高阶Schrdinger型方程的两层高精度恒稳差分格式

众所周知,高阶Schro¨dinger方程在量子力学、非线性光学及流体力学中都有广泛的应用。本文对高阶Schro¨dinger型方程 u t=i(-1)m 2mu x2m(其中i=-1,m为正整数),利用待定系数法,构造出一个两层高精度的隐式差分格式。其截断误差阶为O((Δt)2+(Δx)6),比同类格式精度高2～4阶,并用Fourier分析法证明了它是绝对稳定的。最后,数值例子表明本文格式比著名的Crank-Nicolson格式精度高10-2～10-7,这说明我们的格式是有效的,理论分析与实际计算相吻合。     

高阶Schr(o)dinger型方程的两层高精度恒稳差分格式

众所周知, 高阶Schrodinger方程在量子力学、非线性光学及流体力学中都有广泛的应用.本文对高阶Schrodinger型方程(eu/et)＝I(-1)m(e2mu)/(ex2m)(其中I＝-1,m为正整数),利用待定系数法,构造出一个两层高精度的隐式差分格式.其截断误差阶为O((Δt)2+(Δx)6),比同类格式精度高2～4阶,并用Fourier分析法证明了它是绝对稳定的.最后,数值例子表明本文格式比著名的Crank-Nicolson格式精度高10-2～10-7,这说明我们的格式是有效的,理论分析与实际计算相吻合.     

污染扩散方程高精度紧致格式及其稳定性分析

针对污染扩散方程提出了时间任意阶精度的显式格式,并对该格式的稳定性和精度进行了分析,理论结果表明:一阶精度的计算格式是传统的显格式,其稳定条件为:s≤1/2(s=D.Δt/Δx2,D为扩散系数,Δt为时间步长,Δx为空间步长),随着保留精度阶数的增加,稳定性范围也会随之增大;当保留无穷阶精度时,格式是无条件稳定的。这也就从一个侧面揭示了稳定性与时间精度之间的关系,为高性能数值计算格式的构思提供了可以借鉴的原则。数值算例的结果表明,本文格式具有一定的实用性。     

基于HLL-HLLC的高阶WENO格式及其应用研究

HLL-HLLC格式能够克服HLLC在强激波附近的激波不稳定现象,并且保持了HLLC的低耗散特性,是一种适合更大马赫数范围的近似黎曼求解器。本文从RANS方程出发,将HLL-HLLC近似黎曼求解器结合五阶WENO重构,实现了对无粘通量的高阶离散;同时,采用完全守恒形式的四阶中心差分格式处理粘性项,建立了RANS 方程的高阶数值求解格式。通过对四个经典算例,钝头体、 ONERA M6机翼、DLR F6-WB翼身组合体和DLR F6-WBNP复杂外形的数值模拟,考察了两种WENO改进格式在复杂流场中的表现,研究了高阶格式的收敛特性;给出了在复杂流动中 WENO自由参数的推荐值,以增强求解的收敛性。算例结果表明,本文构造的高阶格式鲁棒性好,能够显著改善激波位置和激波强度,捕获更丰富的流场细节,满足复杂工程应用需求。     

基于HLL-HLLC的高阶WENO格式及其应用研究

HLL-HLLC格式能够克服HLLC在强激波附近的激波不稳定现象,并且保持了HLLC的低耗散特性,是一种适合更大马赫数范围的近似黎曼求解器。本文从RANS方程出发,将HLL-HLLC近似黎曼求解器结合五阶WENO重构,实现了对无粘通量的高阶离散;同时,采用完全守恒形式的四阶中心差分格式处理粘性项,建立了RANS方程的高阶数值求解格式。通过对四个经典算例,钝头体、ONERA M6机翼、DLR F6-WB翼身组合体和DLR F6-WBNP复杂外形的数值模拟,考察了两种WENO改进格式在复杂流场中的表现,研究了高阶格式的收敛特性;给出了在复杂流动中WENO自由参数的推荐值,以增强求解的收敛性。算例结果表明,本文构造的高阶格式鲁棒性好,能够显著改善激波位置和激波强度,捕获更丰富的流场细节,满足复杂工程应用需求。     

浅水方程组合型超紧致差分格式

提出一族组合型超紧致差分格式(CSCD),对CSCD的数值特性作了分析,并同其他中心型差分格式进行比较。从定性角度,得出同阶中心差分格式中,CSCD格式的截断误差系数最小的结论。从定量角度,利用Fou-rier分析方法分析了CSCD格式的分辨率,并同其他中心型差分格式比较,得出CSCD格式有较高的分辨率的结论。把10阶CSCD格式应用于KdV-Burgers方程和浅水方程的数值模拟,给出两个应用算例。数值实验表明CSCD格式不仅有理论上的高精度,而且有良好的稳定性和收敛性。     

数值摄动算法及其CFD格式

作者提出的数值摄动算法把流体动力学效应耦合进NS方程组和对流扩散（CD）方程离散的数学基本格式（MBS）,特别是耦合进最简单的MBS即一阶迎风和二阶中心格式之中,由此构建成一系列新格式,称呼方便和强调耦合流体动力学起见,称它们为流体力学基本格式（FMBS）。构建FMBS的主要步骤是把MBS中的通量摄动重构为步长的幂级数,利用空间分裂和导出的高阶流体动力学关系式,把结点变量展开成Taylor级数,通过消除重构格式修正微分方程的截断误差诸项求出幂级数的待定系数,由此获得非线性FMBS。FMBS的公式是MBS与 （及 ）之简单多项式的乘积, 和 分别是网格Reynolds数和网格CFL数。FMBS和MBS使用相同结点,简单性彼此相当,但FMBS精度高稳定范围大,例如FMBS包含了许多绝对稳定和绝对正型、高阶迎风和中心有限差分（FD）格式和有限体积（FV）格式,这些格式对网格Reynolds数的任意值均为不振荡格式。可见对不振荡CFD格式的构建,数值摄动算法提供了不同于调节数值耗散等常见的人为构建方法,而利用流体力学自身关系以及把迎风机制通过上、下游摄动重构引入中心MBS的解析构建方法,FMBS除了直接应用于流体计算外;对于通过调节数值耗散、色散和数值群速度特性重构高分辨率格式的研究,最简单FMBS提供了比最简单MBS更精确、但同样简单的基础和起步格式。FMBS用于计算不可压缩流,可压缩流,液滴萃取传质,微通道两相流等,均获得良好数值结果或与已有Benchmark解一致的数值结果。已有文献称数值摄动算法为新型高精度格式和高的算法和高的格式;本文FMBS比数值摄动格式的称呼可更好反映FMBS的物理内容。文中也讨论了值得进一步研究的一些课题,该法亦可用于其它一些数学物理方程（例如,简化Boltzmann方程、磁流体方程、KdV-Burgers方程等）MBS耦合物理动力学效应的重构。      

二维对流扩散方程的欧拉—拉格朗日分裂格式

本文在[1]基础上发展了一种有效的处理大P_e(R_e)数、非定常二维对流扩散方程的欧拉-拉格朗日(E-L)分裂格式,由于方法本质上与区域形状无关,且不需再分网格,因此是一种无网格的E-L方法,特别对于定常流动,E.-L.分裂格式可以导致比一阶迎风格式更精确的单调、无振荡格式,文中对于常系数、变系数和非线性的二维非定常和定常对流扩散方程的(初)边值问题进行了数值计算,数值结果与精确解的比较表明,本方法具有很好的精度,解是单调无振荡的,比通常一阶迎风格式具有较少的数值扩散,最大计算网格P-e(R-e)数可达100—500。     

求解浅水波方程的半离散中心迎风方法

将Jin's的界面方法应用到求解双曲守恒型方程的半离散中心迎风方法中,给出了一种新的求解浅水波方程的半离散中心迎风差分方法。对于源项,不是采用传统的单元均值而是采用单元界面处的值来近似,使所得格式对稳定态的求解是均衡的。且已证明所给的二阶精度的求解格式保持水深的非负性,这一特性使其能够较好的处理干河床问题。使用该方法产生的数值粘性(与O(Δ2r-1)同阶)要比交错的中心格式小(与O(Δx2r/Δt)同阶),而且由于数值粘性与时间步长无关,从而时间步长可根据稳定性需要尽可能的小,因此适用于稳定态的求解。     

一种求解双曲方程新有有限差分算法

本文提出一种适于求解一阶双曲系统的新的差分格式。它的建立方法是：将所要求解的方程与解的空间导数所满足的微分方程同时离散化，然后再通过插值函数构成封闭的离散变量代数方程。在线性情况下的误差分析表明：该格式的幅值与位相误差均小于常用的一，二阶差分格式，当其应于非线性气动方程求解时，基本上可以消除数值扩散与振荡这两种非正常现象。     

The ionization-rate constant at high temperatures high electron concentrations

The electron distribution function and the rate constant for ionization of atoms by electron impacts have been calculated as they apply to the conditions that are characteristic of a shock wave — namely, the energy distribution of the electrons and the ionization-rate constants are determined as functions of the temperature of the heavy particles. The energy dependence of the effective cross section for the excitation of an atom by electron impact is assumed to be linear. Equations of the Fokker-Planck type are used in the solution of the problem, and the range of temperatures and concentrations in which the deviation of the distribution from Maxwellian leads to a substantial change of the ionization-rate constant is determined.Translated from Zhurnal Prikladnoi Mekhaniki i Tecknicheskoi Fiziki, No. 2, pp. 32–40, March–April, 1971.     

Velocity field analysis of the high density,high pressure diesel spray

In this study, particle image velocimetry (PIV) measurements have been performed extensively on a non-reactive dense diesel spray injected from a single orifice injector, under various injection pressure and steady ambient conditions, in a constant flow chamber. Details of PIV setup for diesel spray measurement without additional seeding are explained first. The measured velocity profiles are compared to those obtained from other similar measurements performed in a different institution, as well as those obtained from a 1D spray model simulation, presenting in both cases a good level of agreement. In addition, the velocity fields under various injection pressures and ambient densities show the dominant effects of these parameters on the behavior of diesel spray. The self-similarity of the transverse cut profiles of axial velocity is evaluated, showing that the measurements are in agreement with the hypothesis of self-similar velocity profiles. Finally, the effect of injection pressure and ambient density on the velocity fluctuations is presented and analyzed as well. While the experimental results presented here could help to understand the complex diesel fuel–air mixing process during injection, they also provide additional spray velocity data for future computational model validation, following the main idea of the Engine Combustion Network.     

Achieving high strength and high ductility in nanostructured metals: Experiment and modelling

Engineering nanostructures in metallic materials such as nanograins and nanotwins can promote plastic performance significantly. Nano/ultrafine-grained metals embedded in coarse grains called bimodal metals and nanotwinned polycrystalline metals have been proved to possess extensively improved yield strength whilst keeping good ductility. This paper will present an experimental study on nanostructured stainless steel prepared by surface mechanical attrition treatment (SMAT) with surface impacts of lower strain rate (10 s^?1–10³ s^?1) and higher strain rate (10⁴ s^?1–10⁵ s^?1). Microstructure transition has been observed from the original γ-austenite coarse grains to α′-martensite nanograins with bimodal grain size distribution for lower strain rates to nanotwins in the ultrafine/coarse grained austenite phase for higher strain rates. Meanwhile, we will further address the mechanism-based plastic models to describe the yield strength, strain hardening and ductility in nanostructured metals with bimodal grain size distribution and nanotwinned polycrystalline metals. The proposed theoretical models can comprehensively describe the plastic deformation in these two kinds of nanostructured metals and excellent agreement is achieved between the numerical and experimental results. These models can be utilized to optimize the strength and ductility in nanostructured metals by controlling the size and distribution of nanostructures.     

Advanced damper with high stiffness and high hysteresis damping based on negative structural stiffness

High structural damping combined with high stiffness is achieved by negative stiffness elements. Negative incremental structural stiffness occurs when a column with flat ends is subjected to snap-through buckling. Large hysteresis (i.e., high damping) can be achieved provided the ends of the column undergo tilting from flat to edge contact. The column configuration provides high structural stiffness. Stable axial dampers with initial modulus similar to that of the parent material and with enhanced damping were designed built and tested. Effective damping of approximately two and stiffness-damping product of approximately 200 GPa were achieved in such dampers consisting of stainless steel columns. This is a significant improvement for this figure of merit (i.e., the stiffness-damping product), which generally cannot exceed 0.6 GPa for currently used damping systems.     

基于高性能DSP和高精度A/D的导航计算机系统

为提高某型号低成本捷联惯性导航系统的性能,设计了一套高性能导航计算机系统.研究了目前导航计算机系统的发展情况,针对各种方案的优缺点,以高性能数字信号处理器TMS320C6727(DSP)、现场可编程门阵列(FPGA)和高精度模数转换器件(AD)为核心,设计了一套高精度数据采集、硬件数字滤波和实时信号处理的高性能导航计算机系统.该方案的实验结果表明,在约100 s的跑车时间内,纯惯导位置误差为10 m;此设计方案满足了捷联惯性导航系统小型化、低功耗、低成本和实时性要求的要求,提高了捷联惯导系统的精度.     

高速、高动态下的捷联惯导空中粗对准方法

针对空中高速、高动态飞行条件下的捷联惯导系统初始对准问题,提出了一种对飞行动态过程和飞行平稳性不加限制的条件下,获得初始的位置、速度和姿态信息的粗对准方法,推导了利用GPS所测速度与惯性测量组件比力输出,通过惯性比力方程求解飞行载体姿态的粗对准方法,分析了影响对准性能的因素,并研制了对准仿真验证系统,通过设定航迹的计算机仿真,以及采用实测飞行数据的半物理仿真验证了该方法的有效性与精度.仿真验证结果表明,本对准方法可在载体任意动态过程进行初始对准,在对准精度与快速性方面均可满足高速、高动态下捷联惯导系统的粗对准精度要求.     

A free-flight experiment of projectiles ranging from high subsonic to high supersonic Mach numbers

This paper reports a preliminary experiment with a free-flight range which was designed to be able to be driven by means of a sort of fast-acting valve. The notable characteristics pertinent to this type of range is the pliancy of operation and also the wide coverage of flight speed from the high subsonic to the high supersonic range. For both spherical and vehicle models, flight tests were conducted with shadowgraph observations and flight speed measurements in order to examine the capability of this type of facility.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Phenomena of high polymer solutions while flowing through capillaries at high rates of shear

Generally solutions of high polymers show a shear-rate dependent flow behaviour and so the properties of these fluids have to be measured under conditions of shear corresponding to the practical service. Capillary viscometry is suitable for achieving high rates of shear but relaxation phenomena can effect the results, which is proved experimentally. The flow behaviour of a lubricant blended with a high polymer additive is measured and a graphical representation of the dependence of flow behaviour on temperature and rate of shear is recommended.