应用数学和力学

2002 Vol. 23, No. 6

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Element Functions of Discrete Operator Difference Method

TIAN Zhong-xu, TANG Li-min, LIU Zheng-xing

2002, 23(6): 551-557.

Abstract(2172) PDF(720)

Abstract:
The discrete scheme called discrete operator difference for differential equations was given.Several difference elements for plate bending problems and plane problems were given.By investigating these elements,the ability of the discrete forms expressing to the element functions was talked about.In discrete operator difference method,the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not.According to this point,discrete operator difference method is a method with good performance.

A Note on Delta-Perturbation Expansion Method

HE Ji-huan

2002, 23(6): 558-562.

Abstract(2296) PDF(844)

Abstract:
The Delta-perturbation expansion method,a kind of new perturbation technique depending upon an artificial parameter Delta was studied.The study reveals that the method exits some advantages,but also exits some limitations.To overcome the limitations,the so-called linearized perturbation method proposed by HE Ji-huan can be powerfully applied.

Dynamic Production Prediction and Parameter Identification for Gas Well With Vertical Fracture

GUO Da-li, LIU Ci-qun, ZHAO Jin-zhou

2002, 23(6): 563-568.

Abstract(2025) PDF(802)

Abstract:
In order to devoid the hard work and factitious error in selecting charts while analyzing and interpreting hydraulic fracturing fracture parameters,on the basis of the non-Darcy flow factor,this paper put out the non-Darcy flow mathematical model of real gas in the formation and fracture,established the prodution history automatic matching model to identify fracture parameters,and offered the numerical solutions of those models,which took the variation of fracture conductivity in production process.These results offered a precise and reliable method to understand formation,analyze and evaluate the fracturing treatment quality of gas well.

Solution of the Rayleigh Problem for a Power-Law Non-Newtonian Conducting Fluid via Group Method

Mina B. Abd-el-Malek, Nagwa A. Badran, Hossam S. Hassan

2002, 23(6): 569-575.

Abstract(2360) PDF(629)

Abstract:
An investigation is made of the magnetic Rayleigh problem where a semi-infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non-Newtonian power law fluid of infinite extent.The solution of this highly non-linear problem is obtained by means of the transformation group theoretic approach.The one-parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions.Effect of the some parameters on the velocity u(y,t) has been studied and the results are plotted.

Mathematical Modeling of Near-Wall Flows of Two-Phase Mixture With Evaporating Droplets

WANG Bo-yi, A. N. Osiptsov

2002, 23(6): 576-582.

Abstract(1860) PDF(516)

Abstract:
In the framework of the two-continuum approach,using the matched asymptotic expansion method,the equations of a laminar boundary layer in mist flows with evaporating droplets were derived and solved.The similarity criteria controlling the mist flows were determined.For the flow along a curvilinear surface,the forms of the boundary layer equations differ from the regimes of presence and absence of the droplet inertia deposition.The numerical results were presented for the vapor-droplet boundary layer in the neighborhood of a stagnation point of a hot blunt body.It is demonstrated that,due to evaporation,a droplet-free region develops near the wall inside the boundary layer.On the upper edge of this region,the droplet radius tends to zero and the droplet number density becomes much higher than that in the free stream.The combined effect of the droplet evaporation and accumulation results in a significant enhancement of the heat transfer on the surface even for small mass concentration of the droplets in the free stream.

Research of Regularity of Throwing Movement for Solid Particle on the Shaker’s Screen

YAO Heng-shen, DU Jian, ZHANG Ming-hong

2002, 23(6): 583-587.

Abstract(2422) PDF(605)

Abstract:
By means of Delta-function&unit step function to express the force of solid particle on plane inertial shakers screen,a mathematics model of the differential equation type was set up and solved.According to analysis of the solution,the relation is given between the throw period&displacement with the parameters of shaker design&solid particle.The method of numerical value calculation&analysis for the relation is given too.

Nonlinear Evolution Analysis of T-S Disturbance Wave at Finite Amplitude in Nonparallel Boundary Layers

TANG Deng-bin, XIA Hao

2002, 23(6): 588-596.

Abstract(2058) PDF(578)

Abstract:
The nonlinear evolution problem in nonparallel boundary layer stability was studied.The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived.The developed numerical method,which is very effective,was used to study the nonlinear evolution of T-S disturbance wave at finite amplitudes.Solving nonlinear equations of different modes by using predictor-corrector and iterative approach,which is uncoupled between modes,improving computational accuracy by using high order compact differential scheme,satisfying normalization condition,determining tables of nonlinear terms at different modes,and implementing stably the spatial marching, were included in this method.With different initial amplitudes,the nonlinear evolution of T-S wave was studied.The nonlinear nonparallel results of examples compare with data of direct numerical simulations(DNS)using full Navier-Stokes equations.

Third Order Nonlinear Singularly Perturbed Boundary Value Problem

WANG Guo-can, JIN Li

2002, 23(6): 597-603.

Abstract(1904) PDF(847)

Abstract:
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied.Based on the given results of second order nonlinear boundary value problem,the upper and lower solutions method of third order nonlinear boundary value problems by making use of volterra type integral operat or was established.Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem.An example is given to demonstrate the applications.

Oscillatory Properties of the Solutions of Nonlinear Delay Hyperbolic Differential Equations of Neutral Type

LIU An-ping, HE Meng-xing

2002, 23(6): 604-610.

Abstract(2030) PDF(767)

Abstract:
By making use of the integral inequalities and some results of the functional differential equations,oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations of neutral type with multi-delays were investigated and a series of sufficient conditions for oscillations of the equations were established.The results fully indicate that the oscillations are caused by delay and hence reveal the difference between these equations and those equations without delay.

Ishikawa Iterative Process for Constructing Solutions of m-Accretive Operator Equations

ZENG Liu-chuan

2002, 23(6): 611-618.

Abstract(2044) PDF(779)

Abstract:
The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized.Moreover,the error estimates of approximate solutions for locally Lipschitzian and m-accretive operator equations are established.

Theoretical Analysis of Using Airflow to Purge Residual Water in an Inclined Pipe

SHEN Fang, YAN Zong-yi, ZHAO Yao-hua, Kiyoshi Horii

2002, 23(6): 619-626.

Abstract(2207) PDF(748)

Abstract:
A refined theoretical analysis for using the spiral airflow and axial airflow to purge residual water in an inclined pipe was presented.The computations reveal that,in most cases,the spiral flow can purge the residual water in the inclined pipe indeed while the axial flow may induce back flow of the water,just as predicted in the experiments presented by Horii and Zhao et al.In addition,the effects of various initial conditions on water purging were studied in detail for both the spiral and axial flow cases.

Double Method of Characteristics to Analyze Hydraulic-Thermal Transients of Pipeline Flow

DENG Song-sheng, ZHOU Ming-lai, PU Jia-ning

2002, 23(6): 627-634.

Abstract(2060) PDF(668)

Abstract:
The hydraulic and thermal transients in pipeline flow were studied.The method of characteristics for hydraulic transient analysis of batch transport of pipeline flow had been improved.The thermal transient equation,in which the term with v³ was involved,had been inferred,while the corresponding method of characteristics was constructed.The double method of characteristics,which can be used to study the coherent hydraulic-thermal transients of batch transport of pipeline flow,was developed.

Sensitivity of Single-Phase Flow in Low-Permeability Heterogeneous Reservoirs

CHENG Shi-qing, ZHANG Shen-zhong, HUANG Yan-zhang, ZHU Wei-yao

2002, 23(6): 635-642.

Abstract(2146) PDF(623)

Abstract:
Theoretical equations for computing sensitivity coefficients of wellbore pressures to estimate the reservoir parameters in low-permeability reservoirs conditioning to non-Darcy flow data at low velocity were obtained.It is shown by a lot of numerical calculations that the wellbore pressures are much more sensitive to permeability very near the well than to permeability a few gridboocks away from the well.When an initial pressure gradient existant sensitivity coefficents in the region are closer to the active well than to the observation well.Sensitivity coefficients of observation well at the line between the active well and the observation well are influenced greatly by the initial pressure gradient.

Nonlinear Analysis of a Cracked Rotor With Whirling

LI Xiao-feng XU Ping-yong, SHI Tie-lin, YANG Shu-zi

2002, 23(6): 643-652.

Abstract(2054) PDF(579)

Abstract:
Nonlinear dynamics of a cracked rotor with whirling were analyzed and were compared to a rotor without whirling.Distinct differences have been found in bifurcation,amplitude,orbit and Poincare map when carrying on this comparison.Complicated dynamics may be found when a cracked rotor has its whirling speed.The results revealed may be useful in crack-early-detection and diagnosis.

A Posteriori Error Estimate of the DSD Method for First-Order Hyperbolic Equations

KANG Tong, YU De-hao

2002, 23(6): 653-660.

Abstract(2134) PDF(592)

Abstract:
A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented,which can be used to adjust space mesh reasonably.A numerical example is given to illustrate the accuracy and feasibility of this method.