共查询到20条相似文献,搜索用时 22 毫秒
1.
The propagation of a long wave in a three-dimensional curved duct with variable cross section is studied in this paper. It is shown that a three-dimensional Helmholtz equation can be decomposed into a two-dimensional Laplace (or Poisson) equation and a one-dimensional Webster equation by the curvilinear orthogonal coordinate system, non-dimensionization of reduced wave equation and regular perturbation with small parameterka, wherek is the wave number anda is the characteristic radius of the duct. The influences of the duct's geometric parameters (the area variation of the cross section, the curvature and torsion of the central line) on the asymptotic expansion of the solution are analysed. It is concluded that the effects of the variation of the cross sectional area first appear in the first term of the asymptotic expansion, and when the cross section shape has certain symmetric properties, the effects of the curvature and torsion of the central line first appear in the third and the fourth terms, respectively. An example of long wave propagation in a curved circular duct is also given at the end of this paper. 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.
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
4.
轴对称正交异性圆环壳的齐次完全渐近解 总被引:1,自引:0,他引:1
承受轴对称载荷的正交异性圆环壳的静力分析,归结为求解一非齐次二阶复变量方程.当所含参数μ较大时,常采用渐近解法.因方程含一阶转点,所以求全域一致有效且达到薄壳理论精度的完全渐近解较为困难.过去,齐次解只求到一级近似.本文采用广义Airy函数方法,求出了高级近似.这样,轴对称正交异性圆环壳的齐次解第一次有了达到薄壳理论精度的完全的渐近展开. 相似文献
5.
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
6.
各向异性平板开孔动应力集中问题的研究 总被引:2,自引:0,他引:2
采用各向异性平板弯曲波动理论及摄动方法,对正交各向异性平板开孔弯曲波的散射及动应力集中问题进行了分析研究,得到了此种平板稳态弯曲波动问题的渐近形式的分析解。同时采用保角映射技术,为求解正交各向异性平板开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。 相似文献
7.
8.
A Conservative Difference Scheme for Conservative Differential Equation with Periodic Boundary 总被引:3,自引:0,他引:3
蔡新 《应用数学和力学(英文版)》2001,22(10):1210-1215
1 DifferentialEquationandDifferentiabilityPropertiesoftheSolutionInthispaper,weconsidertheconservativeformandsingularperturbedordinarydifferentialequationwithperiodicboundaryvalueproblem :Lu(x) ≡ε(p(x)u′(x) )′ (q(x)u(x) )′-r(x)u(x) =f(x) ( 0 <x<1 ) ,( 1 )u( 0 ) ≡u( 1 ) ,lu≡u′( 1 )… 相似文献
9.
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
10.
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
11.
A class of boundary value problems for a third-order differential equation with a turning point is considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for the boundary value problem is constructed. 相似文献
12.
In this paper, an asymptotic expansion solution of the constitutive equation of hardening materials is presented. Its 1st asymptotic integration can give an approximate one with good enough accuracy and the second asymptotic one improves the precision of solutions further. The steps of its algorithms are fairly simple and clear, and its computational workload is considerably reduced. It can be easily incorporated into a general purpose finite element program.The Chinese original of this article was published in the Chinese edition ofActa Mechanica Solida Sinica, No. 1, 1986. 相似文献
13.
D. Leguillon 《International Journal of Solids and Structures》2011,48(6):884-892
Determination of the length of a short crack at the root of a v-notch, from a full kinematic field measurement, is performed using a direct method. It is based on a matched asymptotic expansions procedure together with the theory of singularities. The first corrective term of the outer expansion can be straightforwardly expressed as a function of the crack length. Its extraction is achieved through the calculation of the associated generalized stress intensity factors for elastic homogeneous materials as well as bimaterials. Numerical simulations are carried out on a finite element solution disturbed by a random noise. In addition, the method used to compute the generalized stress intensity factors proved accurate and robust. 相似文献
14.
An asymptotic expansion of the solution of a nonhomogeneous matrix difference equation of general form is obtained. The case when there is no bound on the differences of the arguments is considered. The effect of the roots of the characteristic equation is taken into account. The asymptotic behavior of the remainder is established depending on the asymptotics of the free term of the equation.
相似文献15.
In this paper,we consider a singular perturbation elliptic-parabolic partial differentialequation for periodic boundary value problem,and construct a difference scheme.Using themethod of decomposing the singular term from its solution and combining an asymptoticexpansion of the equation,we prove that the scheme constructed by this paper convergesuniformly to the solution of its original problem with O(τ h~2). 相似文献
16.
《Particuology》2022
The particle number density in the Smoluchowski coagulation equation usually cannot be solved as a whole, and it can be decomposed into the following two functions by similarity transformation: one is a function of time (the particle k-th moments), and the other is a function of dimensionless volume (self-preserving size distribution). In this paper, a simple iterative direct numerical simulation (iDNS) is proposed to obtain the similarity solution of the Smoluchowski coagulation equation for Brownian motion from the asymptotic solution of the k-th order moment, which has been solved with the Taylor-series expansion method of moment (TEMOM) in our previous work. The convergence and accuracy of the numerical method are first verified by comparison with previous results about Brownian coagulation in the literature, and then the method is extended to the field of Brownian agglomeration over the entire size range. The results show that the difference between the lognormal function and the self-preserving size distribution is significant. Moreover, the thermodynamic constraint of the algebraic mean volume is also investigated. In short, the asymptotic solution of the TEMOM and the self-preserving size distribution form a one-to-one mapping relationship; thus, a complete method to solve the Smoluchowski coagulation equation asymptotically is established. 相似文献
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18.
By combining a perturbation technique with a rational approximation of vector-valued function, we propose a new approach to non-linear oscillations of conservative single-degree-of-freedom systems with odd non-linearity. The equation of motion does not require to contain a small parameter. First, the Lindstedt-Poincare perturbation method is used to obtain an asymptotic analytical solution. Then the range of validity of the analytical representation is extended by using the vector-valued rational approximation of functions. For constructing the rational approximations, all that is needed is the coefficients of the perturbation expansion being considered. General approximate formulas for period and the corresponding periodic solution of a non-linear system are established. Two examples are used to illustrate the effectiveness of the proposed method. 相似文献
19.
We consider the integral form of the radiative transfer equation over a large interval. This equation describes the radiative transfer of energy in a star. The asymptotic expansion of the solution is constructed and justified. The method of asymptotic partial decomposition of domain is applied. Numerical results are discussed. To cite this article: G. Panasenko et al., C. R. Mecanique 330 (2002) 735–740. 相似文献
20.
Solution of the plane stress problems of strain-hardening materials described by power-law using the complex pseudo-stress function 总被引:1,自引:0,他引:1
In the present paper,the compatibility equation for the plane stress problems of power-law materials is transformed into a biharmonic equation by introducing the so-calledcomplex pseudo-stress function,which makes it possible to solve the elastic-plastic planestress problems of strain hardening materials described by power-law using the complexvariable function method like that in the linear elasticity theory.By using this generalmethod,the close-formed analytical solutions for the stress,strain and displacementcomponents of the plane stress problems’of power-law materials is deduced in the paper,which can also be used to solve the elasto-plastic plane stress problems of strain-hardeningmaterials other than that described by power-law.As an example,the problem of a power-law material infinite plate containing a circular hole under uniaxial tension is solved byusing this method,the results of which are compared with those of a known asymptoticanalytical solution obtained by the perturbation method. 相似文献