrices and projections, we find all terms of the asymptotic expansion in the noncritical case.Translated from Neliniini Kolyvannya, Vol. 7, No. 2, pp. 155–168, April–June, 2004. 相似文献
20.
本文对两种硬化指数的弹塑性材料界面裂纹尖端场进行了分析。通过对渐近场的计算,讨论了尖端场位移匹配问题和一阶静水压力场的存在,使应力解更加完备。 相似文献