共查询到20条相似文献,搜索用时 15 毫秒
1.
Everett Jones 《Journal of computational physics》1981,40(2):411-429
The Keller box method (“Numerical Solutions of Partial Differential Equations, Vol. 2” (B. Hubbard Ed.), pp. 327–350, Academic Press, New York, 1970) was applied to incompressible flow past a flat plate to demonstrate that the basic computation region must extend outward from the wall until the outer boundary conditions are effectively obtained. The Keller box method was modified to include an asymptotic outer solution for the case of the self-similar solution for compressible flow in a boundary layer. Initial application of the basic and modified Keller box methods to incompressible flow past a flat plate showed similar rates of convergence but smaller RMS error for the same basic range of the independent variable when the asymptotic outer solution is applied. Furthermore, extension of the solution beyond the range of the independent variable for the numerical solution using the resulting asymptotic solution produced RMS error at least as small as the RMS error on the range of the numerical solution. Also, when the asymptotic solution was applied, a smaller range of independent variables could be used in the numerical solution to obtain the same RMS error. Numerical results for compressible flow were qualitatively the same as for the case with the incompressible velocity profile except the rate of iterative convergence was slightly slower. Application of asymptotic outer solution for incompressible flow at a two dimensional stagnation point produced similar results with smaller relative improvements. For compressible flow with smaller favorable pressure gradients than the stagnation point and with adverse pressure gradients, significant improvements were again obtained. Examination of the errors associated with the asymptotic solution reveals that greatest success is obtained for flows with thicker boundary layers and shows that the boundary layer at a two dimensional stagnation point is too thin for small error in the asymptotic solution. Despite relatively large errors in the asymptotic solutions for boundary layer in strong favorable pressure gradients where the boundary layer is thin, the boundary layer solutions generally showed improvement in error and reduction in computation times. 相似文献
2.
A singularly perturbed reaction diffusion problem forthe nonlinear boundary condition with two parameters 下载免费PDF全文
A class of singularly perturbed initial boundary value
problems of reaction diffusion equations for the nonlinear boundary
condition with two parameters is considered. Under suitable
conditions, by using the theory of differential inequalities, the
existence and the asymptotic behaviour of the solution for the initial boundary
value problem are studied. The obtained solution indicates that
there are initial and boundary layers and the thickness of the
boundary layer is less than the thickness of the initial layer. 相似文献
3.
《Journal of Quantitative Spectroscopy & Radiative Transfer》1987,38(6):457-474
The integral form of the radiation transfer equation, with spherical symmetry for a non-isotropic, time-dependent, inhomogeneous, non-scattering medium is given for arbitrary initial and boundary conditions. The optical depth is generalized to an optical retardation and a separation parameter is introduced to separate boundary and initial conditions. The static solution is identical to the asymptotic form of the time-dependent solution. 相似文献
4.
5.
We consider the one-dimensional focusing nonlinear Schrödinger equation (NLS) with a delta potential and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin boundary conditions at the origin. We follow the method of Bikbaev and Tarasov which utilizes a Bäcklund transformation to extend the solution on the half-line to a solution of the NLS equation on the whole line. We study the asymptotic stability of the stationary 1-soliton solution of the equation under perturbation by applying the nonlinear steepest-descent method for Riemann?CHilbert problems introduced by Deift and Zhou. Our work strengthens, and extends, the earlier work on the problem by Holmer and Zworski. 相似文献
6.
Kristian Berland 《Superlattices and Microstructures》2011,50(4):411-418
A general, system-independent, formulation of the parabolic Schrödinger–Poisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptotic boundary conditions. The solution gives a simple relation between the band bending and sheet charge density at an interface. Approximative analytical expressions for the potential profile and wave function are developed based on properties of the exact solution. Specific tests of the validity of the assumptions leading to the general solution are made. The assumption of complete screening by the ground state is found be a limitation; however, the general solution provides a fair approximate account of the potential profile when the bulk is doped. The general solution is further used in a simple model for the potential profile of an AlN/GaN barrier structure. The result compares well with the solution of the full Schrödinger–Poisson equation. 相似文献
7.
U. M. Titulaer 《Journal of statistical physics》1984,37(5-6):589-607
We derive asymptotic series for the expansion coefficients of a function in terms of the Pagani functions, which occur in the boundary layer solutions of the Klein-Kramers equation. The results enable us to determine the density profile in the stationary solution of this equation near an absorbing wall from the numerically determined velocity distribution at the wall, with an accuracy of about 2%. We also obtain information about the analytic behavior of the density profile: this profile increases near the wall with the square root of the distance to the wall. Finally, the asymptotic analysis leads to an understanding of the slow convergence of variational approximations to the solution of the absorbing-wall problem and of the exponents that occur when one studies the variational approximations to various quantities of interest as functions of the number of terms in the variational ansatz. This is used to obtain a better variational estimate for the density at the wall. 相似文献
8.
For the implicit solution to the cubically nonlinear equation of the Riemann wave (a simple wave equation), its exact explicit
Fourier transform is obtained. The latter corresponds to the transformation of the initial sinusoidal profile until the discontinuity
formation and, beyond it, to the asymptotic behavior of the same profile at large distances. The significance of the given
solutions for the problems with cubic nonlinearity is identical to the significance of the well-known Fubini solution and
the limiting version of the Fay solution for conventional nonlinear acoustics. 相似文献
9.
The asymptotic behavior of the Cauchy problem for the wave equation with variable velocity and localized initial conditions on the line, semi-axis, and an infinite starlike graph is described. The solution consists of a short-wave and long-wave parts; the shortwave part moves along the characteristics, while the long-wave part satisfies the Goursat or Darboux problem. In the case of a star-like graph, the distribution of energy with respect to the edges is discussed; this distribution depends on the arrangement of the eigensubspaces of the unitary matrix that defines the boundary condition at the vertex of the star. 相似文献
10.
《Solid State Ionics》2006,177(1-2):53-58
The dynamic faradic properties of the lithium ion batteries are primarily determined by the process of lithium ion insertion into a porous electrode. In this paper, we present an analytical result of the intercalating process of Li/Li+ into a spherical particle of graphite or cobalt oxide immersed in a conductive electrolyte. Using the finite integral transform method, an exact solution to the concentration profile was obtained for arbitrary linear initial and boundary conditions. To avoid analytical difficulties with respect to the boundary conditions of second kind, the method of pseudo-steady-state is applied. The final solution uniformly converges, and can be used for accurate and fast dynamic modelling and simulation. 相似文献
11.
This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space
in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time
which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion
involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term.
This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl
equations within the boundary layer. The error term is written as a sum of first order Euler and Prandtl corrections plus
a further error term. The equation for the error term is weakly nonlinear; its linear part is the time dependent Stokes equation.
This error equation is solved by inversion of the Stokes equation, through expressing the solution as a
regular (Euler-like) part plus a boundary layer (Prandtl-like) part. The main technical tool in this analysis is the Abstract
Cauchy-Kowalewski Theorem.
Received: 5 September 1996 / Accepted: 14 July 1997 相似文献
12.
Gregory J. Galloway Kristin Schleich Donald M. Witt 《Communications in Mathematical Physics》2012,310(2):285-298
We use existence results for Jang’s equation and marginally outer trapped surfaces (MOTSs) in 2 + 1 gravity to obtain nonexistence
of geons in 2 + 1 gravity. In particular, our results show that any 2 + 1 initial data set, which obeys the dominant energy
condition with cosmological constant Λ ≥ 0 and which satisfies a mild asymptotic condition, must have trivial topology. Moreover,
any data set obeying these conditions cannot contain a MOTS. The asymptotic condition involves a cutoff at a finite boundary
at which a null mean convexity condition is assumed to hold; this null mean convexity condition is satisfied by all the standard
asymptotic boundary conditions. The results presented here strengthen various aspects of previous related results in the literature.
These results not only have implications for classical 2 + 1 gravity but also apply to quantum 2 + 1 gravity when formulated
using Witten’s solution space quantization. 相似文献
13.
Kawashima Shuichi Nishibata Shinya Zhu Peicheng 《Communications in Mathematical Physics》2003,240(3):483-500
We investigate the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for the compressible Navier–Stokes equation in a half space. The main concern is to analyze the phenomena that happens when the fluid blows out through the boundary. Thus, it is natural to consider the problem in the Eulerian coordinate. We have obtained the two results for this problem. The first result is concerning the existence of the stationary solution. We present the necessary and sufficient condition which ensures the existence of the stationary solution. Then it is shown that the stationary solution is time asymptotically stable if an initial perturbation is small in the suitable Sobolev space. The second result is proved by using an L2-energy method with the aid of the Poincaré type inequality.The second author's work was supported in part by Grant-in-Aid for Scientific Research (C)(2) 14540200 of the Ministry of Education, Culture, Sports, Science and Technology and the third author's work was supported by JSPS postdoctoral fellowship under P99217. 相似文献
14.
Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation 下载免费PDF全文
This paper considers a class of boundary value problems for the semilinear singularly perturbed fractional differential equation.Under the suitable conditions,first,the outer solution of the original problem is obtained;secondly,using the stretched variable and the composing expansion method the boundary layer is constructed;finally,using the theory of differential inequalities the asymptotic behaviour of solution for the problem is studied and the uniformly valid asymptotic estimation is discussed. 相似文献
15.
A modified theory of a boundary layer associated with a periodic capillary-gravitational motion on the free surface of an infinitely deep viscous liquid is proposed. The flow in the boundary layer is described in terms of a simplified (compared with the complete statement) model problem a solution to which correctly reflects the main features of an exact asymptotic solution: the rapid decay of the flow eddy part with depth of the liquid and insignificance of some terms appearing in the complete statement. The boundary layer thickness at which the discrepancy between the exact asymptotic solution and model solution is within a given margin is estimated. 相似文献
16.
J. Hristov 《The European physical journal. Special topics》2011,193(1):229-243
The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach
to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown
coefficients and the concept of penetration (boundary layer). The prescribed profile satisfies the boundary conditions imposed
by the boundary layer that allows its coefficients to be expressed through its depth as unique parameter. The integral approach
to the fractional subdiffusion equation suggests a replacement of the real distribution function by the approximate profile.
The solution was performed with Riemann-Liouville time-fractional derivative since the integral approach avoids the definition
of the initial value of the time-derivative required by the Laplace transformed equations and leading to a transition to Caputo
derivatives. The method is demonstrated by solutions to two simple fractional subdiffusion equations (Dirichlet problems):
1) Time-Fractional Diffusion Equation, and 2) Time-Fractional Drift Equation, both of them having fundamental solutions expressed
through the M-Wright function. The solutions demonstrate some basic issues of the suggested integral approach, among them:
a) Choice of the profile, b) Integration problem emerging when the distribution (profile) is replaced by a prescribed one
with unknown coefficients; c) Optimization of the profile in view to minimize the average error of approximations; d) Numerical
results allowing comparisons to the known solutions expressed to the M-Wright function and error estimations. 相似文献
17.
A. E. Choque Rivero Yu. I. Karlovich A. E. Merzon P. N. Zhevandrov 《Russian Journal of Mathematical Physics》2012,19(3):373-384
We make more precise the Limiting Amplitude Principle in the two-dimensional scattering of an incident plane harmonic wave by a wedge. We find the long-time asymptotic regime of convergence of the amplitude of the cylindrical wave diffracted by the vertex of a wedge to the limiting amplitude of the solution to the corresponding stationary problem. The asymptotics turns out to be uniform on compacta and depends on the magnitude of the wedge and the profile of the incident wave. The cases of Dirichlet-Dirichlet and Dirichlet-Neumann boundary conditions are considered. 相似文献
18.
Tai-Ping Liu 《Communications in Mathematical Physics》1977,55(2):163-177
We study the asymptotic behavior of the solution of the initial and initial-boundary value problem of hyperbolic conservation laws when the initial and boundary data have bounded total variation. It is shown that the solution converges to the linear superposition of traveling waves, shock waves and rarefaction waves. The strength and speed of these waves depend only on the values of the data at infinity.Results obtained at the Courant Institute of Mathematical Sciences, New York University while the author was a Visiting Member at the Institute; this work was supported by the National Science Foundation, Grant NSF-MCS 76-07039On leave from the University of Maryland, College Park, USA 相似文献
19.
We discuss the asymptotic behavior of certain models of dissipative systems obtained from a suitable modification of Kac caricature of a Maxwellian gas. It is shown that global equilibria different from concentration are possible if the energy is not finite. These equilibria are distributed like stable laws, and attract initial densities which belong to the normal domain of attraction. If the initial density is assumed of finite energy, with higher moments bounded, it is shown that the solution converges for large-time to a profile with power law tails. These tails are heavily dependent of the collision rule. 相似文献
20.
《Combustion Theory and Modelling》2013,17(3):259-270
We study the rigorous asymptotic stability of a Chapman - Jouguet (CJ) detonation wave in the limit of small resolved heat release (SRHR). We show that the solution exists globally and that the solution converges uniformly to a shifted CJ detonation wave as t + for initial data which are small perturbations of the CJ detonation wave. A CJ detonation wave is characterized by the property that the speed at the end of it is sonic. A similar phenomenon occurs for a shock profile when the flux function is nonconvex. We use the weighted energy method to overcome the difficulty. The proper choice of the weight cancels the degenerate property of the CJ detonation at the tail. The nonmonotonic part, or the expansive part, of the profile caused by the chemical reaction is treated by the characteristic energy estimate under the assumption of SRHR. 相似文献