近海热水在潮汐河流共同作用下对流扩散的三维数值方法

本文提出一种模拟近海热水在潮汐和河流共同作用下对流扩散的三维数值方法。这是一种将三次样条函数、边界拟合坐标差分法和有限元法结合起来的破开算子方法。用此方法,本文给出了矩形渠道温度场的计算结果。     

对流占优扩散问题的特征线法-差分法计算格式

本文用特征线目的和有限差分目的相结合的数值目的来求解对流问题和对流占优扩散问题,提出了两个计算格式,并给出了数值例子。     

对流扩散方程的涡区分离解法

对流扩散方程是流体计算中一个基本方程,常用的数值方法导至解一个高阶的代数方程组,要求较大的存贮量和较长的计算时间。本文提出一种涡区分离解法,它利用对流扩散方程的迎风性质,把涡区从对流支配区分离出来,仅在各个涡区建立代数方程组并求解。而在对流支配区,则充分利用其抛物性,只需采用显式格式进行计算。由于在各涡区建立的这些方程组阶数和带宽都较小,因此要求存贮量较小,计算速度较快。对于雷诺数较大,涡区范围较小的问题,该方法特别有效。     

求解N-S方程的多边形网格与三角形网格对比

本文介绍了基于边的数据结果离散对流扩散方程的方法,编制了适用于任意多边形单元网格的有限容积法计算程序,利用方腔自然对流、外掠后台阶和移动顶盖驱等算例考察了三角形网格与多边形网格在数值计算方面的性能差别.结果表明,采用三角形网格收敛较慢且不容易获得网格无关的解,而采用与三角形网格对偶的多边形网格则收敛较快且易获得网格无关的解.     

定态对流扩散方程的渐近数值方法

本文提出了一种求解定态对流扩散方程的渐近数值方法,在边界层附近不必取很细的网格,对模型问题的数值计算表明,利用中等大小的步长就可得到边界层内的数值解。     

谱元方法求解正方形封闭空腔内的自然对流换热

提出谱元方法计算正方形截面封闭空腔内的自然对流问题,具体求解了原始变量速度和压力的不可压Navier-Stokes方程和温度方程,所有的求为量均采用Chebyshev谱逼近,Navier-Stokes方程和温度方程的时间离散采用时间分裂法,非线性项用4阶Runge-Kutta法,扩散项用Crank-Nicolson半隐方法,获得了与文献发表的基准解较一致的计算结果。     

数值模拟水环境污染的一种L∞稳定的分步杂交方法

本文提出了一种数值求解对流扩散方程的分步杂交方法。在不规则的三角形网格上,采用迎风离散格式或改型特征线方法处理对流算子;采用集中质量的有限元方法处理扩散算子。详细分析了这种算法的稳定性同题,在数学上严格证明了在满足①Δt≤min((2d)/v,(d²)/(3K)),其中d是三角形网格中最短垂线的长度,V和K分别为流场中的最大速度和扩散系数。②所有三角形的内角θ≤π/2的条件下,整个计算格式是L_∞稳定的,从而保证了在海洋环境和水质的数值模拟中海水的盐度、污染物的浓度和核电站冷却水系统中的超温不会出现负值。应用非线性的对流扩散方程对此方法的精度和收敛性进行了检验。通过数值解与精确解的比较,表明本方法的数值耗散很小,用改型特征线方法处理对流算子较迎风离散格式有更高的精度;两种处理对流算子的方法都没有伪振荡现象发生。本方法由于具有算法简单、L_∞稳定、计算网格灵活等优点,可推广使用于实际的海洋环境(潮波、海流、海洋污染)、港口和海湾的数值模拟以及不可压粘性流和对流传热同题的数值计算。     

具有纵向外肋片的水平复合管外表面自然对流换热的数值计算

为了方便而有效地模拟具有纵向外肋片的水平复合管外表面大空间自然对流换热的数值计算时计算区域外边界条件,本文提出一种新的边界条件处理方式。数值实验表明,用该条件计算的具有恒壁温的水平圆柱外表面自然对流换热数值解与文献中的基准解相比,平均Nu数的误差在0.5％以下。本文在极坐标系下,采用固体区与流体区耦合计算原始变量法,模拟计算了具有纵向外肋片的水平复合管外表面在不同肋片高度和肋片数下的自然对流换热量。数值计算表明,管外布置6个对称的肋片时,在肋片相对高度h/r04.0时,对换热最为有利,对应的肋片管平均肋效率为87.92％;而在相同肋片高度下,布置8个对称的肋片时,换热量最大。     

随机对流扩散方程的数值仿真

本文针对对流一扩散随机过程在随机输入（即随机输运和源项）,作用下进行数值仿真。我们先将对流扩散随机微分方程中的随机函数采用有限项截断的多项式浑沌展开（Polynomial Chaos Expansion）展开,再由Galerkin映射法得到求解浑沌展开系数的确定性方程组。这是一个在物理空间包含多尺度解的大方程组。为此我...     

输油管道油流静电带电数值计算

对输油管道内油品流动带电问题的数值计算进行了研究.紊流条件下的电荷输运方程是一个对流占优的对流扩散反应方程,采用算子分裂法,将该方程分解为纯对流方程、纯扩散方程和纯反应方程,分别采用特征线法和差分法求解.算例证明,该方法能准确描述管道内电荷分布,因而提供了一种获取冲流电流的可靠方法.     

Design and analysis of coherent OCDM en/decoder based on photonic crystal

The design and performance analysis of a new coherent optical en/decoder based on photonic crystal (PhC) for optical code -division -multiple (OCDM) are presented in this paper. In this scheme, the optical pulse phase and time delay can be flexibly controlled by photonic crystal phase shifter and time delayer by using the appropriate design of fabrication. According to the PhC transmission matrix theorem, combination calculation of the impurity and normal period layers is applied, and performances of the PhC-based optical en/decoder are also analyzed. The reflection, transmission, time delay characteristic and optical spectrum of pulse en/decoded are studied for the waves tuned in the photonic band-gap by numerical calculation. Theoretical analysis and numerical results indicate that the optical pulse is achieved to properly phase modulation and time delay, and an auto-correlation of about 8 dB ration and cross-correlation is gained, which demonstrates the applicability of true pulse phase modulation in a number of applications.     

湿蒸汽两相流动问题的耦合求解

控制湿蒸汽两相流动(汽相和液相)的方程个数多,其数值模拟通常采用将两相分开、两相间用参数传递的方法来处理。本文首次尝试将湿蒸汽两相流动汽相和液相的8个控制方程统一求解,推导了这一方程组的特征值及对应的特征向量,结合控制体积方法,采用TVD格式和时间推进法数值求解这一耦合方程组,研发了相应计算软件。对二维喷管中的自发凝结和非均质凝结算例进行的数值模拟和分析,表明了本文方法和计算软件的有效性和可靠性。     

多模激光束通过时间变化相位片变换的数值分析

根据衍射积分公式,对连续多模激光束通过随时间变化相位片的变换特性进行了数值模拟,详细地讨论了相位片单元尺寸和相位变化频率对多模光束光滑和能量分布的影响。数值模拟结果很好地解释了实验结果。     

双波长数字全息相位解包裹方法研究

使用两个不同的波长分别记录数字全息图,分别由数值再现得到每个波长对应的包裹相位图,再求得两者的相位差得到等效波长的相位图,通过此双波长相位解包裹方法得到连续的相位分布以消除相位包裹。通过数值模拟研究了双波长相位解包裹方法,搭建了双波长数字全息实验系统,并利用660nm和671nm两个波长的激光对标准石英平片和平凹透镜进行了相衬成像。通过双波长相位解包裹方法得到了连续的相位分布,实验结果与数值模拟结果具有较好的一致性,证明了双波长相位解包裹方法的有效性。     

On the nucleation of hadronic domains in the quark-hadron transition

We present numerical results on bubble profiles, nucleation rates and time evolution for a weakly first-order quark-hadron phase transition in different expansion scenarios. We confirm the standard picture of a cosmological first-order phase transition, in which the phase transition is entirely dominated by nucleation. We also show that, even for expansion rates much lower than those expected in heavy-ion collisions nucleation is very unlikely, indicating that the main phase conversion mechanism is spinodal decomposition.     

基于局部加密纯无网格法非线性Cahn-Hilliard方程的模拟

为数值求解描述不同物质间相位分离现象的高阶非线性Cahn-Hilliard(C-H)方程,发展了一种基于局部加密纯无网格有限点集法(local refinement finite pointset method,LR-FPM).其构造过程为:1)将C-H方程中四阶导数降阶为两个二阶导数,连续应用基于Taylor展开和加权最小二乘法的FPM离散空间导数;2)对区域进行局部加密和采用五次样条核函数以提高数值精度;3)局部线性方程组求解中准确施加含高阶导数Neumann边值条件.随后,运用LR-FPM求解有解析解的一维/二维C-H方程,分析粒子均匀分布/非均匀分布以及局部粒子加密情况的误差和收敛阶,展示了LR-FPM较网格类算法在非均匀布点情况下的优点.最后,采用LR-FPM对无解析解的一维/二维C-H方程进行了数值预测,并与有限差分结果相比较.数值结果表明,LR-FPM方法具有较高的数值精度和收敛阶,比有限差分法更易数值实现,能够准确展现不同类型材料间相位分离非线性扩散现象随时间的演化过程.     

Phase Locking and Chaos in a Josephson Junction Array Shunted by a Common Resistance

The dynamics of a Josephson junction array shunted by a common resistance are investigated by using numerical methods. Coexistence of phase locking and chaos is observed in the system when the resistively and capacitively shunted junction model is adopted. The corresponding parameter ranges for phase locking and chaos are presented. When there are three resistively shunted junctions in the array, chaos is found for the first time and the parameter range for chaos is also presented. According to the theory of Chernikov and Schmidt, when there are four or more junctions in the array, the system exhibits chaotic behavior. Our results indicate that the theory of Chernikov and Schmidt is not exactly appropriate.     

Comparison between instantaneous and integral intensities in dynamic speckle pattern interferometry

A new speckle measurement technique called temporal speckle pattern interferometry or time sequential speckle pattern interferometry has been developed recently. Its principle is that by capturing the temporal speckle patterns related to the object deformation or displacement, the whole-field displacement, the amplitude of the vibrating object and the shape of the tested object can be calculated through speckle intensity fluctuation scanning technique or Fourier-transforming method. In this paper, we combine the analytical and numerical methods to simulate the properties of the time demodulation in temporal speckle patterns interferometry techniques. The performance of three kinds of temporal phase sequences, power, exponential and harmonic phase sequences, are studied with the parameters of temporal speckle intensity fluctuation, the value of the spatial phase term, optical integral time of the recording camera and the initial phase of the temporal speckle intensities. The results indicate that the normalized value and period change of the instantaneous intensity are nearly coincident with that of the integral intensity for the harmonic temporal phase sequences and are different for the power and exponential temporal phase sequences.     

Thermodynamics and phase transitions in two-dimensional Yukawa systems

The results of numerical simulations of strongly-coupled two-dimensional dissipative Yukawa systems are presented. The thermodynamic characteristics of these systems were studied, namely the internal energy, the specific heat and the entropy. For the first time, it is discovered that the considered characteristics have two singular points on the melting line; one of these points corresponds to the first-order phase transition from crystal to the hexatic phase, and another point corresponds to the second-order phase transition from the hexatic phase to the isotropic liquid. The obtained results are compared to the existing numerical and analytical data.     

超声平面波经颅成像相位校正方法

超声平面波经颅成像时,由于颅骨对超声传播的影响引起图像质量下降,需要对颅骨造成的超声相位畸变进行校正.为此,该文研究了两种相位补偿方法:基于近似射线声学的理论方法和基于时间反转的数值计算方法,并利用数值仿真对比了两种方法的补偿和成像效果.结果表明:无论使用近似射线法还是时间反转法,都能够有效地校正因颅骨造成的相位畸变;...