A New Version of Smoothed Point Method to Simulate Linear Elastic Wave Propagation

By using the kernel function of the smoothed particle hydrodynamics (SPH) and modification of statistical volumes of the boundary points and their kernel functions, a new version of smoothed point method is established for simulating elastic waves in solid. With the simplicity of SPH kept, the method is easy to handle stress boundary conditions, especially for the transmitting boundary condition. A result improving by de-convolution is also proposed to achieve high accuracy under a relatively large smooth length. A numerical example is given and compared favorably with the analytical solution.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Application of laser cladding technology to improve the interface of thermal barrier coatings

The present study is focused on improvement of the adhesion properties of the interface between plasma-sprayed coatings and substrates by laser cladding technology (LCT), Within the laser-clad layer there is a gradient distribution in chemical composition and mechanical properties that has been confirmed by SEM observation and microhardness measurement. The residual stress due to mismatches in thermal and mechanical properties between coatings and substrates can be markedly reduced and smoothed out. To examine the changes of microstructure and crack propagation in the coating and interface during loading, the three-point bending test has been carried out in SEM with a loading device. Analysis of the distribution of shear stress near the interface under loading has been made using the FEM code ANSYS, The experimental results show clearly that the interface adhesion can be improved with LCT pretreatment, and the capability of the interface to withstand the shear stress as well as to resist microcracking has been enhanced.

Numerical Study on Flow Field and Temperature Distribution in Growth Process of 200 mm Czochralski Silicon Crystals

The melt flow and temperature distribution in a 200 mm silicon Czochralski furnace with a cusp magnetic field was modeled and simulated by using a finite-volume based FLUTRAPP ( Fluid Flow and Transport Phenomena Program) code. The melt flow in the crucible was focused, which is a result of the competition of buoyancy, the centrifugal forces caused by the rotations of the crucible and crystal, the thermocapillary force on the free surfaces and the Lorentz force induced by the cusp magnetic field. The zonal method for radiative heat transfer was used in the growth chamber, which was confined by the crystal surface, melt surface, crucible, heat shield, and pull chamber. It was found that the cusp magnetic field could strength the dominant counter-rotating swirling flow cell in the crucible and reduce the flow oscillation and the pulling-rate fluctuation. The fluctuation of dopant and oxygen concentration in the growing crystal could thus be smoothed.

模拟弹塑性碰撞的修正SPH方法

从基本的无网格光滑粒子法SPH(Smoothed Particle Hydrodynamics)近似出发,修正了模拟固体力学中大变形弹塑性碰撞的SPH方法.在边界处采用修正的边界条件,弹塑性分析过程中采用增量理论计算应力,迭代过程中用守恒光滑法进行滤波修正消除拉力不稳定.对SPH方法进行了程序实现,给出了杆弹塑性碰撞的算例.计算分析表明,SPH方法节点的影响域较大、精度较相同节点间距有限元法的结果有一定差距,但是通过增加粒子数量可以提高SPH的精度,保持了其简单性和计算大变形的特性.

SPH方法在模拟线弹性波传播中的运用

通过对固体中波动问题的模拟建立了一种光滑粒子法的新形式,一种运用SPH的核函数的类似有限体积法的计算方法.通过对统计体积的修正以及对边界粒子的核函数修正,较好地解决了SPH方法中长期以来制约其被广泛应用的主要问题之一边界条件的表述.在此基础上成功地在光滑粒子法中实现了透射边界条件的模拟.同时利用反卷积修正使得较大粒子间距下的计算结果的精度大大提高.这种方法不但保持了SPH的简单性,而且很容易实现应力边界条件.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Large-eddy simulation of flows past a flapping airfoil using immersed boundary method

The numerical simulation of flows past flapping foils at moderate Reynolds numbers presents two challenges to computational fluid dynamics: turbulent flows and moving boundaries. The direct forcing immersed boundary (IB) method has been devel- oped to simulate laminar flows. However, its performance in simulating turbulent flows and transitional flows with moving boundaries has not been fully evaluated. In the present work, we use the IB method to simulate fully developed turbulent channel flows and transitional flows past a stationary/plunging SD7003 airfoil. To suppress the non-physical force oscillations in the plunging case, we use the smoothed discrete delta function for interpolation in the IB method. The results of the present work demonstrate that the IB method can be used to simulate turbulent flows and transitional flows with moving boundaries.

光滑粒子动力学方法中粒子分布与数值稳定性分析

光滑粒子动力学(SPH)作为一种拉格朗日型无网格粒子方法,已经成功地应用于包括含多相流动界面以及移动边界的可压缩和不可压缩流体运动的研究中.通过对Poiseuille流动的深入研究,探索了SPH方法中粒子分布对计算精度的影响,揭示了一种因为粒子不规则分布而导致的数值不稳定现象.研究显示,这种数值不稳定性起源于SPH方法粒子近似过程中的不连续性.使用了一种新的粒子近似格式以确保SPH方法中粒子近似的连续性.计算结果表明,这种新的粒子近似格式对于规则和不规则的粒子分布都能得到稳定精度的结果.

利用消衍射透镜列阵及光谱色散平滑实现焦斑均匀辐照

提出将空间域的透镜列阵法和时间域的光谱色散平滑法结合起来实现靶面的均匀辐照．消衍射型透镜列阵能获得边缘陡峭且顶部较平坦的准近场焦斑，光谱色散平滑则能有效地抹平焦斑内部由多光束干涉引起的细密条纹．数值结果显示，通过该方案能获得均匀性较好的焦斑．进一步分析了光谱色散平滑单元中位相调制和光栅的参数对辐照均匀性的影响，发现参数的选取要在焦斑均匀性和能量利用率之间取得合理平衡，以在整体上获得最佳的均匀辐照效果．

Improved uniformity of target illumination by combining a lens array and the technique of spectral dispersion

A scheme using a lens array and the technique of spectral dispersion is presented to improve target illumination uniformity in laser produced plasmas. Detailed two-dimensional simulation shows that a quasi-near-field target pattern, of steeper edges and without side lobes, is achieved with a lens array, while interference stripes inside the pattern are smoothed out by the use of the spectral dispersion technique. Moving the target slightly from the exact focal plane of the principal focusing lens can eliminate middle-scale-length intensity fluctuation further. Numerical results indicate that a well-irradiated laser spot with small nonuniformity and great energy efficiency can be obtained in this scheme. (c) 2007 American Institute of Physics.

利用二维光谱色散和透镜列阵改善靶面辐照均匀性

利用二维光谱色散平滑技术和透镜列阵(LA)来改善激光驱动器中靶面的辐照均匀性。通过消衍射透镜列阵可得到包络陡峭且中小空间尺度均匀性较好的焦斑。当在光路中加入二维光谱色散平滑单元后,光束在两个互相垂直的方向发生光谱色散,多光束干涉所引起的细密条纹也将在很大程度上被抹平,如果把横向热传导平滑效应也考虑在内,高空间频率的强度波动可进一步被消除。二维理论模拟结果表明采用该方案可获得顶部平坦边缘陡峭的焦斑,而且该方案无需仔细调整靶面的位置,实际应用较方便。

银杉的遗传多样性及系统位置的研究一兼论松科的分子系统学

银杉属Cathaya是我国著名植物学家陈焕镛和匡可任建立的松科单型属，该属是否成立及该属在松科中的系统位置至今仍众说不一。银杉Cathazyaargyro phylla是银杉属的唯一幸存种，被誉为第三纪的活化石，并被列为我国一级保护的濒危植物，也是世界植物红皮书所列少数几种濒危裸子植物之一，保护区虽已设立数个，但该物种的濒危原因仍为未解之谜。本文针对上述问题开展了松科植物的分子系统学研究，探讨了银杉属的系统位置及松科的属间关系，并通过遗传多样性的研究探讨了银杉的濒危机制及保护策略。 1．松科的分子系统学研究 为选取合适的分子标记，本文先探讨了ITS-1在松科等裸子植物中的系统学价值。对1 6种裸子植物（其中含松科10属12种）的ITS-1的扩增结果如下：ITS-1在裸子植物属闻存在极大的长度变异(约600-2600bp)，因而不适用于属级以上的系统学研究;在同属种中，ITs-1的长度虽较一致，但与被子植物的ITS-1相比，裸子植物的ITS-1太长(如在松属中超过2600bp)，难以进行大规模研究。银杉属ITS-1的扩增产物中，一个片段的长度与松属ITS-1的长度相当，另一个片段的长度与云杉属ITS-l的长度相当，这三属间的关系值得进一步研究。此外，在松科植物ITS-1的研究中必须注意真菌“污染”这一问题。 由于ITS不适用于裸子植物属间关系的研究，因而本文运用rbcL-accD基因片段及trnK基因的PCR-RFLP分析探讨银杉属的系统位置及松科的属间关系。rbcL和trnK虽然都是叶绿体基因，但位于trnK内含子区的natK基因与rbcL基因在所受的选择压及进化速率上相差甚远，通过这两个基因研究结果的比较有助于评价系统树的可靠性。此外，考虑到松科的10个属中有9个属的rbcL基因序列已被测定，我们补测了银杉属的rbcL基因序列，进而对松科10个属的rbcL基因序列进行了全面分析。PCR -RFLP分析及rbcL基因的序列分析结果如下： A. PCR扩增的松科rbcL-accD基因片段均长约2550bp，属间没有明显的长度变异，1 8种限制性内切酶的单酶切及7种组合双酶切共获得86个酶切位点，其中54个为变异位点。PAUP和MEGA软件分析均表明：银杉属、松属、黄杉属和落叶松属构成一个单系群，且银杉属与松属的关系似乎近于它与另外二属的关系，但这一结果来得到bootstrap分析的较强支持;黄杉属近缘于落叶松属;冷杉属近缘于油杉属。 B．PCR扩增出的松科trnK基因均长约2557bp，在属间也没有明显的长度变异。16种限制性内切酶的单酶切及7种组合双酶切共获得92个酶切位点，其中68个为变异位点。变异位点中的35个具有系统发育信息，其中28个位于matK基因上。分布于整个trnK基因上的informative位点和仅分布于matK基因上的informative位点分别用于PAUP(version 3.1.1)分析，且PAUP分析中分别用Wagner简约法和Dollo筒约法构建系统树。总体看来，Wager简约树和Dono简约树的结构基本一致（Cedrus的位置除外）：Abies、Keteleeria、Tsuga和Pseudolarix分为一支，且这一支在所有的简约树中均得到分辨;Pseudotsuga近缘于Larix,而Abkes相对近缘于Keteleeria; Cathaya与Ables-Keteleeria-Pseudolarix-Tsuga这一支的关系较远，它与松科的其它属聚在一起，但b∞tstrap分析也不支持它与任何一个属有很近的关 系，说明Cathaya是比较孤立的一个属。Cedrus的位置较特殊，在Wagner简约树中它位于松属以外的其它8个属的基部（因松属为外类群），而在Dollo筒约树中它位于Al}ies-Kete~eer uz-Pseudo/zr/x- Tsuga达一支的基部，并且它与这一支的关系得到了bootstrap分析的较强支持。 C．银杉的rbeL基因长1425bp，其序列与松科其它9个属的rbcL基因序列均有较大差异，从遗传距离(Mega软件中的P-distance)上看，银杉属作为一个属是无可非议的。PAUp和Mega软件分析均表现：Abies、Keteleeria、Pseudolter和Tsuga分为一支，且Cathaya与这一支的关系较远;Pseuaiotsuga近缘于Larix,且这二属间的关系得到了bootstrap分析的强烈支持;Abies近缘于Keteleeria，Pseudolarix近缘于Tsuga，且这两支也得到了bootstrap分析的较强支持;Cathaya与Pinus聚为一支，但支持强度不高。Cetirus的位置与trnK基因的PCR-RFLP分析结果极为相似。 根据rbcL-accD基因片段及trnK基因的PCR-RFLP分析以及rbcL基因的序列分析可以得出如下结论：<1> Cathaya作为一个属不仅是成立的，而且是一个较为孤立的属，将它置于其它任何属内都是不正确的，该属与Abies-Keteleer ia-Pseudolarx-Tsuga这一支的关系较远，相对而言Cathaya与Pinus的关系可能稍近一些。<2>松科主要分为两大支：一支含Abies、KeteZeera、Pseudolarx和Tsuga，该支中Abies近缘于KetelaeriaPseudolarix近缘于Tsuga;另一支含Pseudotsuga、Larix、Cathaya、Pinus和Picete，该支中Pseudotsuga明显近缘于Larix;Cedrus可能更近于Abies-Keteleeria-Pseudolarix-Tsuga这一支。 2．银杉的遗传多样性研究 本研究运用随机扩增多态DNA(RAPD)方法对银杉的1 1 3个个体（分别采自现存全部4个居群：金佛山、花坪、大瑶山和八西山)进行了遗传多样性检测。21个1O-mer的寡核苷酸引物共检测11个位点，其中42个位点是多态的，占37%，这一多态位点百分率仅为裸子植物多态位点百分率平均值的一半左右，说明银杉的遗传多样性水平很低。对多态位点的分析发现银杉屠群内发生了十分严重的遗传漂变，因而导致屠群间的强烈分化。AMOVA分析表明：银杉的遗传变异中，34.7%的变异存在于居群闻，这一数值是裸子植物GST平均值(6。8%)的5倍多;在金佛山屠群中，17%的遗传变异存在于亚居群间，这一数值也是裸子植物GsT平均值的两倍多。银杉的这一居群遗传结构与其它裸子植物的居群遗传结构截然不同。此外，我们提出了度量遗传多样性水平的分化指数概念及其计算方法，并发现遗传多样性水平的高低与生境的复杂程度有一定的相关性。 银杉的遗传多样性水平很低，其适应幅必然很窄，且由于严重的遗传漂变导致居群间的强烈分化，使基因流受阻，进而产生严重的近交，近交又使银杉的适应能力进一步下降，并使极为有限的遗传多样性进一步丧失，这种恶性循环会导致银杉濒危程度的加剧，甚至绝灭。 鉴于银杉独特的居群遗传结构，即有相当大一部分遗传变异存在于居群之间，取样保护时，不仅要在每个居群中取足够多的个体，而且要在尽可能多的居群中取样。就原地保护而言，由于每个居群和亚居群都有独特的基因型，因而都具有保护价值。另外，人工加强居群间的基因流（如人工授粉）对提高银杉各居群的适应能力肯定是有益的。