一种改进的光滑粒子流体动力学前处理方法

为了便于对任意边界形状的计算域快速地布置均匀粒子,提出了一种改进的光滑粒子流体动力学前处理方法.该方法是在2012年Colagrossi等提出的算法基础上进行改进后得到的.Colagrossi等提出的算法能够计算一些简单外形分布比较均匀的粒子.然而当光滑长度与初始粒子间距的比值较大时该方法在计算过程中会出现较强的数值震荡问题,收敛速度慢;而且在计算过程中可能会遭遇流体粒子穿透固体壁面的问题.本文通过引入未知因素修正的平滑粒子动力学模型来提高计算稳定性,并通过对边界附近的流体粒子施加边界力来避免流体粒子穿透固体壁面.算例验证结果表明,利用改进后的光滑粒子流体动力学前处理方法能够快速地对各种边界形状的计算域分布均匀粒子,并且避免了流体粒子穿透固体壁面的问题.     

移动坐标系FDTD方法在脉冲波传播中的应用

通过在时域有限差分(FDTD)方法中引入移动坐标系,解决了一般FDTD方法处理脉冲长距离传播时面临的困难。推导了移动坐标系下的场方程和FDTD差分格式,并将该方法应用于模拟波导中电磁脉冲的传播。计算结果表明,在传播过程中,脉冲波包沿传播方向逐渐展宽,脉冲的峰值场强变小,同时出现了色散现象,脉冲中传播较慢的成分逐渐移向尾部,产生带尾态,这与一般FDTD方法得到的计算结果接近。多个频率的计算结果表明,该方法与一般FDTD方法得到的数据的相对误差小于0.1%,验证了方法的可行性和正确性。     

轴流压缩机转子叶栅内粒子沉积及对其性能影响的数值研究

计算了一轴流压缩机入口级的三维流场,在此基础上,通过UDF引入作用于旋转坐标系下固体粒子上的附加 力,计算了该入口级动叶内粒子的运动轨迹和叶面上粒子的沉积分布情况,并在此基础上模拟了由于粒子沉积所引起的压 缩机动叶叶栅的性能恶化,为发展气动防沉三维叶片的优化设计提供了研究基础。     

基于MPS方法的汽泡凝结数值模拟研究

采用移动粒子半隐式(MPS)方法对静止过冷水中单个汽泡的凝结现象进行了数值模拟,研究了不同初始压力和初始直径时饱和蒸汽汽泡凝结过程,获得了凝结过程中汽泡形状、当量直径和压力的变化规律;汽泡初始压力为0.1～0.5MPa,初始直径为2mm、3mm和5mm;过冷水压力为0.1MPa,温度为70℃。结果表明两相界面不存在压差时,凝结过程中汽泡始终保持球形,汽泡当量直径逐渐减小,压力近似不变;相界面存在压差时,凝结过程中汽泡从球形逐渐变为心形、半月形,汽泡当量直径和压力会出现周期性振荡,且初始压力越大振荡幅度越大。     

三角形金属纳米粒子的光力特性研究

基于麦克斯韦应力张量理论,对多边形金纳米粒子在聚焦场下的光力特性进行了研究。以三角形金纳米粒子为例,从粒子在聚集场中的受力情况出发,分别研究了具有圆对称能量分布的聚焦场和具有三角形能量分布的聚焦场对三角形金纳米粒子的捕获特性。研究结果表明,当使用圆对称聚焦场时,可对边长为50～350 nm的三角形金纳米粒子实现稳定捕获;当使用三角形聚焦场时,在粒子以和聚焦场形状匹配的角度进入聚焦场的情况下,可对边长为100～350 nm的三角形金纳米粒子实现稳定捕获。将圆对称聚焦场和三角形聚焦场对三角形金纳米粒子的捕获特性进行比较,发现三角形聚焦场在x方向的捕获力要强于圆对称聚焦场;而在y方向,三角形聚焦场对粒子的捕获范围要大于圆对称聚焦场。该工作研究了三角形的金属纳米粒子在不同形状聚焦场下的光力捕获特性,为基于非球形金属粒子的光学操纵在拉曼光谱超分辨成像、粒子微加工等领域的应用奠定了理论基础。     

EMC效应与光锥量子场论

本文指出应用无穷大动量坐标系的编时微扰理论,或其等效形式,一般坐标系的光锥微扰理论处理轻子原子核深度非弹散射时,脉冲近似的适用条件成立并可忽略末态相互作用的贡献.为此,本文把光锥量子场论应用于强子-介子场,引入一个原子核的相对论性复合粒子模型,然后在此模型中应用脉冲近似来讨论轻子原子核深度非弹散射.     

水斗非定常自由水膜流三维贴体数值模拟

本研究采用水斗三维非正交贴体坐标系进行了非定常自由水膜流动的数值解析。对不规则水斗内表面采用三维非正交贴体坐标系下离散点进行拟合,推导了曲面离散点的法向矢量和曲面微元面高斯曲率、平均曲率等几何特征量的计算公式,进而导出流体粒子在运动方向上曲率计算式。在水斗三维贴体坐标系中,还推导了流体粒子在水斗曲面上的运动控制方程。最后对某水轮机水斗内表面非定常自由水膜流进行了数值模拟,得到其非定常水膜流态分布。     

空心阴极类火花放电初始电离过程的PIC/MCC模拟

采用粒子模拟与蒙特卡罗相结合(PIC/MCC)的方法,应用静电模型,编写了准三维的模拟程序.该程序能够较好地描述空心阴极类火花放电初始电离过程的演化步骤.通过研究电离过程的细节,可以认为该阶段电离过程是空心阴极效应和局部强电场共同作用的结果.从起始电离到空心阴极初始阶段,局部强电场在电离过程中起到了支配作用;随后空心阴极效应占据主导地位. 关键词： 粒子模拟 蒙特卡罗 空心阴极 类火花放电     

预测声屏障插入损失的抛物方程法及其初始声场研究

Salomons建立的抛物方程(CNPE)方法可以预测非均匀环境中的声屏障插入损失。但是该方法在声屏障与声源距离较近时会产生较大误差。文中通过理论分析发现产生该问题的原因在于CNPE方法所使用的Gauss初始场仅适用于小仰角(10°以内)范围内的声波。为解决Gauss初始场引起的问题,推导了可以用于较大仰角声波的更高阶数的Gauss初始场。通过数值仿真对比了不同阶数的初始场在CNPE方法中的效果。结果表明:4阶初始场是最适合CNPE方法的初始场,将该初始场与CNPE方法相结合,可以准确预测当声屏障与声源距离较近时的插入损失.      

基于深度学习的粒子场数字全息成像研究进展

粒子场的数字全息成像中，由一幅粒子场全息图重建出高精度的三维粒子场分布，是数字全息技术领域的经典问题之一。相比于传统反向重建算法，深度学习算法可以从单个全息图直接重建出三维粒子场来简化算法复杂度，提高计算效率和准确率。介绍国内外研究团队将深度学习算法结合数字全息技术实现粒子场数字全息成像的研究进展，从不同粒子表征方法入手，叙述了支持向量机、全连接神经网络、全卷积网络、U-Net网络、深度神经网络在粒子场数字全息成像中粒子表征及粒子场反向重建过程中的应用原理、实现途径和准确率。最后指出了深度学习算法在这一研究领域的优势及目前基于深度学习算法的不足，并对如何进一步提高该方法的准确率进行了展望。     

移动边界问题的时空域正则区域迭代配点法

考虑热传导方程的移动边界问题,其定解区域随着时间而变化。构造一种时空域上的高精度数值算法求解1+1维移动边界问题。在时空域上假设一个初始移动边界位置,构成移动边界问题的不规则计算区域,选择一个适当的正则区域（矩形区域）完全覆盖所计算的不规则区域,在正则区域上利用移动边界约束条件和固定边界条件,采用时空域重心插值配点法求解1+1维扩散方程,得到正则区域上扩散方程数据。采用二维重心插值计算假设移动边界上函数关于时间偏导数的数值,进而利用一维重心插值配点法求解移动界面控制常微分方程,得到新的假设移动界面位置。重复上述流程,最终得到问题的数值解和移动界面的最终位置。通过典型数值算例验证所建立的数值方法的有效性和数值计算精度。     

振动NACA0012翼型的移动网格数值模拟

利用流体力学方程的积分形式给出非结构移动网格上离散格式,利用自适应移动网格方法移动网格,进而得到网格速度.对振动Naca0012翼型问题,分三种类型确定网格速度,再结合Riemann问题的解法器构造数值通量,得到移动网格单元上新的物理量.数值实验表明这种格式同时具有高效、高分辨率的特点.     

A scaled boundary node method applied to two-dimensional crack problems

A boundary-type meshless method called the scaled boundary node method(SBNM) is developed to directly evaluate mixed mode stress intensity factors(SIFs) without extra post-processing.The SBNM combines the scaled boundary equations with the moving Kriging(MK) interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter.As a result,the SBNM requires only a set of scattered nodes on the boundary,and the displacement field is approximated by using the MK interpolation technique,which possesses the δ function property.This makes the developed method efficient and straightforward in imposing the essential boundary conditions,and no special treatment techniques are required.Besides,the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction.Therefore,the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip.Numerical examples using the SBNM for computing the SIFs are presented.Good agreements with available results in the literature are obtained.     

Boundary element-free method for elastodynamics

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.     

Boundary element-free method for elastodynamics

1 Introduction In recent years, more and more attention has been paid to researches on the meshless (or meshfree) method, which makes it a hot direction of computational mechanics[1,2]. The meshless method is the approximation based on nodes, then the large deformation and crack growth problems can be simulated with the method without the re-meshing technique. And the meshless method has some advantages over the traditional computa- tional methods, such as finite element method (FEM) and boun…     

Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method

The methods for simulating surface tension with smoothed particle hydrodynamics (SPH) method in two dimensions and three dimensions are developed. In 2D surface tension model, the SPH particle on the boundary in 2D is detected dynamically according to the algorithm developed by Dilts [G.A. Dilts, Moving least-squares particle hydrodynamics II: conservation and boundaries, International Journal for Numerical Methods in Engineering 48 (2000) 1503–1524]. The boundary curve in 2D is reconstructed locally with Lagrangian interpolation polynomial. In 3D surface tension model, the SPH particle on the boundary in 3D is detected dynamically according to the algorithm developed by Haque and Dilts [A. Haque, G.A. Dilts, Three-dimensional boundary detection for particle methods, Journal of Computational Physics 226 (2007) 1710–1730]. The boundary surface in 3D is reconstructed locally with moving least squares (MLS) method. By transforming the coordinate system, it is guaranteed that the interface function is one-valued in the local coordinate system. The normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated. Surface tension force acts only on the boundary particle. Density correction is applied to the boundary particle in order to remove the boundary inconsistency. The surface tension models in 2D and 3D have been applied to benchmark tests for surface tension. The ability of the current method applying to the simulation of surface tension in 2D and 3D is proved.     

K2_SPH方法及二维破碎波的模拟

通过对一些关键技术的改进,特别是自由表面的判断方法和改进的固壁边界条件,使K2_SPH方法能够模拟破碎波问题,完整实现波浪的爬升、翻转、破碎等过程.对大幅液舱晃荡问题的模拟表明,K2_SPH方法较传统SPH方法在波形和压力分布都有明显改进.     

The case of escape probability as linear in short time

We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is linear in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behaviour, quantum absorption, time of arrival, quantum measurements, and more.     

Boundary Fractal Dimensions from Sections of a Particle Profile

The fractal dimension of particles is commonly evaluated from complete particle boundaries. In this work, a study has been made of the self-similar nature of complete and incomplete boundary profiles of a range of morphologically different copper powders. Boundary images were captured from SEM micrographs of particle boundaries at a range of magnifications up to nearly 14000X. An algorithm was developed to compute the fractal dimension of boundary segments. This algorithm was tested against the Koch Island fractal, and was found to give excellent estimates of the fractal dimension. For the particle system studied, the boundary fractal was found to be sensitive to magnification with appreciable drops in value at high magnification. This demonstrates that the particles studied did not have true fractal boundaries and the use of fractal theory to study particle surface roughness must be used with caution.     

An analytical solution to Li/Li+ insertion into a porous electrode

The dynamic faradic properties of the lithium ion batteries are primarily determined by the process of lithium ion insertion into a porous electrode. In this paper, we present an analytical result of the intercalating process of Li/Li⁺ into a spherical particle of graphite or cobalt oxide immersed in a conductive electrolyte. Using the finite integral transform method, an exact solution to the concentration profile was obtained for arbitrary linear initial and boundary conditions. To avoid analytical difficulties with respect to the boundary conditions of second kind, the method of pseudo-steady-state is applied. The final solution uniformly converges, and can be used for accurate and fast dynamic modelling and simulation.