应用数学和力学

1994 Vol. 15, No. 8

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Numerical Modeling of the lnitial Stage of the Generation of Unsteady Vortices from Sharp Corner in Plane Compressible Flow

Huang Dun, Yang Chun

1994, 15(8): 665-670.

Abstract(2381) PDF(522)

Abstract:
The impingement of a plane shock wave in air on a rectangular or triangular obstacle is simulated numerically with high resolution TVD(total variation diminishing) scheme in finite volume formulation with Schwarz transformation in mesh generation. The mesh lines are quite adaptive to the physical features of the unsteady flow field and concentrate locally near the corners. At the initial stage the flow field is complex, and the scale of viscous diffusion is verr small and the viscosity of fluid in computation may be neglected. The unsteadr generation of concerntrated vortices downstream of the sharp corner as the result of the nonnuiformity of both temperature and entropy fields in ptane.hzviscid compressible fluid, induced by bow shock wave. is shown clearly and in accordance with optical measurements, performed by our request.

On the Partially Ordered Methods in the Study of lmplicit Variational lnequalities

Zhang Shi-sheng, Rao Ling

1994, 15(8): 671-678.

Abstract(1913) PDF(474)

Abstract:
By using the partially ordered methods, the existence problem of solutions for more general implicit variational inequalities of mo,lotone type in Hausdorff topological linear spaces are considered. As application we utilize the results presented in this paper to study the existence of solutions for Nash equilibrium problem and the semi-linear elliptic differential equations.

Singularly Perturbed Methods in the Theory of Optimal Control of Systems Governed by Partial Differential Equations

Tian Gen-bao, Lin Zong-chi

1994, 15(8): 679-684.

Abstract(2169) PDF(485)

Abstract:
In this paper, the various problems associated with the optimal control of srstems governed by partial differential equations are introduced by using singular.ly perturbed methods for analysis based on state equations, or the cost function and also state equations defined in perturbed domains.

Coincidence point Theorems in Probabilistic Metric Spaces with a Convex Structures

Wee Tae Park, Keun Saeng Park, Yeol Je Cho, Jong Kyu Kim

1994, 15(8): 685-697.

Abstract(2365) PDF(626)

Abstract:
In this paper we draw some coincidence and common fixed point theorems for nonlinear hybrid contraction mappings on probabilistic metric spaces with a convex structure.

The High Precision Open Boundary Conditions Designed for Transient Waves

Zou Guang-yuan

1994, 15(8): 699-707.

Abstract(1738) PDF(495)

Abstract:
In Refs. [2-4] there is an Adaptive Open Boundary Condition(AOBC) designed.for transient waves which overcomes the limitation of the existing Open Boundary Condition(OBC) and can be used for the cases of waves with arbitrary incident angles. In this article a new family of high or,der AOBC has been designed on the basis of the above mentioned AOBC with the first order. In comparison with all other OBC with the same order, this new family of AOBC has the highest precision.

The Re-Examination of Determining the Coefficient of the Amplitude Evolution Equation in the Nonlinear Theory of the Hydrodynamic Stability

Luo Ji-sheng

1994, 15(8): 709-712.

Abstract(1830) PDF(423)

Abstract:
One of the key problems in the nonlinear theory qf the hydrodynamic stability is to determine the law of the evolution of the disturbance velocity amplitude. The methods, which have been obtained, can only be used for quasi-neutral flow and have some artificial factors. In this paper, a method is proposed for this problem.

Finite Element Analysis for the Unsteady Nearshore Circulation Due to Wave-Current Interaction(Ⅰ)──Nnmerical Model

Wu Wei-xiong

1994, 15(8): 713-718.

Abstract(1638) PDF(517)

Abstract:
In this paper, a numerical model for predicting the unsteady nearshore circulation due to wave-current interaction was proposed. In addition to the traditional continuity, momentum and energy equations, the dispersion and refraction relations were included in the governing equations. Moreover, the effects of lateral shears, wind, radiation and bottom stresses were analysed in the governing equations. Therefore, we expect that this model may more completely and exactly reflect the law of wave-current interaction.In part(Ⅱ) we will adopt the.selective lumping two-step explicit finite element method to solve the model, and some examples will be presented.

Integral Invariants of a Holonomic Dynamical System Naseer Ahmed

Naseer Ahmed

1994, 15(8): 719-727.

Abstract(2061) PDF(466)

Abstract:
This paper uses Poincare's formalism to study the integral invariants of a conservative holonomic dynamical system. Introducing new parameters for the asrnchronous variation, a generalization of the Poincare and Poincaré-Cartan integral invariants is presented.

Numerical Studies for a Model Describing Complexity

Huang Xin, Liu Zeng-rong

1994, 15(8): 729-732.

Abstract(2122) PDF(458)

Abstract:
A simple model based on the discussion for infinite dimensional system is introduced to investigate the dynamical complexity for continuous system. By using immerical, methods, we show the dynamical behaviors of the model appear to correspond to universal language and context-sensitive language.

The Libration Points in Photogravltational Restricted Three-Body Problem

Zheng Xue-tang, Yu Li-zhong, Qin Yi-ping

1994, 15(8): 733-739.

Abstract(2128) PDF(479)

Abstract:
The photogravitational restricted three-body problem in which the mass reduction factors of two primaries q₁, q₂ [-∞, 1] are studied and an analytic method to estimate the number of libration points and to calculate their location is given in this paper. The results show that in photogravitational restricted three-body problem, the number of libration points is from one to seven for different q₁ and q₂. As application, the motion of dust grain like comet tail in the solar system is also discussed.