关于定积分的演变与发展

积分的学习一直是高等数学中的重点和难点.本文通过对积分发展过程的介绍,使读者对这段历史有很明确的认识,尤其是积分的分割近似思想,这样可以进一步帮助读者理解积分的概念掌握积分的计算.

牛顿与莱布尼兹和他们的微积分评述

介绍牛顿和莱布尼兹的生平以及他们的研究成果,主要是关于微积分基本定理,即牛顿-莱布尼兹公式的来龙去脉,他们各自独立发明了微积分的过程和时间,让我们更加崇敬伟人们和他们的巨大贡献。

IMPROVED ALGORITHM FOR CFD/CSD COUPLED SYSTEM DESIGN AND CALCULATION

The data information transfer and time marching strategies between computational fluid dynamics （CFD） and computational structural dynamics （CSD） play crucial roles on the aeroelastic analysis in a time domain. An improved CFD/CSD coupled system is designed, including an interpolation method and an improved loosely coupled algorithm. The interpolation method based on boundary element method （BEM） is developed to transfer aerodynamic loads and structural displacements between CFD and CSD grid systems, it can be universally used in fluid structural interaction solution by keeping energy conservation. The improved loosely coupled algo-rithm is designed, thus it improves the computational accuracy and efficiency. The new interface is performed on the two-dimensional （2-D） extrapolation and the aeroelastie response of AGARD445.6 wing. Results show that the improved interface has a superior accuracy.

FLOW FIELD ANALYSES OF PLANE JET AT LOW REYNOLDS NUMBERS USING LATTICE BOLTZMANN METHOD

A two-dimensional（2-D） incompressible plane jet is investigated using the lattice Boltzmann method（LBM） for low Reynolds numbers of 42 and 65 based on the jet-exit-width and the maximum jet-exit-velocity. The results show that the mean centerline velocity decays as x-1/3 and the jet spreads as x2/3 in the self-similar region, which are consistent with the theoretical predictions and the experimental data. The time histories and PSD analyses of the instantaneous centerline velocities indicate the periodic behavior and the interaction between periodic components of velocities should not be neglected in the far field region, although it is invisible in the near field region.

Methods of Random Fatigue Design for Vehicle Transmission System Components

Some representative working conditions were measured, and the amplitude distribution rule of each representative working condition after analysis of measured data was got. The building of 2 D distributing function between the range and the mean of random load was discussed. Experiment was carried out to get the fatigue strength data of the material of transmission component. Accessing the P S a S m N camber of combined load of bending and torsion on this material after analysis. And the process of calculating the 2 D fatigue life in multi working condition was discussed.

Numerical modeling of the 2D time-domain transient electromagnetic secondary field of the line source of the current excitation

To effectively minimize the electromagnetic field response in the total field solution, we propose a numerical modeling method for the two-dimensional （2D） time- domain transient electromagnetic secondary field of the line source based on the DuFort- Frankel finite-difference method. In the proposed method, we included the treatment of the earth-air boundary conductivity, calculated the normalized partial derivative of the induced electromotive force （Emf）, and determined the forward time step. By extending upward the earth-air interface to the air grid nodes and the zero-value boundary conditions, not only we have a method that is more efficient but also simpler than the total field solution. We computed and analyzed the homogeneous half-space model and the fiat layered model with high precision--the maximum relative error is less than 0.01% between our method and the analytical method--and the solution speed is roughly three times faster than the total-field solution. Lastly, we used the model of a thin body embedded in a homogeneous half-space at different delay times to depict the downward and upward spreading characteristics of the induced eddy current, and the physical interaction processes between the electromagnetic field and the underground low-resistivity body.

Finite element numerical simulation of 2.5D direct current method based on mesh refinement and recoarsement

To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.

New numerical algorithm of gas-liquid two-phase flow considering characteristics of liquid metal during mold filling

A new program is developed for gas-liquid two-phase mold filling simulation in casting. The gas fluid, the superheated liquid metal and the liquid metal containing solid grains are assumed to be governed by Navier-Stokes equations and solved through Projection method. The Level set method is used to track the gas-liquid interface boundary. In order to demonstrate the correctness of this new program for simulation of gas-liquid two-phase mold filling in casting, a benchmark filling experiment is simulated （this benchmark test is designed by XU and the filling process is recorded by a 16-mm film camera）. The simulated results agree very well with the experimental results, showing that this new program can be used to properly predicate the gas-liquid two-phase mold filling simulation in casting.

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

To speed up three-dimensional （3D） DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method （AGMG）. We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner （AGMG-CG） to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling （3DDCXH）. In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

DC LOOP-CURRENT DETECTING AND RESTRAINING METHODS FOR PARALLEL INVERTER SYSTEM

DC component is contained in inverter output voltage due to many reasons such as the zero-point deviation of operational amplifiers and the differences between power switching transistors′ characteristics. For the parallel inverter system without output isolation transformers, the difference of DC components of the output voltage can cause large DC loop-current among modular inverters. Aiming at this problem, this paper studies several DC loop-current detecting and restraining methods. By digital adjustment with high precision on the DC components of reference sine wave, the DC components of inverter′s output voltage can be adjusted to restrain DC loop-current. Experimental results prove that the DC loop-current detecting and restraining methods have a good performance.

EFFECT OF WALL FUNC TION IN NUMERICAL STUDY ON TURBULENT IMPINGING JET

A low Reynolds number k-ε model is used in the numeri cal study on a circular semi-confined turbulent impinging jet . The result is c ompared with that of the standard k-ε model and a refined k-ε mode l, which re-consi-dered the fluctuating pressure diffusion term in the dissipa tion rate equation (ε-equation) through modeling. It shows that the low Re ynolds number k-ε model and the standard k-ε model yield very poor performance, while the predicting ability of the refined k-ε model is mu ch improved , especially for the turbulent kinetic energy k. So it can be co ncluded that the poor performance of the standard k-ε model is owing to t he incorrect considering the effect of the fluctuating pressure diffusion term r ather than the use of the wall function near the wall just as presumed in the re ference.

Filtering Method of Aero⁃engine Load Spectrum Based on Rain Flow Counting

A filtering method of aero-engine load spectrum based on the rain flow counting is proposed in this paper.Firstly,the original load spectrum is counted through the rain flow method to get the peak and valley values.Then,some data points in the original load spectrum are added between the peak and valley values.Finally,the filtering spectrum is obtained.The proposed method can reflect the path information of the original load spectrum.In addition,it can also eliminate the noise in the signal and improve the efficiency of signal processing,which is of practical significance for the research of aero-engine.

Fatigue Life Assessment of Top Tensioned Risers Under Vortex-Induced Vibrations

The fatigue life of top tensioned risers under vortex-induced vibrations (VIVs) with consideration of the effect of internal flowing fluid on the riser is analyzed in the time domain.The long-term stress histories of the riser under VIVs are calculated and the mean stresses,the number of stress cycles and amplitudes are determined by the rainflow counting method.The Palmgren-Miner rule for cumulative damage theory with a specified S-N curve is used to estimate the fatigue life of the riser.The corresponding numerical programs numerical simulation of vortex-induced vibrations (NSVIV) which can be used to calculate the VIV response and fatigue life of the riser are compiled.Finally the influences of the riser's parameters such as flexural rigidity,top tension and internal flow velocity on the fatigue life of the riser are analyzed in detail and some conclusions are drawn.

An analogy-based method for strong convection forecasts in China using GFS forecast data

This paper describes an analogue-based method for producing strong convection forecasts with conventional outputs from numerical models.The method takes advantage of the good performance of numerical models in predicting synoptic-scale weather situations.It calculates the convective parameters as predictors to detect the favorable-occurrence environment of strong convections.Times in the past when the forecast parameters are most similar to those forecast at the current time are identified by searching a large historical numerical dataset.The observed strong convection situations corresponding to those most similar times are then used to form strong convection forecasts for the current time.The method is applied as a postprocess of the NCEP Global Forecast System(GFS)model.The historical dataset in which the analogous situations are sought comprises two years of summer(June–September)GFS 6-to 48-h forecasts.The strong convection forecast is then generated every 6 h over most regions of China,provided the availability of strong convection observations.The results show that the method performs well in predicting strong convections in different regions of China.Through comparison with another postprocessing strong convection forecast method,it is shown that the convective-parameter threshold problem can be solved by employing the analogy method,which considers the local historical conditions of strong convection occurrence.

Determination of a Pore Structure Parameter of Porous Media by Analysis of Percolation Network Model

According to the simulation of nitrogen sorption process in porous media with three-dimensional network model, and the analysis for such a process with percolation theory, a new method is proposed to determine a pore structure parameter--mean coordination number of pore network, which represents the connectivity among a great number of pores. Here the 'chamber-throat' model and the Weibull distribution are used to describe the pore geometry and the pore size distribution respectively. This method is based on the scaling law of percolation theory after both effects of sorption thermodynamics and pore size on the sorption hysteresis loops are considered. The results show that it is an effective procedure to calculate the mean coordination number for micro- and meso-porous media.

TVD SCHEME WITH CHEMICAL REACTION FLOW AND ITS APPLICATION IN COMBUSTION GAS JETTING FLOW

By conjugating features of combustion gas jetting flows of the solid-rocket and using mathematical methods, a numerical scheme is systematically derived based on Harten′s standard TVD scheme, which fits for the flow with high temperature, pressure and velocity. The rational calculation formula of pressure partial derivation is also given out. By using the chemical kinetics knowledge, problems of multi-component and finite rate chemical reaction contained in combustion gas of the rocket flow field are discussed. The method for solving the mass source term of chemical reaction is clarified. Taking 9 reaction equations with 12 components as an example and utilizing the established calculation program, the free jetting flow field of the rocket is simulated. Numerical results show the correctness of the numerical scheme.

A generalized cover renewal strategy for multiple crack propagation in two-dimensional numerical manifold method

Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the topology of the two-cover system poses a challenge for multiple crack propagation problems and there are few references.In this study,a robust and efficient strategy is proposed to update the cover system of the numerical manifold method in simulation of multiple crack propagation problems.The proposed algorithm updates the cover system with a bottom-up process:1)identification of fractured manifold elements according to the previous and latest crack tip position;and 2)local topological update of the manifold elements,physical patches,block boundary loops,and non-persistent joint loops according to the scenario classification of the propagating crack.The proposed crack tracking strategy and classification of the renewal cases promote a robust and efficient cover renewal algorithm for multiple crack propagation analysis.Three crack propagation examples show that the proposed algorithm performs well in updating the cover system.This cover renewal methodology can be extended for numerical manifold method with polygonal mathematical covers.

A Numerical Method on Inverse Determination of Heat Transfer Coefficient Based on Thermographic Temperature Measurement

The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dimensional correction method （MODCM）, along with the finite volume method, is employed for both two- and three-dimensional inverse problems. A series of numerical experiments are conducted in order to verify the effectiveness of the method. In addition, the effect of the temperature measurement error, the ending criterion of the iteration, etc. on the result of the inverse problem is investigated. It is proved that the method is a simple, stable and accurate one that can solve successfully the inverse heat conduction problem.

Numerical Study of Steam-Water Separators with Wave-type Vanes

Droplet behavior in the wave-type flow channel is discussed, especially with the secondary .droplet generation due to impingement of droplets on the wall considered. A numerical method is suggested to simulate tile droplet behavior in the flow field. Calculations are compared With experimental data on the ; pressure drop and separating efficiency. Good agreement exists between the calculations and air-water experiments. The numerical method developed gives a reasonable description of the droplet deposition and secondary droplet generation, and it can be applied to predict the performance of wave-type vane separators.

Baseflow Characteristics in Alpine Rivers-a Multicatchment Analysis in Northwest China

As a component of streamflow, baseflow is critical for regulating seasonal distribution of river fows and stabilizing water supplies. Water resources in the arid area of Northwest China are mainly from multiple catchments in the alpine that could be influenced by varieties of climatic, land cover, soil and geological factors. While numerous studies have been done on streamflow, systematic analysis of baseflow in the alpine river systems is scare. Based on historical daily streamflow data and the automated digital filter method of baseflow separation, this study investigated characteristics of hydrographs of overland flow, streamflow and baseflowof river systems fed by rainfall, snowmelt, glacier melt or mixtures of these. This study also calculated the recession constants and baseflow indices of 65 river systems. While the recession constant was o.oo34- o.o728 with a mean of o.o18, the baseflow index was 0.27-0.79 with a mean of 0.57. Further, Spearman＇s correlation analysis showed that the baseflow index was significantly correlated with catchment climatic factors （e.g., precipitation and temperature）, topographic factors （e.g., elevation and slope） and aquifer properties represented by the recession constant. Multiple regression analysis indicated that the factors explained 65% of the variability of baseflow index in the studv area.