液体NMR中平板间多量子相干受限扩散行为的有限差分模拟

将平板间单量子相干受限扩散理论表述推广到多量子相干,并结合积算符矩阵、Bloch方程和有限差分方法进行模拟. 通过模拟找出平板间受限扩散信号衰减随平板间距变化的规律,并与实际体系比较. 结果表明：平板间n量子相干的自旋回波信号衰减曲线与单量子类似,且其产生同样衍射图样所需的脉冲梯度场强度仅为单量子的1/|n|,可用于测量微小的平板间距. 本文的模拟方法可进一步推广到复杂体系的研究.     

求解可压Navier-Stokes方程的对称超紧致差分格式及其并行算法

考查了超紧致差分方法,并将其精度同传统差分格式和紧致差分格式做了比较,结果显示超紧致方法具有良好求解效率.用分块流水线方法设计了超紧致差分格式的并行算法,进行数值实验及并行性能分析.     

基于紧致差分格式的高效时域有限差分算法

探讨一种基于紧致差分格式的高效时域有限差分算法(high-order compact-FDTD),该方法不仅提高计算精度,而且网格结点少、内存使用率和CPU时间大为降低.利用紧致格式FDTD方法实现无耗波导系统及光子晶体光纤中电磁波传播的数值模拟.通过计算实例验证算法的高效性.     

Modeling Chemically Reactive Flow of Sutterby Nanofluid by a Rotating Disk in Presence of Heat Generation/Absorption

In this article we investigate the flow of Sutterby liquid due to rotating stretchable disk. Mass and heat transport are analyzed through Brownian diffusion and thermophoresis. Further the effects of magnetic field, chemical reaction and heat source are also accounted. We employ transformation procedure to obtain a system of nonlinear ODE's. This system is numerically solved by Built-in-Shooting method. Impacts of different involved parameter on velocity, temperature and concentration are described. Velocity, concentration and temperature gradients are numerically computed. Obtained results show that velocity is reduced through material parameter. Temperature and concentration are enhanced with thermophoresis parameter.     

不可压缩流基于块预处理的并行有限元计算

发展了一个模拟非定常不可压缩粘性流的并行有限元求解器,时间离散使用具有二阶精度的隐式中点格式,基于三维非结构四面体网格剖分,使用高阶混合有限元离散速度场（P2）和压力场（P1）.全离散格式产生的代数方程组是大型、稀疏、非对称和病态的,基于修正的压力对流扩散预处理（PCD）和精心设计的子问题迭代执行策略,采用预处理的GMRES迭代法来高效求解线性方程组.利用相同的子问题迭代策略,同时给出基于最小二乘交换子（LSC）预处理的并行效率对比.大量数值算例验证了算法的精度、可扩展性和可靠性.三维驱动方腔流模拟结果（Re=3200.0）清晰地显示了方腔流中主涡（PE）、下游二次涡（DSE）、上游二次涡（USE）、侧壁涡（EWV）和TGL涡的存在.     

二维半导体问题在复合网格上的有限差分格式

半导体器件的瞬时状态由3个方程组成的非线性偏微分方程组的初边值问题决定.依据实际数值模拟的需要,提出了一类二维半导体问题在时空局部加密复合网格上的有限差分形式,电场位势方程、电子和空穴浓度方程分别用五点差分格式和修正迎风格式近似,且在交界面上采用线性插值,并给出了电子和空穴浓度的最大模误差估计,最后给出了数值算例.     

保持对称性的二维Lagrange流体力学有限差分方法

广泛应用的二维直角坐标系下的Wilkins有限差分格式在计算一维柱面问题时,通过等角度划分周向网格能够获得严格的对称性,非等角度划分周向网格会产生较严重的不对称性.通过分析Wilkins有限差分格式在处理非等角度划分周向网格的一维柱面问题时破坏对称性的原因,指出周向网格的非等角度划分产生了周向压力分量,从而产生了周向加速度分量和周向运动速度,以此为基础提出一种对该有限差分格式进行修正的方法,将节点处的周向压力分量做算术平均运算,以消除周向压力分量,只剩径向压力分量起作用.因而该修正方法在以任意角度划分周向网格的条件下都能够保持严格的对称性.通过几个典型算例验证该结论,对对称流动,修正方法与原始方法所获得的结果一致,对非对称流动,二者有微小差异.     

用拉普拉斯变换差分法求解试井分析中的一维渗流问题

结合拉普拉斯变换和有限差分法给出求解试井分析中一维渗流问题的拉普拉斯变换差分法:首先对渗流方程采用拉普拉斯变换消去时间变量得到拉普拉斯空间数学模型,采用有限差分法求解拉普拉斯空间数学模型,最后通过拉普拉斯反演算法得到井底压力或产量.通过与有限差分法结果和解析解对比,拉普拉斯变换差分法比有限差分法计算误差小.虽然单步计算耗时长,但计算任意时刻结果时对空间网格的适应性和不依赖其它时刻计算结果的特性使得拉普拉斯变换差分法在试井分析中有非常好的应用前景.     

紧致方法对流动换热及静态分岔的模拟

发展了基于投影法的紧致方法求解流动换热问题,对顶盖驱动流和侧壁加热的方腔内自然对流换热问题进行了数值模拟。与其它传统方法相比,紧致方法能在较少的网格结点下获得精度较高的计算结果。进一步,采用所发展的紧致方法对不同工况下的Rayleigh-Benard对流及其静态分岔现象进行了数值模拟。数值计算结果表明当长宽比变大时,底部努塞尔数会有小幅度增加。当长宽比为8时,用所发展的紧致方法不同的初场可以得出三种不同的流场和温度场。与基于QUICK格式的SIMPLE算法相比,所发展的紧致方法可以多预测一种静态分岔现象。     

A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE's

The Courant-Friedrichs-Lewy condition (The CFL condition) is appeared in the analysis of the finite difference method applied to linear hyperbolic partial differential equations. We give a remark on the CFL condition from a view point of stability, and we give some numerical experiments which show instability of numerical solutions even under the CFL condition. We give a mathematical model for rounding errors in order to explain the instability.     

一种基于磁通和电磁能流的磁扩散问题求解格式

针对一维磁场扩散问题设计一种显式的有限体积离散格式。格式的第一个特征是不仅将磁场的扩散表达为单元边界上的磁通流, 同时将能量方程中的欧姆加热也表达为单元边界上的电磁能量流, 该特征能够更好地保证磁场能与内能的总量守恒。格式的第二个特征是将单元边界上的磁通量和电磁能通量进行截断, 在极端电阻率存在的磁扩散问题求解过程中, 该特征能够一定程度上放宽稳定性条件对显式格式时间步长的限制。     

Mathematical Analysis for Peristaltic Flow of Two Phase Nanofluid in a Curved Channel

This paper describes the theoretical analysis for peristaltic motion of water base nanofluid containing distinct types of the nanoparticles like Cu, TiO₂, and Al₂O₃. Equations of nano fluid are modelled and simplified by constructing the suppositions of low Reynolds number as well as long wave length. The reduced equations are solved exactly. Solutions are represented through graphs. Outcomes for the velocity, temperature, pressure rise and stream lines are analyzed graphically. The work presented here is based on the fictitious values, however some other values can be tested experimentally.     

Natural Convection of Fe_3O_4-Ethylene Glycol Nanofluid under the Impact of Electric Field in a Porous Enclosure

Free convection of Fe_3O_4-Ethylene glycol nanofluid in existence of Coulomb forces is studied. Effect of thermal radiation is taken into account. Properties of nanofluid are varied with supplied voltage and shape of nanoparticles. The bottom wall is considered as positive electrode. Control Volume based Finite Element Method is used to obtain the results, which are the roles of Darcy number(Da), radiation parameter(Rd), Rayleigh number(Ra), nanofluid volume fraction(φ), and supplied voltage(?φ). Results indicate that Nusselt number is an enhancing function of supplied voltage and Darcy number. Maximum values for temperature gradient are occurred for platelet shape nanoparticles.     

A High-Accuracy Finite Difference Scheme for Solving Reaction-Convection-Diffusion Problems with a Small Diffusivity

This paper is devoted to a new high-accuracy finite difference scheme for solving reaction-convection-diffusion problems with a small diffusivity $\varepsilon$. With a novel treatment for the reaction term, we first derive a difference scheme of accuracy $\mathcal{O}(\varepsilon^2 h + \varepsilon h^2 + h^3)$ for the 1-D case. Using the alternating direction technique, we then extend the scheme to the 2-D case on a nine-point stencil. We apply the high-accuracy finite difference scheme to solve the 2-D steady incompressible Navier-Stokes equations in the stream function-vorticity formulation. Numerical examples are given to illustrate the effectiveness of the proposed difference scheme. Comparisons made with some high-order compact difference schemes show that the newly proposed scheme can achieve good accuracy with better stability.     

基于模拟有限差分的低渗透油藏非达西油水两相流动数值模拟

在模拟有限差分研究单相非线性流动基础上,进一步推广到低渗透油藏非达西油水两相流动数值模拟中,以拟线性流动模型对该方法的基本原理进行详细阐述,建立相应的数值计算格式,并采用IMPES方法对其两相流问题进行求解,通过数值算例验证方法的正确性和适用性.     

用基于磁场的改进型有限差分法分析光波导的全矢量本征模

提出一种改进的有限差分法,用以求解全矢量磁场波方程,分析光波导承载的全矢量本征模.离散交叉项时,采用与波导结构无关的六点差分格式,考虑磁场分量的导数在芯包分界处的不连续性,比传统四点差分格式有更高的计算精度.分析阶跃型光纤、矩形和脊形光波导的全矢量本征模问题,给出全矢量基模的磁场分布及其归一化传播常数,揭示全矢量本征模的混合特性,所得结果与解析法、高精度模横向谐振法的结果吻合,验证了方法的收敛性与计算精度.     

质子交换膜燃料电池波浪形平行流场研究

质子交换膜燃料电池的传统平行流场存在着传质不佳,高电流密度下大量的液态水无法及时排出导致性能急剧下降等问题.提出了一种新型的波浪形平行流场并利用数值模拟方法优化了波浪形平行流场的几何结构.结果表明,相比于传统平行流场,波浪形平行流场不仅能够有效促进氧气的传输,还能加快液态水的去除,采用波浪形平行流场的PEMFC最大输出...     

JEMS- FDTD超大规模并行计算测试

介绍了JEMS- FDTD在大规模并行计算机上进行的并行性能测试,包括网格片大小对性能的影响、单节点MPI/OPENMP混合并行性能、多节点MPI/OPENMP混合并行性能、大规模并行性能等。同时,也给出了一个包含电大尺寸复杂、真实结构模型的算例,并对其进行了计算、分析。测试表明,JEMS- FDTD可高效使用数万个处理器核进行并行计算。大型算例测试表明：JEMS- FDTD可针对电大尺寸复杂、真实结构模型进行有效的计算、分析。     

Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme

Analyses were performed on the dispersion overshoot and inverse dissipation of the high-order finite difference scheme using Fourier and precision analysis. Schemes under discussion included the pointwise- and staggered-grid type, and were presented in weighted form using candidate schemes with third-order accuracy and three-point stencil. All of these were commonly used in the construction of difference schemes. Criteria for the dispersion overshoot were presented and their critical states were discussed. Two kinds of instabilities were studied due to inverse dissipation, especially those that occur at lower wave numbers. Criteria for the occurrence were presented and the relationship of the two instabilities was discussed. Comparisons were made between the analytical results and the dispersion/dissipation relations by Fourier transformation of typical schemes. As an example, an application of the criteria was given for the remedy of inverse dissipation in Weirs and Martin's third-order scheme.