共查询到20条相似文献,搜索用时 15 毫秒
1.
S. S. P. Shen 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(1):122-138
Critical long surface waves forced by locally distributed external pressure applied on the free surface in channels of arbitrary cross section are studied in this paper. The fluid under consideration is inviscid and has constant density. The upstream flow is uniform and the upstream velocity is assumed to be near critical, i.e.,u
0=u
c
++0(2), where 0<1 andu
c
is the critical velocity determined by the geometry of the channel. The external pressure applied on the free surface as the forcing is
2
P(x). Then the first order perturbation of the free surface elevation satisfies a forced Korteweg-de Vries equation (fK-dV). It is shown in this paper that: (i) If
(supercritical), the stationaryfK-dV has two cusped solitary wave solutions; (ii) if
(subcritical), the stationaryfK-dV has a downstream cnoidal wave solution; (iii) when=
L
, the unique stationary solution of thefK-dV is a wave free hydraulic fall; (iv) if=
d
=–
L
, thefK-dV has a jump solution; and (v) if
L
<<
c
, thefK-dV does not have stationary solutions. Some free surface profiles and bifurcation diagrams are presented. 相似文献
2.
3.
A high-order accurate method is proposed for analyzing the isothermal rarefied gas flow in an infinitely long channel with an arbitrarily shaped cross section (Poiseuille flow). The basic idea behind the method is the use of hybrid unstructured meshes in physical space and the application of a conservative technique for computing the gas velocity. Examples of calculations are provided for channels of various cross sections in a wide range of Knudsen numbers. Schemes of the first-, second-, and third orders of accuracy in space are compared. 相似文献
4.
Translated from Issledovaniya po Prikladnoi Matematike, No. 17, pp. 27–46, 1990. 相似文献
5.
V. M. Babich 《Journal of Mathematical Sciences》1985,30(5):2373-2378
An asymptotic approach to the theory of the skin-effect is developed. An important part in the construction of the asymptotics is the pasting of the asymptotic expansions. The determination of the asymptotic expression for the electromagnetic field and the current density reduces to the solving of a sequence of Dirichlet problems.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 128, pp. 13–20, 1983.In conclusion, I consider a pleasant obligation to express my gratitude to A. M. Il'in for useful consultations. 相似文献
6.
S. B. Raevskii A. A. Titarenko 《Computational Mathematics and Mathematical Physics》2009,49(12):2103-2116
A method is proposed for solving the boundary value problem of electromagnetic waves propagating in an open dielectric waveguide
with an arbitrary cross section. The method combines the representation of solutions in the form of a continuous spectrum,
the Fourier integral method, and the Galerkin variational procedure. 相似文献
7.
A variational formulation of the vertically-integrated differential equations for free surface wave motion is presented. A finite element model is derived for solving this nonlinear system of hydrodynamic equations. The time integration scheme employed is discussed and the results obtained demonstrate its good stability and accuracy.Several applications of the model are considered: the first problem is an open channel of uniform depth and the second an open channel of linearly varying depth. The ‘inflow’ boundary condition is prescribed in terms of the velocity which represents a wavemaker and/or a flow source, while the ‘outflow’ boundary condition is specified in terms of the water elevation. The outflow condition is adjusted for two cases, a reflecting boundary (finite channel) and a non-reflecting boundary (open-ended channel). The latter boundary condition is examined in some detail and the results obtained show that the numerical model can produce the non-reflecting boundary that is similar to the analytical radiation condition for waves. Computational results for a third problem, involving wave reflection from a submerged cylinder, are also presented and compared with both experimental data and analytical predictions.The simplicity and the performance of the computational model suggest that free surface waves can be simulated without excessively complicated numerical schemes. The ability of the model to simulate outflow boundary conditions properly is of special importance since these conditions present serious problems for many numerical algorithms. 相似文献
8.
I. A. Molotkov 《Journal of Mathematical Sciences》1978,9(4):570-576
A curved waveguide of variable thickness filled with an inhomogeneous medium is considered. Shortwave asymptotic equations are obtained which describe the waveguide modes near the critical cross section. The amplitudes of waves reflected from the critical cross section and also of waves filtering through the postcritical section of the waveguide are obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 181–188, 1974. 相似文献
9.
Yu. N. Podil'chuk Yu. K. Rubtsov P. N. Soroka 《Journal of Mathematical Sciences》1995,74(4):1124-1128
We describe an approach to the solution of problems of reflection of harmonic elastic waves from a convex indrical cavity
of arbitrary section, on the basis of Debye ray, series. We obtain a system of linear algebraic equations to determine the
constants of integration and expressions for determining the stresses in the elastic medium surrounding the convex cylindrical
cavity. We give the results of computation of the stresses that arise as a result of the action of a planar harmonic rarefaction
wave on a cylindrical cavity in the shape of elliptic and parabolic cylinders and on a cylindrical cavity whose section is
a Munger oval. Four figures. Bibliography: 7 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 10–16, 1991. 相似文献
10.
The propagation of nonstationary normal waves in a thin waveguide with variable properties along its course is considered. Along space-time rays the eikonal and transport equations are integrated, and asymptotic formulas for these waves are obtained. It is observed that for some types of initial data the effect of overturning of a wave packet of a normal wave is possible.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 89, pp. 210–218, 1979. 相似文献
11.
This article studies the evolutionary problem for linear gravity waves on the surface of water in a uniform, symmetric channel which is excited by an antisymmetric pressure force of frequency ω at the free surface. It is shown that there is a countably infinite set of frequencies {ω0, ω1, …} which give rise to resonance phenomena: the amplitude of the wave motion grows like t1/2 as t→∞ in a sense which is precisely specified. Under pressure forcing at any other frequency the solution obeys the principle of limiting amplitude. These results are obtained by combining methods developed for problems in acoustic waveguides with regularity theory for elliptic boundary‐value problems in non‐smooth domains. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
12.
The diffraction of a plane longitudinal harmonic wave on a cavity with a smooth curvilinear cross section in a rectilinearly
orthotropic medium is solved by using small perturbations in the elastic moduli and introducing generalized wave potentials.
Results are presented from a numerical analysis of the dynamic stresses in the near diffraction field and at the boundary
of an elliptical cavity including variations in the relative incident wavelength, eccentricity of the cavity, and degree of
anisotropy of the medium.
Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 102–110, 1999. 相似文献
13.
D. V. Valovik 《Computational Mathematics and Mathematical Physics》2011,51(9):1622-1632
A boundary value problem for Maxwell’s equations describing propagation of TM waves in a nonlinear dielectric layer with arbitrary
nonlinearity is considered. The layer is located between two linear semi-infinite media. The problem is reduced to a nonlinear
boundary eigenvalue problem for a system of second-order nonlinear ordinary differential equations. A dispersion equation
for the eigenvalues of the problem (propagation constants) is derived. For a given nonlinearity function, the dispersion equation
can be studied both analytically and numerically. A sufficient condition for the existence of at least one eigenvalue is formulated. 相似文献
14.
15.
John M. Hong Cheng-Hsiung Hsu Bo-Chih Huang 《Journal of Differential Equations》2012,253(4):1088-1110
In this paper we study the existence and uniqueness of the generalized stationary waves for one-dimensional viscous isentropic compressible flows through a nozzle with discontinuous cross section. Following the geometric singular perturbation technique, we establish the existence and uniqueness of inviscid and viscous stationary waves for the regularized systems with mollified cross section. Then, the generalized inviscid stationary waves are classified for discontinuous and expanding or contracting nozzles by the limiting argument. Moreover, we obtain the generalized viscous stationary waves by using Helly?s selection principle. However, due to the choices of mollified cross section functions, there may exist multiple transonic standing shocks in the generalized stationary waves. A new entropy condition is imposed to select a unique admissible standing shock in generalized stationary wave. We show that, such admissible solution selected by the entropy condition, admits minimal total variation and has minimal enthalpy loss across the standing shock in the limiting process. 相似文献
16.
Numerical guided mode solutions of arbitrary cross sectional shaped waveguides are obtained using a finite difference (FD) technique. The standard FD scheme is appropriately modified to capture all discontinuities, due to the change of the refractive index, across the waveguides’ interfaces taking into account the shape of each interface at the same time. The method is applied to the vector Helmholtz equation formulated to describe the electric or magnetic fields in the waveguide (one field is retrieved from the other through Maxwell’s equations). Computational cost is kept to a minimum by exploiting sparse matrix algebra. The waveguides under study have arbitrary cross sectional shape and arbitrary refractive index profile. 相似文献
17.
Ranis N. Ibragimov Dmitry E. Pelinovsky 《Communications in Nonlinear Science & Numerical Simulation》2008,13(10):2104-2113
We consider existence of three-dimensional gravity waves traveling along a channel of variable depth. It is well known that the long-wave small-amplitude expansion for such waves results in the stationary Korteweg–de Vries equation, coefficients of which depend on the transverse topography of the channel. This equation has a single-humped solitary wave localized in the direction of the wave propagation. We show, however, that there exists an infinite set of resonant Fourier modes that travel at the same speed as the solitary wave does. This fact suggests that the solitary wave confined in a channel of variable depth is always surrounded by small-amplitude oscillatory disturbances in the far-field profile. 相似文献
18.
Erik Wahlén 《Journal of Differential Equations》2009,246(6):2468-691
19.
M. A. Maiskaya 《Mechanics of Composite Materials》1973,9(2):330-332
The author discusses the state of deformation of a packing ring of oval cross section. He suggests a method of calculating the elongations of the horizontal and vertical diameters of the oval from the results of an interpretation of photoelastic patterns with finite deformations. The calculated values agree with experimental measurements.Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 368–370, March–April, 1974. 相似文献
20.
V. I. Plis 《Journal of Applied Mathematics and Mechanics》1983,47(6):756-760
The Wiener-Hopf method is used to derive an exact solution of the problem of diffraction of Kelvin waves in a rotating channel containing a semi-infinite wall. A numerical analysis of the solution is carried out. The nature of the waves propagating in the channel is considered. 相似文献