负磁剪切等离子体中离子温度梯度驱动不稳定性分析

采用打靶法,数值求解了在负磁剪切托卡马克等离子体中离子温度梯度驱动的复本征模方程.数值计算表明,环向旋转剪切流可以整体上改变剪切板η_i不稳定性.在等离子体极小q磁面附近的芯部区域,环向剪切流有稳定η_i模的作用.     

金属覆层五层光波导正常模和异常模的理论分析

本文应用自适应套孔爬山法求解五层金属光波导复本征方程,计算得到了TM00模的正常解和异常解,给出了正常解和异常解的模场分布情况,并对正常解和异常解对应模式的激发情况进行了分析.     

一类奇异复本征方程组的数值计算

1引言 在研究离子温度梯度（ITG）驱动不稳定性中，当电磁效应被考虑后，常会碰到求解下述复本征方程组：     

高能粒子对托卡马克气球模稳定作用的数值分析

用数值方法分析了高能捕获粒子对托卡马克气球模不稳定性的影响.利用变步长RKF积分方法求解了相应的微分-积分方程边值问题.数值结果表明,气球模不稳定区随高能粒子压强增大而缩小,充分说明了高能捕获粒子能部分或全部抑制气球模不稳定性.     

零折射率手征包层光纤中导模的奇异特性

对零折射率手征介质(介电常量和磁导率同时等于零的手征介质)作为包层的光纤中模式的奇异特性进行了理论研究.给出了导模的电磁场分布公式,推导出导模色散方程和功率的数学表达式,通过数值计算,给出了不同手征参量情形下的色散曲线,讨论了手征参量对归一化功率的影响,发现了导模的一些奇异特性,如存在表面波模、基模单模区,出现传播常量...     

撕裂模研究中一类奇异边值问题的数值解法

在数值求解自洽螺旋平衡方程的基础上,计算了撕裂模不稳定性对电流分布的依赖关系,考虑了外螺旋场对安全因子的影响。我们采用了动态交替隐式法来加速平衡方程的收敛,用差分方法有效地处理了具有两个奇点的奇异边值问题。     

弱相对论捕获电子哨声模不稳定性

本文讨论了弱相对论的捕获电子在磁镜位形中对哨声波不稳定性的影响。在简化的箱子模型下,用摄动法求解了带有弱相对论捕获电子效应的本征方程。发现各向异性热电子可以驱动哨声模不稳定性,而相对论效应使不稳定性的各向异性阈值升高,增长率的最大值减小并使不稳定性向低频方向移动。 关键词：     

零折射率手征包层光纤中导模的奇异特性

 对零折射率手征介质（介电常量和磁导率同时等于零的手征介质）作为包层的光纤中模式的奇异特性进行了理论研究.给出了导模的电磁场分布公式,推导出导模色散方程和功率的数学表达式,通过数值计算,给出了不同手征参量情形下的色散曲线,讨论了手征参量对归一化功率的影响,发现了导模的一些奇异特性,如存在表面波模、基模单模区,出现传播常量双值、模式交叉、功率储存现象等,特别是出现了纤芯和包层中的功率都为负值的完全后向波奇异模式.     

原子-异核-三聚物分子转化系统暗态的动力学不稳定性

研究了受激拉曼绝热过程中原子-异核-三聚物分子转化系统暗态的动力学稳定性.通过将量子哈密顿对应到经典哈密顿,并求解和分析线性化经典运动方程后得到的哈密顿-雅克比矩阵本征值,解析地得到了原子-三聚物暗态的动力学不稳定性发生的条件.并以异核原子⁸⁷Rb和⁴¹K混合凝聚体为例,数值地给出了系统发生动力学不稳定性的区域.研究发现,这种动力学不稳定性是由粒子之间的相互作用带来的.此外,还发现系统动力学不稳定性的发生不仅与哈密顿-雅克比矩阵是否出现实数或复数的本征值有关,还 关键词： 原子-异核-三聚物分子转化系统 暗态 受激拉曼绝热过程 动力学不稳定性     

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以磁流体理论为基础,采用基于有限体积法的通量差分分裂格式数值求解具有双曲保守律形式的电阻磁流体方程组.编写C++程序对平板几何位形下的等离子体双撕裂模进行了长时间数值模拟,得到双撕裂模不稳定性的演化图景,捕捉到了双撕裂模非线性发展过程中磁场重联的几个典型阶段,讨论了等离子体电阻和两个有理面之间的距离对双撕裂模不稳定性非线性发展的影响.为研究磁流体动力学提供了一种可行的高精度数值算法.     

三维激光烧蚀瑞利-泰勒不稳定性并行计算

给出了用三维激光烧蚀不稳定性程序求解的物理方程组,简要介绍了所用的数值方法.根据所模拟问题的物理性质和数值模拟方法探索了在多处理机上实行并行计算的技术和方法,并行效率达75%,在此基础上进行了三维多模激光烧蚀不稳定性的数值模拟,深化了对有关物理规律的认识.     

Determination of band structure in one-dimensional complex photonic crystals: A bandedge approach

We present a numerical stable method to easily compute bandgaps of one-dimensional complex basis photonic crystals using novel bandedge equations rather than the traditional dispersion equation. The bandedge equations are derived by the concept of scattering matrix and concisely expressed by the transport coefficients with operations of multiplication and addition only. It is not required to calculate the global transfer matrix or the cosine of Bloch phase to avoid numerical instability. Moreover, we present closed-form expressions to calculate the global scattering matrix without using recursive computation. Finally, numerical examples show that use of the derived bandedge equation has better numerical stability than using the traditional dispersion equation for the band structure analysis.     

二维浅水波方程的数值激波不稳定性

研究二维浅水波方程的数值激波不稳定性问题.线性稳定性分析和数值实验表明,格式的临界稳定性与数值激波的不稳定现象有重要的联系.基于扰动量的增长矩阵分析,本文将高分辨率的数值格式和HLL格式进行特定的加权,设计一类新的混合型数值格式.其中可以调节非线性波速的HLLC与HLL的混合格式,数值试验展示了消除浅水波方程激波不稳定现象的有效性和鲁棒性.     

Numerical simulation of the hydrodynamic instability experiments and flow mixing

Based on the numerical methods of volume of fluid (VOF) and piecewise parabolic method (PPM) and parallel circumstance of Message Passing Interface (MPI), a parallel multi-viscosity-fluid hydrodynamic code MVPPM (Multi-Viscosity-Fluid Piecewise Parabolic Method) is developed and performed to study the hydrodynamic instability and flow mixing. Firstly, the MVPPM code is verified and validated by simulating three instability cases: The first one is a Riemann problem of viscous flow on the shock tube; the second one is the hydrodynamic instability and mixing of gaseous flows under re-shocks; the third one is a half height experiment of interfacial instability, which is conducted on the AWE’s shock tube. By comparing the numerical results with experimental data, good agreement is achieved. Then the MVPPM code is applied to simulate the two cases of the interfacial instabilities of jelly models accelerated by explosion products of a gaseous explosive mixture (GEM), which are adopted in our experiments. The first is implosive dynamic interfacial instability of cylindrical symmetry and mixing. The evolving process of inner and outer interfaces, and the late distribution of mixing mass caused by Rayleigh-Taylor (RT) instability in the center of different radius are given. The second is jelly layer experiment which is initialized with one periodic perturbation with different amplitude and wave length. It reveals the complex processes of evolution of interface, and presents the displacement of front face of jelly layer, bubble head and top of spike relative to initial equilibrium position vs. time. The numerical results are in excellent agreement with that experimental images, and show that the amplitude of initial perturbations affects the evolvement of fluid mixing zone (FMZ) growth rate extremely, especially at late times.     

迎风紧致格式求解Hamilton-Jacobi方程

基于Hamilton-Jacobi(H-J)方程和双曲型守恒律之间的关系,将三阶和五阶迎风紧致格式推广应用于求解H-J方程,建立了高精度的H-J方程求解方法.给出了一维和二维典型数值算例的计算结果,其中包括一个平面激波作用下的Richtmyer Meshkov界面不稳定性问题.数值试验表明,在解的光滑区域该方法具有高精度,而在导数不连续的不光滑区域也获得了比较好的分辨效果.相比于同阶精度的WENO格式,本方法具有更小的数值耗散,从而有利于多尺度复杂流动的模拟中H-J方程的求解.     

Distribution coefficient algorithm for small mass nodes in material point method

When using the time explicit material point method to simulate interaction of materials accompanied by large deformations and fragmentation, one often encounters a numerical instability caused by small node mass, because acceleration on a mesh node is obtained by dividing the total force on the node by the mass of the node. When the material points are in the far sides of the cells containing the node, typically happening near material interfaces, the node mass can be very small leading to artificially large acceleration and then numerical instability. For the case of small material deformations, this instability is typically avoided by placing the material points away from cell boundaries. For cases with large deformations, with the exception of initial conditions, there is no control on locations of the material points. The instability caused by small mass nodes is often encountered. To avoid this instability tiny time steps are usually required in a numerical calculation.     

惯性约束聚变激光烧蚀驱动内界面不稳定性数值模拟

利用水平集方法和三阶本质无振荡(ENO)方法研究了流体力学界面不稳定性和激光烧蚀驱动内界面不稳定性数值模拟,并用数值算例与LARED-S程序的运算结果进行了比较.数值结果表明此方法计算惯性约束聚变激光烧蚀驱动内界面不稳定性的有效性和精确性.     

集总式放大波分复用链路中交叉相位调制的边带不稳定性

集总式放大链路中，放大器的周期分布，等效于形成一折射率光栅，它为四波混频提供了相位匹配的条件，产生边带不稳定性．本文通过解析和数值模拟的方法，研究了周期集总式放 大链路中，交叉相位调制边带不稳定性．解析研究中，根据耦合方程的稳态解，计算了反常 色散与正常色散光纤链路中由于扰动而产生的边带不稳定性的增益；数值模拟中，利用分裂 步长傅里叶变换法与Monte_Carlo方法，得出了输出光脉冲的频谱，说明输出光脉冲频谱中 产生新的边带．两种方法的计算结果表明，在周期集总式放大光通信链路中，存在交叉相位 调制边带不稳定性，两种方法得到的结论基本一致． 关键词： 交叉相位调制 边带不稳定性 集总式放大     

管道后传声数值模拟的不稳定波抑制

在管道后传声的数值模拟中,必须考虑平均流剪切层的散射效应,然而在非均匀剪切流动下时域求解线化欧拉方程会面临Kelvin-Helmholtz不稳定波产生和放大的难题。已有的不稳定波抑制技术通常很难获得令人满意的结果。本文采用一种混合方法,首先引入有限时段的宽频声源波包将声波和不稳定波分离,进而采用声源滤波器技术对不稳定波进行抑制。数值验证算例选择半无限长轴对称环形硬壁直管道,采用计算气动声学方法时域求解2.5维线化欧拉方程,无背景流动的数值解与解析解符合很好,验证了程序的精度与可靠性,非均匀流动算例则表明所采用波包加声源滤波器混合方法对不稳定波抑制效果明显,对声场影响很小,充分显示了该方法的精度与可行性。     

A new particle method for simulating breakup of liquid jets

A corrected smoothed particle hydrodynamics (CSPH) method for simulating two-phase flows including surface tension is presented. The effects of the instability in the compressional regime and particle deficiency are suppressed by adopting a new smoothing kernel and its gradient corrections. The insensitivity to the compressional instability of the adopted method is confirmed by numerical tests. The method is validated and calibrated through a series of standard numerical tests and showed quantitative agreements. The method is extended to two-dimensional jet breakup problems and provided good comparison to the theoretical and experimental results. In particular, the numerical model exhibits the transition from the jetting to dripping when the Weber number is close to its theoretical critical value.