中子裂变链统计涨落问题的数值计算方法

研究了弱中子源驱动下,裂变系统中子裂变链统计涨落问题的数值计算方法。进行了数值计算建模、数值方法分析、数值计算检验、一类问题概率分布函数的统计涨落特征量的数值计算示范。特例数值检验表明:只要数值解方程组阶数(截断) N足够大,数值解满足归一(守恒) 律、指数增长律,并与精确解析解一致。对于非定常裂变系统中子裂变链统计涨落问题提出了一维等效模型下数值模拟的方法。     

A hybrid numerical simulation of isotropic compressible turbulence

A novel hybrid numerical scheme with built-in hyperviscosity has been developed to address the accuracy and numerical instability in numerical simulation of isotropic compressible turbulence in a periodic domain at high turbulent Mach number. The hybrid scheme utilizes a 7th-order WENO (Weighted Essentially Non-Oscillatory) scheme for highly compressive regions (i.e., shocklet regions) and an 8th-order compact central finite difference scheme for smooth regions outside shocklets. A flux-based conservative and formally consistent formulation is developed to optimize the connection between the two schemes at the interface and to achieve a higher computational efficiency. In addition, a novel numerical hyperviscosity formulation is proposed within the context of compact finite difference scheme for the smooth regions to improve numerical stability of the hybrid method. A thorough and insightful analysis of the hyperviscosity formulation in both Fourier space and physical space is presented to show the effectiveness of the formulation in improving numerical stability, without compromising the accuracy of the hybrid method. A conservative implementation of the hyperviscosity formulation is also developed. Combining the analysis and test simulations, we have also developed a criterion to guide the specification of a numerical hyperviscosity coefficient (the only adjustable coefficient in the formulation). A series of test simulations are used to demonstrate the accuracy and numerical stability of the scheme for both decaying and forced compressible turbulence. Preliminary results for a high-resolution simulation at turbulent Mach number of 1.08 are shown. The sensitivity of the simulated flow to the detail of thermal forcing method is also briefly discussed.     

Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions

A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on the constructed SKIE. Its performance is illustrated via several numerical examples.     

间断有限元方法求解一维非平衡辐射扩散方程

研究一维非平衡辐射扩散方程的数值方法.通过求解间断系数热传导方程的广义黎曼问题,得到一种带加权数值流量,基于该数值流量构造了一类新型的间断有限元方法.在时间离散上采用向后Euler方法,形成的非线性方程组采用Picard迭代求解.数值试验表明该方法具有捕捉大梯度的能力,而且能适应扩散系数间断的情形.     

Implicit schemes for real-time lattice gauge theory

We develop new gauge-covariant implicit numerical schemes for classical real-time lattice gauge theory. A new semi-implicit scheme is used to cure a numerical instability encountered in three-dimensional classical Yang-Mills simulations of heavy-ion collisions by allowing for wave propagation along one lattice direction free of numerical dispersion. We show that the scheme is gauge covariant and that the Gauss constraint is conserved even for large time steps.     

奇异微分方程边值问题的数值解法

本文给出求解奇异微分方程边值问题的正则化方法。解在奇点邻域内展开成级数形式,在余下区间上推导出正则边值问题,应用差分方法求解,并给出收敛结果和数值算例。     

基于微波工作室的盘荷波导耦合器设计方法

提出了一种新的盘荷波导耦合器数值设计方法; 通过分析Kyhl提出的耦合器调节原理, 将输入阻抗之间的相差关系转换为耦合器输入波导的边界条件关系, 由此 利用Microwave Studio的EigenMode Solver求解本征值问题来实现对耦合器 调谐、调匹配过程的模拟; 并给出一个实例来说明数值计算方法的可行性和可靠性.     

Simulation of statistical errors in a high-rate fiber-optic communications line

Simple analytical formulas are derived for the approximation of the error probability of data transmission in fiber-optic communications lines. A direct numerical simulation of the propagation of narrow and wide optical pulses is performed. A good agreement of the analytical approximation and the numerical results is demonstrated.     

共轭梯度法求解多宗量瞬态热传导反问题

提出瞬态热传导反问题中热物性参数和边界条件多宗量反演的一般数值求解模式,导出了敏度计算公式,并用共轭梯度法求解,探讨了测点数目、测量误差和变量初值对反演结果的影响,并进行了数值验证.     

Non-linear propagation in near sonic flows

A non-linear analysis is developed for sound propagation in a variable-area duct in which the mean flow approaches choking conditions. A quasi-one-dimensional model is used and the non-linear analysis represents the acoustic disturbance as a sum of interacting harmonics. The numerical procedure is stable for cases of strong interaction and is able to integrate through the throat region without any numerical instability.     

Numerical solution of the direct scattering problem through the transformed acoustical wave equation.

A transformation is applied to the acoustical wave equation to obtain a new equivalent form that does not contain gradients of the pressure. A new technique, based on the spectral method, is developed for the numerical solution of the direct time domain scattering problem. Modeling techniques for obtaining accurate solutions are discussed and numerical examples are presented.     

基于WENO重构的熵稳定格式求解浅水方程

针对浅水方程,提出一种数值求解格式:空间方向采用满足熵稳定条件的数值通量,并在单元交界面处进行高阶WENO重构,时间上的推进采用强稳定的Runge-Kutta方法.模拟一维和二维经典问题,结果表明,该格式具有分辨率高、基本无振荡性等特点.     

Analytical energy gradients for dynamical simulations of trans polyacetylene chains within the Pariser-Parr-Pople Hamiltonian

Exact analytical energy gradients for the Pariser-Parr-Pople (PPP) Hamiltonian are derived. A comparison of computer times for dynamical simulations of trans-Polyacetylene (t-PA) using analytical and numerical gradients is given. The numerical method is shown to lead to serious difficulties both computationally and from the point of view of numerical accuracy. In fact, using the analytical method, it turned out that the computational effort for the gradient calculation is negligible compared to that for the SCF iteration in each time step of a simulation. On the other hand, using the numerical method the gradient calculation is the time consuming bottle-neck of a simulation. A previously presented method for the gradient calculation in the Hückel type Su-Shrieffer-Heeger (SSH) Hamiltonian which was thought to be approximative, is shown to be exact.     

耦合边处理的特征无反射边界条件研究

详细分析特征无反射边界条件(Characteristic Non-reflecting Boundary Conditions)中边耦合处理方法,提出耦合处理的数学方法,数值模拟表明,该方法处理声波扰动时有明显的优势.对可压缩圆孔射流进行直接数值模拟,结果与试验吻合较好,表明提出的耦合边处理的特征边界数学分析方法是可行的.     

Analysis of the evolution of perturbations in a magnetized collisionless plasma with an integral-equation technique

Summary A technique recently proposed to study the classical problem of the evolution of small perturbations in a collisionless unmagnetized plasma is extended to a magnetized plasma. A time-convolutive integral equation for the plasma density is obtained from the Vlasov equation for a homogeneous plasma in a uniform, stationary magnetic field. The equation can be solved by means of simple numerical algorithms and, in some cases, analytical solutions can be obtained. The procedure proves to be analytically simpler than the classical one and is more convenient from a numerical point of view. Techniques of solution are presented and analytical and numerical results for electrostatic perturbations are discussed.     

隐-显积分因子间断Galerkin方法求解二维辐射扩散方程

提出一种求解二维非平衡辐射扩散方程的数值方法.空间离散上采用加权间断Galerkin有限元方法,其中数值流量的构造采用一种新的加权平均;时间离散上采用隐-显积分因子方法,将扩散系数线性化,然后用积分因子方法求解间断Galerkin方法离散后的非线性常微分方程组.数值试验中在非结构网格上求解了多介质的辐射扩散方程.结果表明:对于强非线性和强耦合的非线性扩散方程组,该方法是一种非常有效的数值算法.     

Finite-element method in the space-time domain for nonstationary electrodynamics

A new numerical method for solving problems of nonstationary electrodynamics is suggested that uses integro-differential equations and finite-element representation of fields. Examples of numerical calculations are given.     

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.     

Energy based simulation of a Timoshenko beam in non-forced rotation. Influence of the piano hammer shank flexibility on the sound

A nonlinear model for a vibrating Timoshenko beam in non-forced unknown rotation is derived from the virtual work principle applied to a system of beam with mass at the end. The system represents a piano hammer shank coupled to a hammer head. An energy-based numerical scheme is then provided, obtained by non-classical approaches. A major difficulty for time discretization comes from the nonlinear behavior of the kinetic energy of the system. This new numerical scheme is then coupled to a global energy-preserving numerical solution for the whole piano. The obtained numerical simulations show that the pianistic touch clearly influences the spectrum of the piano sound of equally loud isolated notes. These differences do not come from a possible shock excitation on the structure, or from a changing impact point, or a “longitudinal rubbing motion” on the string, since neither of these features is modeled in our study.     

A lattice Bhatnagar--Gross--Krook model for a class of the generalized Burgers equations

A new lattice Bhatnagar--Gross--Krook (LBGK) model for a class of the generalized Burgers equations is proposed. It is a general LBGK model for nonlinear Burgers equations with source term in arbitrary dimensional space. The linear stability of the model is also studied. The model is numerically tested for three problems in different dimensional space, and the numerical results are compared with either analytic solutions or numerical results obtained by other methods. Satisfactory results are obtained by the numerical simulations.