三维对流扩散方程非等距网格上的四阶紧致格式及其多重网格方法

提出了数值求解三维变系数对流扩散方程非等距网格上的四阶精度19点紧致差分格式,为了提高求解效率,采用多重网格方法求解高精度格式所形成的大型代数方程组。数值实验结果表明本文方法对于不同的网格雷诺数问题,在精确性、稳定性和减少计算工作量方面均明显优于7点中心差分格式。     

磁化尘埃等离子体中的冲击波及其横向扰动稳定性

利用双曲函数法得到ZKB方程的一组冲击波解,并对波在横向扰动下的动力学稳定性进行研究.对冲击波解进行线性稳定性分析,并构造高精度的有限差分格式求解所得本征值问题.结果表明：对于正耗散的情形,该冲击波在线性意义下稳定;对于负耗散情形,该冲击波在线性意义下不稳定.构造有限差分格式对受扰动的冲击波进行非线性动力学演化,结果表明：对于正耗散的情况,该冲击波是稳定的.     

相对论性流体力学方程组的数值解法

本文叙述了用有限差分方法求解相对论性流体力学方程组的数值解的方法,给出了差分格式推导的详细步骤及处理含有相变问题的求解方法,并给出了若干具体问题的解的图象。     

带扩散项色散方程的交替分组差分方法

给出了逼近带扩散项色散方程的非对称差分格式,并用这些差分公式构造了求解色散方程的交替分段差分算法,算法是无条件稳定的,能直接在并行机上使用,并给出了模型问题的试验结果.     

蒙特卡罗方法在解微分方程边值问题中的应用

介绍了蒙特卡罗方法的基本原理以及随机数的产生方法。基于蒙特卡罗方法的思想,结合有限差分方法,建立了求解微分方程边值问题的随机概率模型,并以第一类边界条件的拉普拉斯方程和一个给定初值及边界条件的非稳态热传导方程为数值算例,研究了蒙特卡罗方法在求解微分方程边值问题中的应用。结果表明:利用蒙特卡罗方法,不仅可以有效解决给定边界条件的微分方程,对于给定初值条件的微分方程,也可以从时域有限差分方程出发,采用蒙特卡罗方法进行求解。数值模拟和对误差的理论分析均表明,增加蒙特卡罗试验中的模拟粒子点数,可以提高计算结果的精度。     

求解非线性差分方程孤立波解的直接代数法

推广了求解非线性差分方程孤立波解的直接代数法.用此方法研究了Hybrid晶格方程，借助于符号计算Maple,得到它的新孤波解.这种方法也可用于求解其他的差分方程. 关键词： 微分-差分方程 Hybrid晶格方程 行波解 孤     

薄板弯曲问题的变分-差分方法

从最小势能原理出发,使用变分-差分方法构造带有弯曲边梁的薄板的小挠度弯曲问题的差分格式,所得格式仅依赖板面网格结点,从而避免了由于引入虚拟网格结点而带来的问题;编制求解差分方程组的MATLAB程序,给出数值模拟结果.     

求解隐式差分方程的并行算法

本文研究了求解隐式差分方程的并行算法,其基本想法是把差分方程组化为若干个子方程组来求解,文中给出了直接法和迭代法,证明了迭代法的收敛性。为了说明分段隐式迭代方法的有效性,文中针对扩散方程的具体例子给出了数值试验计算结果。     

基于量子微扰的AlGaN/GaN异质结波函数半解析求解

基于量子力学微扰理论的分析，得到AlGaN/GaN异质结波函数的半解析模型.给出了模型的理论分析和计算结果.对于相同问题，给出了与差分算法的对照结果.与传统的差分方法相比，半解析方法具有收敛性强、大规模问题计算效率高的特点，更适合作为AlGaN/GaN异质结量子阱的求解算法. 关键词： AlGaN GaN 量子阱 薛定谔方程     

离心叶轮及无叶扩器内湍流的非结构化网格数值解法

利用非结构化网格上的有限体积法对三维湍流进行了数值研究,提出了不用求解单元顶点处变量值的二阶混合差分格式,既避免了复杂耗时的单元顶点处变量值的计算,又避免了普通差分格式在非结构化网格上易于引起网格界面方向相关性问题。最后利用非结构化网格计算程序,数值求解了一台离心风机内叶轮及无叶扩压器通道内三维相对定常湍流,计算结果与实验值的比较表明速度的计算值与实验值吻合较好。     

An Elliptic Grid Generation Technique for the Flow Contraction

In this paper, we determined a numerical solution of the incompressible Navier-Stokes equations for the flow inside the contraction geometry. The governing equations are written in the vorticity-stream function formulations. The numerical solution is based on a technique of automatic numerical generation of a curvilinear coordinate system by transforming the governing equation into computational plane. The transformed equations are approximated using central differences and solved simultaneously by successive over-relaxation iteration.     

Numerical simulation for the flow inside V-shapes using grid generation

In this paper, we determined a numerical solution of the Navier-Stokes equations for the flow of incompressible fluid inside the contraction geometry. The governing equations are written in the vorticity-stream function formulations. The numerical solution is based on a technique of automatic numerical generation of a curvilinear coordinate system by transforming the governing equation into the computational plane. The transformed equations are approximated using central differences and solved simultaneously by the alternating direction implicit method and successive over relaxation iteration method.     

Novel method for solution of coupled radial Schrödinger equations

One of the major problems in numerical solution of coupled differential equations is the maintenance of linear independence for different sets of solution vectors. A novel method for solution of radial Schrödinger equations is suggested. It consists of rearrangement of coupled equations in a way that is appropriate to avoid usual numerical instabilities associated with components of the wave function in their classically forbidden regions. Applications of the new method for nuclear structure calculations within the hyperspherical harmonics approach are given.     

System of matrix-vector equations in the multiconfiguration Hartree-Fock method

A method for determining radial parts of one-electron functions entering the manyelectron basis is proposed within the multiconfiguration Hartree-Fock procedure. The solution of the Hartree-Fock equations is reduced to the solution of a system of matrix-vector equations. Rules of construction of these equations are formulated, and a stable numerical scheme of their solution is found.     

A finite difference method with non-uniform timesteps for fractional diffusion and diffusion-wave equations

An implicit finite difference method with non-uniform timesteps for solving fractional diffusion and diffusion-wave equations in the Caputo form is presented. The non-uniformity of the timesteps allows one to adapt their size to the behaviour of the solution, which leads to large reductions in the computational time required to obtain the numerical solution without loss of accuracy. The stability of the method has been proved recently for the case of diffusion equations; for diffusion-wave equations its stability, although not proven, has been checked through extensive numerical calculations.     

Numerical solution of differential-algebraic equations in mechanical systems simulation

The numerical solution of the differential-algebraic equations of motion of mechanical systems offers many computational challenges. In this paper we describe progress which has been made in understanding the formulation of the equations of motion from the viewpoint of numerical stability, and outline some of the difficulties which must be resolved for efficient and reliable numerical methods in real-time simulation of mechanical systems.     

一种最优控制数值计算方法

本文为解决非线性微分方程自治系统的周期轨道的数值计算,提出了一种最优控制的数值计算方法。其方法的实质是利用连续的打靶法,在非线性最小二乘公式的监护下,附加惩罚函数进行控制来实现的。并利用该法计算了典型的化学反应模型。     

Magnetic Field in a Screw Flow with Fluctuations

We consider the influence of fluctuations in a screw flow of a conducting liquid on the effect of magnetic field self-excitation; the solution of this problem is important for experimental realization of a turbulent dynamo. We propose a theoretical approach based on the solution of averaged equations obtained in the limit of a short correlation time. The applicability of this approach is confirmed by direct numerical simulation of the initial equations. We demonstrate the influence of the correlation of fluctuations on the dynamo effect threshold. It is shown that the solution of the mean-field equations differs from the solution based on direct numerical simulation for a finite correlation time. The advantages and disadvantages of the two approaches are estimates, as well as the importance of the discovered difference in the context of problems of magnetic field self-excitation. The influence of helicity and intermittency on the type of the solution is considered.     

LD泵浦Nd∶YVO4晶体GaAs被动调Q激光理论和实验研究

考虑LD泵浦光强和腔内振荡光强的空间高斯分布以及晶体热效应的影响，给出了Nd∶YVO₄晶体GaAs被动调Q1.06 μm激光的耦合速率方程组，数值求解该方程组获得了输出激光的平均输出功率、脉冲宽度、重复率随泵浦功率的变化特性，所得理论值与实验结果相符.     

大气压下自由燃烧弧的温度场和速度场的数值模拟

采用标准SIMPLE算法，并作了一些修正，给出了具体的计算步骤和流程图，将其应用于磁流体动力学(MHD)方程进行数值求解．得到了轴对称情况下，自由燃烧弧的温度场和速度场的分布，并和实验结果进行了比较。分析了不同辐射模型对温度场的影响，发现辐射导致电弧温度降低，但不同的辐射模型对于电弧的温度影响不大。