一类新的差分格式优化目标函数

对差分格式进行优化处理可以提高其谱精度。与高精度(指Taylor展开精度)格式相比,优化格式放大因子的误差随波数的变化不是单调的,而是必然会出现极值点,这样就存在临界距离R_cr,在此距离内优化格式描述的数值波的积累误差小于高精度格式,而超出此距离后优化格式的误差反而大,对于非定常流及气动声学计算来说,控制差分格式的临界距离是必要的。一般的优化目标函数以每个时间推进步的误差为基础(即放大因子法),R_cr不能在优化过程中确定。对此进行分析,指出积累误差的重要性并提出以此为基础的新的优化目标函数,这样在对格式进行优化时可以直接指定临界距离,从而为控制谱精度提供方便。     

混合通量差分格式的比较

系统研究了几种混合通量差分格式的构造方法和耗散模型,分别对低速平板绕流、二维跨音速喷管流动和高超音速钝头体无粘绕流进行了数值模拟,结合先进的EASM湍流模型对格式的粘性分辨率和激波稳定性进行了细致的比较分析.结果表明混合通量差分格式兼顾了FDS和FVS格式的优点,具有较高的间断分辨率和数值稳定性.     

分辨率优化的混合WENO格式

为提高有限差分格式的分辨率,利用傅里叶分析对WENO格式进行色散及耗散优化,并给出优化的线性权重.用优化后的WENO格式与保单调格式（MP）进行加权混合,得到新的加权混合WENO格式（H-WENO）.通过一维激波管问题、Shu-Osher问题及二维双Mach反射问题及R-T不稳定性问题对格式进行数值测试.结果显示,新格式具有强健的激波捕捉能力和对小尺度波结构的高分辨率,与原WENO格式相比改进明显.     

基于DCS5格式的LDDRK算法

基于五阶线性耗散紧致格式(DCS5)和七级龙格原库塔时间积分算法,根据数值增长因子对精确增长因子的最佳逼近原则,提出与DCS5格式耗散性相适应的优化方法,并得到相应的七级五阶低耗散低色散龙格原库塔(LDDRK)算法.求解标量线性对流方程和线化Euler方程得到的一维波传播问题的数值结果显示,七级五阶LDDRK算法的精度优于七级七阶精度的标准龙格原库塔算法.     

一种高精度差分格式

在微分－Ｔｈｏｍｐｓｏｎ变换结合时域有限差分技术计算复杂目标的电磁散射特性的方法中，差分格式的构造和选取与解的精度存在着密切关系。提出一种新的高精度差分格式，其数值实现进一步证实了该方法能精确模拟任意形状目标的电磁磁射过程。     

基于气动声学问题的高阶非线性紧致格式

文章基于线性中心紧致差分格式, 通过非线性加权插值的方法来求解网格中心处的函数值.这类格式保持了原有中心紧致差分格式的高阶精度和低耗散特性, 同时其分辨率也非常高, 由于其非线性插值的机制, 使得这类格式能够捕捉强激波, 所以这类新的高阶非线性紧致格式是一种较好的模拟湍流和气动声学等多尺度问题的方法.      

有限差分-有限元混合方法的隐式格式研究

利用文[1]提出的有限差分-有限元混合方法,给出一种新的有限元隐式格式,它避免了在传统有限元方法中采用隐式格式时需要求解大型带状稀疏矩阵以及存储量大等问题,同时利用差分法中近似因式分解方法和PuliamTH等人为避免块对角矩阵的求解提出的对角化技术,以期提高计算效率。     

构造定常对流扩散方程高精度紧致差分格式的新方法

以一维定常对流扩散方程的高精度差分格式为基础，提出了一种构造二维定常对扩散方程高精度紧致差分格式的新方法，并给出数值例子。     

利用通量限制思想改进紧致格式

利用通量限制思想改进紧致格式计算有间断流场的性能,并设计出一种限制器,该限制器被运用在一系列3至8阶的紧致格式上.数值实验表明,通量限制型紧致格式不仅具有较高的精度和分辨率,而且还能有效地抑制非物理振荡,适用于各种高低Mach数的流动,捕捉到的流场间断所占网格点数少.     

A Three-Point Combined Compact Difference Scheme

A new three-point combined compact difference (CCD) scheme is developed for numerical models. The major features of the CCD scheme are: three point, implicit, sixth-order accuracy, and inclusion of boundary values. Due to its combination of the first and second derivatives, the CCD scheme becomes more compact and more accurate than normal compact difference schemes. The efficient twin-tridiagonal (for calculating derivatives) and triple-tridiagonal (for solving partial difference equation with the CCD scheme) methods are also presented. Besides, the CCD scheme has sixth-order accuracy at periodic boundaries and fifth-order accuracy at nonperiodic boundaries. The possibility of extending to a three-point eighth-order scheme is also included.     

A New Hybrid Possibilistic-Probabilistic Decision-Making Scheme for Classification

Uncertainty is at the heart of decision-making processes in most real-world applications. Uncertainty can be broadly categorized into two types: aleatory and epistemic. Aleatory uncertainty describes the variability in the physical system where sensors provide information (hard) of a probabilistic type. Epistemic uncertainty appears when the information is incomplete or vague such as judgments or human expert appreciations in linguistic form. Linguistic information (soft) typically introduces a possibilistic type of uncertainty. This paper is concerned with the problem of classification where the available information, concerning the observed features, may be of a probabilistic nature for some features, and of a possibilistic nature for some others. In this configuration, most encountered studies transform one of the two information types into the other form, and then apply either classical Bayesian-based or possibilistic-based decision-making criteria. In this paper, a new hybrid decision-making scheme is proposed for classification when hard and soft information sources are present. A new Possibilistic Maximum Likelihood (PML) criterion is introduced to improve classification rates compared to a classical approach using only information from hard sources. The proposed PML allows to jointly exploit both probabilistic and possibilistic sources within the same probabilistic decision-making framework, without imposing to convert the possibilistic sources into probabilistic ones, and vice versa.     

A Second-Order Three-Level Difference Scheme for a Magneto-Thermo-Elasticity Model

This article deals with the numerical solution to the magneto-thermo-elasticity model, which is a system of the third order partial differential equations. By introducing a new function, the model is transformed into a system of the second order generalized hyperbolic equations. A priori estimate with the conservation for the problem is established. Then a three-level finite difference scheme is derived. The unique solvability, unconditional stability and second-order convergence in $L_{\infty}$-norm of the difference scheme are proved. One numerical example is presented to demonstrate the accuracy and efficiency of the proposed method.     

HXMT准直器方案的优化设计

空间硬X射线调制望远镜(HXMT)的性能与探测器的总灵敏面积紧密相关. 利用蒙特卡罗工具对仪器的本底和点扩展函数进行计算分析, 提出了一种优化的准直器构造方案, 能减少探测单元总质量80多千克, 相当于至少5套新探测单元质量. 在同样的卫星载荷质量限制下, 新方案可以增加探测单元, 达到增大总探测灵敏面积, 提升HXMT灵敏度和角分辨率等性能的目的.     

双曲型守恒律的一种高精度TVD差分格式

构造了一维双曲型守恒律方程的一个高精度高分辨率的守恒型TVD差分格式.其主要思想是:首先将计算区域划分为互不重叠的小单元,且每个小单元再根据希望的精度阶数分为细小单元;其次,根据流动方向将通量分裂为正、负通量,并通过小单元上的高阶插值逼近得到了细小单元边界上的正、负数值通量,为避免由高阶插值产生的数值振荡,进一步根据流向对其进行TVD校正;再利用高阶Runge KuttaTVD离散方法对时间进行离散,得到了高阶全离散方法.进一步推广到一维方程组情形.最后对一维欧拉方程组计算了几个算例.     

二维半导体问题在复合网格上的有限差分格式

半导体器件的瞬时状态由3个方程组成的非线性偏微分方程组的初边值问题决定.依据实际数值模拟的需要,提出了一类二维半导体问题在时空局部加密复合网格上的有限差分形式,电场位势方程、电子和空穴浓度方程分别用五点差分格式和修正迎风格式近似,且在交界面上采用线性插值,并给出了电子和空穴浓度的最大模误差估计,最后给出了数值算例.     

A High-Order WENO Finite Difference Scheme for the Equations of Ideal Magnetohydrodynamics

We present a high-order accurate weighted essentially non-oscillatory (WENO) finite difference scheme for solving the equations of ideal magnetohydrodynamics (MHD). This scheme is a direct extension of a WENO scheme, which has been successfully applied to hydrodynamic problems. The WENO scheme follows the same idea of an essentially non-oscillatory (ENO) scheme with an advantage of achieving higher-order accuracy with fewer computations. Both ENO and WENO can be easily applied to two and three spatial dimensions by evaluating the fluxes dimension-by-dimension. Details of the WENO scheme as well as the construction of a suitable eigen-system, which can properly decompose various families of MHD waves and handle the degenerate situations, are presented. Numerical results are shown to perform well for the one-dimensional Brio–Wu Riemann problems, the two-dimensional Kelvin–Helmholtz instability problems, and the two-dimensional Orszag–Tang MHD vortex system. They also demonstrate the importance of maintaining the divergence free condition for the magnetic field in achieving numerical stability. The tests also show the advantages of using the higher-order scheme. The new 5th-order WENO MHD code can attain an accuracy comparable with that of the second-order schemes with many fewer grid points.