Arnoldi方法简述及其在流动稳定性中的应用

流动稳定性问题常常归结于巨型非对称矩阵特征值问题。多数求解巨型非对称矩阵特征问题的算法均是经基本的Arnoldi算法演化而来。首先简述基本的Arnoldi算法; 其次简述基于Arnoldi算法的几类变体, 如显式重启Arnoldi算法,隐式重启Arnoldi算法与多重隐式重启Arnoldi算法; 最后基于Arnoldi算法及其变体结合谱位移技术求解计算流动稳定性问题, 并通过数值实验比较可知结合谱位移技术的多重隐式重启Arnoldi算法的求解效率最高。      

谱方法用于非定常流动计算的隐式求解

本文对谱方法用于周期性非定常流动的隐式求解方法进行了探讨,分析了影响计算稳定性和收敛速度的因素.提出了结合多重网格的隐式求解方法并对算法进行了验证,初步计算表明本文算法具有良好的稳定性和收敛速度.对于周期性非定常流动,结合本文提出的隐式求解的时域谱方法可以达到很高的精度且具有良好的计算效率.     

树形多体Hamilton系统辛算法

研究了树形多体Ｈａｍｉｌｔｏｎ系统的隐式辛算法。用矩阵形式给出了系统的正则方程及其右端函数的Ｊａｃｏｂｉ矩阵，并给出该矩阵的分块算法，可提高计算效率。隐式辛Ｒｕｎｇｅ－Ｋｕｔｔａ算法被采用，数值结果表明给出的算法计算效率高，并可保持长期数值计算的稳定性。     

非线性热传导方程的分组隐式解法及数值结果

对于激光物理研究中提出的一个非线性热传导问题,利用Saul'yev非对称格式构造了适合并行计算的分组隐式解法.数值试验表明,新算法与通常的隐式算法计算精度相当,迭代次数相同.     

基于半隐式算法的反应欧拉方程数值计算

在处理反应欧拉方程中源项所引起的刚性问题时,发展了一种IMEX(Implicit-Explicit)型Additive Runge-Kutta半隐式算法,此方法能够节省计算时间和内存;该算法对方程中的非刚性对流项进行显式计算,刚性源项则用半隐式格式计算。为了验证该算法的可行性,通过对典型的马赫反射、二维气相爆轰、爆轰波的传播和爆轰胞格结构进行了数值模拟。模拟结果表明:该算法能够很好地处理由源项引起的刚性问题,准确地反应马赫反射情况,且得到的胞格结构与实验结果十分吻合。     

虚拟流体方法的显隐算法

基于算子分裂,把欧拉方程分裂成对流项和非对流项两部分,建立一种基于原始变量的二阶显隐算法.由通常的虚拟流体方法显式地预估流场,用隐式的压力修正对预估解进行修正.计算结果表明,这样可以有效增大时间步长,提高计算效率.     

一种基于可见光的隐式成像通信调制算法研究

针对现有可见光隐式成像通信调制算法隐式效果差、算法复杂的问题,提出了一种基于蓝色通道拉普拉斯最高层金字塔的隐式信息调制算法。该算法利用人眼视觉系统对黄蓝分量不敏感的特性,仅对蓝色通道图像进行拉普拉斯金字塔分解,并在最高层嵌入隐式信息。此外,考虑到图像纹理差异对隐式效果的影响,采用图像熵作为衡量图像间纹理复杂程度的指标,设计了一种基于纹理复杂度的图像分类器,并对不同分类图像的隐式效果进行了分析。仿真结果显示,所提调制算法的峰值信噪比平均可达到40.46 dB,相较于一般拉普拉斯金字塔调制算法,性能提升了5 dB,可有效增强系统的隐式效果。     

光伏电池组件隐式、显式单二极管模型准确性对比研究

光伏电池组件非线性输出特性的物理建模及其优化参数的准确提取是光伏发电系统设计计算、性能评估及优化控制的重要前提.相对于传统的隐式单二极管模型,该文在光伏电池显式单二极管模型的基础上利用Lambert W函数推导了光伏组件的显式单二极管模型,提出一种基于重启边界约束Nelder-Mead单纯形算法的参数提取方法rbcNM,并利用两种典型光伏电池组件的实测数据对隐式、显式单二极管模型的准确性进行了对比测试和验证.结果表明:rbcNM算法可以快速准确的提取隐式、显式单二极管模型的优化参数,计算结果与实测数据具有很好的一致性,相对于已有文献在准确度上取得了大幅度的提升;显式单二极管模型的准确性显著高于隐式单二极管模型,对光伏电池组件的电流-电压和功率-电压特性曲线具有更高的拟合精度.     

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.     

一种能克服两方程湍流模型刚性的流热一体化算法

使用流热一体化算法解决传统耦合算法难于处理的流场与固体温度场耦合计算问题.为保证其计算效率,提出一个简单有效的方法用以克服两方程湍流模型刚性.给出该方法的理论证明,并验证其配合多重网格提高LUSGS隐式时间推进法的计算效率.     

High order finite difference methods with subcell resolution for advection equations with stiff source terms

A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers.     

光在二维无序介质中的动态传播过程

用有限时域差分 FDTD 法研究了光在二维无序介质中的动态传播过程.数值模拟了某一高斯脉冲光束入射到无序介质中光场的空间分布随时间的演化,结果表明：在光束入射的初期,能量从光源区向外传播并出现了清晰的波前传播的特点;经过一定的时间后,有部分能量从光源区向外扩散,而大部分能量逐渐聚集在介质中的一些小区域内,这与整体散射模型关于无序介质中光子局域化的研究相吻合,而且更清晰地呈现了形成光子局域化过程中的物理现象及整体散射干涉效应的重要机理作用.     

二阶孤子的传输和相互作用

用分步傅里叶变换法求解二阶孤子传输的非线性薛定谔方程, 得到了在此条件下孤子传输的数值图形, 发现二阶孤子在传输中被压缩, 幅值振荡变化。2个二阶孤子在传输过程中没有出现象2个一阶孤子那样周期性碰撞, 但2个二阶孤子时间间隔较小时, 随传输距离在2个二阶孤子中间周期性地衍生出第3个孤子。研究证明：二阶孤子的传输具有与一阶孤子明显不同的特征。     

Mechanism of stratospheric ozone depletion. 1. On chain processes in the stratosphere

The characteristics of the chain processes of stratospheric ozone depletion are considered. It is shown that the basic feature of these processes is the presence of a limiting stage, which determines the rate of chain propagation in this process and, accordingly, the rate of ozone depletion. It is also shown that the practice, so far widespread in the stratospheric chemistry, of defining the rate-limiting step of the chain process as a single reaction with the lowest rate throughout the stratosphere does not enable to correctly determine the rare of the chain process and leads to a significant overestimation of the latter. Methods for correctly calculating the rate of the limiting step for an arbitrary number of chain propagation reactions and for determining the termination rate and the chain length are for the first time proposed. Application of the developed method is demonstrated by the example of the nitrogen oxide cycle.     

低渗透多孔介质非达西渗流动边界界面追踪

基于低渗透多孔介质非达西不稳定渗流的动边界数学模型,推导动边界移动速度的微分表达式,揭示动边界移动速度与动边界上地层压力关于径向距离的二次导数成正比;由此利用拉格朗日三点插值公式求得动边界附近控制方程的有限差分格式,并对下一时刻动边界的精确位置进行追踪.有限差分方法的数值结果表明界面追踪法可较好地反映低渗透多孔介质非达西不稳定渗流动边界的移动规律.     

Pressure based finite volume method for calculation of compressible viscous gas flows

A pressure based, iterative finite volume method is developed for calculation of compressible, viscous, heat conductive gas flows at all speeds. The method does not need the use of under-relaxation coefficient in order to ensure a convergence of the iterative process. The method is derived from a general form of system of equations describing the motion of compressible, viscous gas. An emphasis is done on the calculation of gaseous microfluidic problems. A fast transient process of gas wave propagation in a two-dimensional microchannel is used as a benchmark problem. The results obtained by using the new method are compared with the numerical solution obtained by using SIMPLE (iterative) and PISO (non-iterative) methods. It is shown that the new iterative method is faster than SIMPLE. For the considered problem the new method is slightly faster than PISO as well. Calculated are also some typical microfluidic subsonic and supersonic flows, and the Rayleigh–Bénard convection of a rarefied gas in continuum limit. The numerical results are compared with other analytical and numerical solutions.     

Numerical solution of under-resolved detonations

A new fractional-step method is proposed for the numerical solution of high speed reacting flows, where the chemical time scales are often much smaller than the fluid dynamical time scales. When the problem is stiff, because of insufficient spatial/temporal resolution, a well-known spurious numerical phenomenon occurs in standard finite volume schemes: the incorrect calculation of the speed of propagation of discontinuities. The new method is first illustrated considering a one-dimensional scalar hyperbolic advection/reaction equation with stiff source term, which may be considered as a model problem to under-resolved detonations. During the reaction step, the proposed scheme replaces the cell average representation with a two-value reconstruction, which allows us to locate the discontinuity position inside the cell during the computation of the source term. This results in the correct propagation of discontinuities even in the stiff case. The method is proved to be second-order accurate for smooth solutions of scalar equations and is applied successfully to the solution of the one-dimensional reactive Euler equations for Chapman–Jouguet detonations.     

多组份流动质量分数保极值原理算法

对基于质量分数的Mie-Gruneisen状态方程多流体组份模型提出了新的数值方法.该模型保持混合流体的质量、动量、和能量守恒,保持各组份分质量守恒,在多流体组份界面处保持压力和速度一致.该模型是拟守恒型方程系统.对该模型系统的离散采用波传播算法.与直接对模型中所有守恒方程采用相同算法不同的是,在处理分介质质量守恒方程时,对波传播算法进行了修正,使之满足质量分数保极值原理.而不作修改的算法则不能保证质量分数在[0,1]范围.数值实验验证了该方法有效.     

Coupled mode perturbation theory of range dependence

The conventional coupled mode solution is combined with perturbation theory to give a fast, accurate range-dependent normal mode solution for deep water acoustic propagation. Perturbation theory is used to calculate the new normal modes at each range step. The new modes are obtained as a linear combination of the modes for the previous step without requiring a numerical solution of the depth-separated wave equation. The process may be repeated for many steps and yields normal modes and eigenvalues which are sufficiently accurate for solution of practical problems in deep water. The method is applied to long-range propagation through oceanic fronts.