基于计算机的光衍射的数值计算与显示

本文研究了基于计算机的光场分布的数值计算与显示方法。从光的菲涅尔衍射、波前相位重构入手,对连续信号进行了离散化处理,给出了数值计算公式。对光波通过矩形孔径、传播后的光场分布进行了数值计算与显示。仿真结果表明数值计算更加直观地展现了光的特性,并提供可视化的验证。     

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.     

串级结构Z扫描特性的分析

对非线性介质串级结构的Z扫描特性进行了分析，分别给出了解析解和数值解. 解析分析主要是基于高斯分解方法（GDM）和分布透镜方法的组合；数值分析采用了Crank-Nicholson有限差分方法和快速汉克尔变换方法(FHT). 同时，也给出了这两种数值分析的使用条件和方法. 将解析结果、数值结果和实验结果进行了比较，结果显示它们具有很好的一致性. 关键词： 串级结构 Z扫描 有限差分方法 快速汉克尔变换     

空间差分格式对有限体积法数值散射的影响

数值散射是辐射传递方程近似算法中最常见的离散误差。本文主要讨论空间差分格式对有限体积法数值散射的影响。构造激光平行及倾斜入射的物理模型,验证和比较阶梯格式、中心差分格式及指数格式下温度场的计算精度及数值散射特性。计算结果表明,在激光平行入射与倾斜入射两种情况下,阶梯格式引起的的数值散射比菱形格式及指数格式要多,但其计算精度高于菱形及指数格式。不同激光入射条件下,各种差分格式表现出的数值散射分布有明显的差异。     

极端相对论快电子分布等离子体中横振荡色散关系

本文对各向同性极端相对论快电子呈幂律分布等离子体中横振荡色散关系进行了解析和数值研究.得到长波支和短波支色散关系的解析表达式.由于解析近似对波数的限制,无法得到全波数空间色散曲线,因此对色散方程进行了数值求解.研究表明,在满足长波支和短波支条件时,解析色散曲线与数值色散曲线完全符合.此外,利用多项式回归的方法对数值结果进行拟合,得到不同参数下快电子分布等离子体横振荡色散关系近似表达式,该结果为进一步研究快电子分布等离子体的性质提供了重要的理论依据. 关键词： 相对论性等离子体 快电子分布 色散关系 数值计算     

热传导方程三层并行差分格式初始条件的计算

给出二维热传导问题的三层差分格式初始条件的一种显式计算方法,对于由此形成的内边界预估校正三层并行差分算法,证明稳定性和收敛性定理.并行数值试验表明,方法稳定,且与通常采用隐式格式计算初始条件的方法相比,易于程序实现;与已有的扰动算法相比,能大幅度减小误差.     

自适应光学系统的数值模拟：动态控制过程和频率响应特性

对自适应光学系统的动态控制过程进行了数值模拟。与自动控制理论的解析分析相比,动态控制过程的数值模拟有其优越性。系统的频率响应特性与动态控制性能密切相关,对自适应光学系统的频率响应特性也进行了数值模拟。模拟计算的结果与实验测量结果符合得很好。还实现了多频率成份的同时计算,可以大大提高计算效率。其结果与单频率结果只在低频下有小的差别,可以满足得到带宽和裕量等参数的实用要求。将频率响应特性的模拟计算与长时间曝光斯特列耳（Strehl)比的数值模拟结合,可得到对自适应光学系统性能的有效评估。     

A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine

Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy.     

光子晶体光纤数值孔径的测量和数值研究

光纤的数值孔径是光纤的重要参数,大数值孔径光纤在激光器和激光感应荧光系统中有很好的应用前景。光子晶体光纤的数值孔径与传统阶跃型光纤不同,它与光波长有密切的关系。因此,本文用光谱仪测量了不同结构的折射率引导型光子晶体光纤的数值孔径,并进行了数值模拟,研究了光波长、包层空气孔直径、孔间距等对光子晶体光纤数值孔径的影响,同时对光子晶体光纤的非线性系数、宏弯损耗、截止波长、有效模面积等与光波长有关的参数进行了研究,取得了满意的结果。     

An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model

We propose a discretization method of a five-equation model with isobaric closure for the simulation of interfaces between compressible fluids. This numerical solver is a Lagrange–Remap scheme that aims at controlling the numerical diffusion of the interface between both fluids. This method does not involve any interface reconstruction procedure. The solver is equipped with built-in stability and consistency properties and is conservative with respect to mass, momentum, total energy and partial masses. This numerical scheme works with a very broad range of equations of state, including tabulated laws. Properties that ensure a good treatment of the Riemann invariants across the interface are proven. As a consequence, the numerical method does not create spurious pressure oscillations at the interface. We show one-dimensional and two-dimensional classic numerical tests. The results are compared with the approximate solutions obtained with the classic upwind Lagrange–Remap approach, and with experimental and previously published results of a reference test case.     

An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

A formally second-order accurate immersed boundary method is presented and tested in this paper. We apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first-order method. The numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high Reynolds number flows with immersed boundaries.     

Abel变换数值反演的离散正则化方法

基于Tikhonov的正则化思想,将Abel变换的理论反演公式与对数值求导的离散正则化处理以及带权的Gauss型积分相结合,给出了Abel变换数值反演的一个新算法,并进行了理论分析与数值实验。结果表明:该算法具有精度高、数值稳定等优点。     

二维氢原子中的基态奇异特性数值精确对角化法

利用数值有限差分法处理二维氢原子的基态波函数时,计算结果发现其存在着数值奇异特性.本文通过构造一套具有正交完备性的离散贝塞尔基函数,并结合基于Lanczos技术的数值精确对角化方法研究二维氢原子中的基态波函数的数值奇异特性,得到的波函数数值解及其相应的本征能量均与解析结果相一致.这套新的完备的离散贝塞尔基函数,可以在研究一些波函数具有数值奇异特性的体系中发挥至关重要的作用.     

环形浅液层内热流体波的可视化实验研究

对外壁加热、内壁冷却、厚度为1.0 mm的环形硅油浅液层内的热毛细对流及其稳定性进行了可视化实验研究,观察到了旋转的螺纹状的热流体波,确定了发生热流体波的临界温差值△Tc=4.8 K,证实了热流体波从两组逐渐演变为一组的发展过程,验证了已有的数值模拟结果.     

Bifurcation structures and transient chaos in a four-dimensional Chua model

A four-dimensional four-parameter Chua model with cubic nonlinearity is studied applying numerical continuation and numerical solutions methods. Regarding numerical solution methods, its dynamics is characterized on Lyapunov and isoperiodic diagrams and regarding numerical continuation method, the bifurcation curves are obtained. Combining both methods the bifurcation structures of the model were obtained with the possibility to describe the shrimp-shaped domains and their endoskeletons. We study the effect of a parameter that controls the dimension of the system leading the model to present transient chaos with its corresponding basin of attraction being riddled.     

Evaluation of numerical scattering in finite volume method for solving radiative transfer equation by a central laser incidence model

The numerical scattering caused by spatial discretization in finite volume method is discussed. Based on an analysis of the generation process of numerical scattering, a physical model of central laser incidence to a two-dimensional rectangle containing semitransparent medium is established to validate the numerical scattering, with Monte Carlo method as benchmark, in which numerical scattering does not exist. Numerical scattering will be affected by spatial grid number, spatial differential schemes and spectral absorption coefficient. With the spatial grid number increasing, numerical scattering will be decreased. The accuracy of the diamond scheme is the highest, and the exponential scheme is a bit lower, the lowest accuracy of the three schemes is the step scheme. The tendency of numerical scattering is reverse, i.e., the step scheme produces minimum numerical scattering, and exponential scheme produces more, while the diamond scheme produces maximum among three methods. When the bias of absorption efficient is high, the numerical scattering cannot be eliminated only by increasing the grid number. If we set the direction of laser incidence as central axis, it can be seen that numerical scattering distributed symmetry along the axis, which can be called as symmetrical cross-scattering. All of the three schemes show symmetrical cross-scattering.     

A New Differential Method Applied to the Study of Arbitrary Cross Section Microstructured Optical Fibers

The present work adapts a recent grating theory called “Fast Fourier factorization” to cylindrical coordinates in order to study microstructured optical fibers (MOFs). Compared with the classical differential method, this new differential method takes into account the truncation of Fourier series and the discontinuities of the fields across the diffracting surface with the help of new factorization rules. The main advantage of this method is that the directrix of the diffracting cylindrical surface is arbitrary and permits anisotropic and inhomogeneous media although its numerical application needs longer computation time, compared with other well-known numerical methods. The S-propagation algorithm is used to avoid numerical contaminations. The numerical results are validated and compared with the well-established Multipole method in the case of a MOF with six circular cylinders. Further, a new cross-sectional profile (with sectorial inclusions) that the Multipole method cannot consider is studied.     

On Physically Unacceptable Numerical Solutions Yielding Strong Chaotic Signals

Physically unacceptable chaotic numerical solutions of nonlinear circuits and systems are discussed in this paper. First, as an introduction, a simple example of a wrong choice of a numerical solver to deal with a second-order linear ordinary differential equation is presented. Then, the main result follows with the analysis of an ill-designed numerical approach to solve and analyze a particular nonlinear memristive circuit. The obtained trajectory of the numerical solution is unphysical (not acceptable), as it violates the presence of an invariant plane in the continuous systems. Such a poor outcome is then turned around, as we look at the unphysical numerical solution as a source of strong chaotic sequences. The 0–1 test for chaos and bifurcation diagrams are applied to prove that the unacceptable (from the continuous system point of view) numerical solutions are, in fact, useful chaotic sequences with possible applications in cryptography and the secure transmission of data.     

Method of fundamental solutions with optimal regularization techniques for the Cauchy problem of the Laplace equation with singular points

The purpose of this study is to propose a high-accuracy and fast numerical method for the Cauchy problem of the Laplace equation. Our problem is directly discretized by the method of fundamental solutions (MFS). The Tikhonov regularization method stabilizes a numerical solution of the problem for given Cauchy data with high noises. The accuracy of the numerical solution depends on a regularization parameter of the Tikhonov regularization technique and some parameters of the MFS. The L-curve determines a suitable regularization parameter for obtaining an accurate solution. Numerical experiments show that such a suitable regularization parameter coincides with the optimal one. Moreover, a better choice of the parameters of the MFS is numerically observed. It is noteworthy that a problem whose solution has singular points can successfully be solved. It is concluded that the numerical method proposed in this paper is effective for a problem with an irregular domain, singular points, and the Cauchy data with high noises.