双曲型方程无振荡选取(NOS)有限差分格式

从几何观点解释了双曲型方程差分格式的TVD条件,导出了常用二阶差分格式的无振荡条件,发展了一种具有时空三阶精度的无振荡选取NOS差分格式.从单个双曲型方程的一些典型算例,显示了该格式高精度、无振荡和逻辑简单的特点,并能有效避免通常使用维数分裂法向二维推广时带来的空间耗散不对称性.     

求解二维双曲型方程的一种基本守恒差分格式

构造了一种求解二维双曲型方程的基本守恒型差分格式,并证明了该格式的数值解是全变差有界的,在光滑区域具有二阶精度,按L¹范数及L^∞范数稳定,且其几乎处处有界收敛的极限解是微分方程的物理解。     

计算流体力学中的高精度数值方法回顾

在过去的二、三十年中,计算流体力学(CFD)领域的高精度数值方法的设计和应用研究非常活跃.高精度数值方法主要针对具有复杂解结构流场的模拟而设计.回顾CFD中主要用于可压缩流模拟的几类高精度格式的发展与应用.可压缩流的一个重要特征是流场中存在激波、界面以及其它间断,同时还常常在解的光滑区域包含复杂结构.这对设计既不振荡又保持高阶精度的格式带来特别的挑战.重点讨论本质无振荡(ENO)、加权本质无振荡(WENO)有限差分与有限体积格式、间断Galerkin有限元(DG)方法,描述它们各自的特点、长处与不足,简要回顾这些方法的发展和应用,重点介绍它们近五年来的最新进展.     

热声波数值模拟的虚假振荡研究

采用可压缩流动的SIMPLE算法对一维封闭空腔内由边界突然加热所引起的非稳态热声波进行了数值模拟,对流-扩散项采用了中心差分、一阶迎风差分、QUICK、及MIJSCL等不同格式。计算表明各种格式均存在不同程度的虚假振荡现象,其大小与热声波的强度及离散格式的形式等多种因素有关。这些结果对热声波的进一步研究及高效可靠的对流差分格式的开发具有重要意义。     

常微分方程边值问题的高阶三对角OCI差分法

本文给出了二阶线性常微分方程两点边值问题(ODETPBVP)的高阶差分格式构造的基本思想,推导出六阶三对角OCI差分格式,并对端点有奇异性的方程进行了极限值处理,消去了奇异性,对边界层问题采用了非均匀网格上的六阶三对角OCI差分格式。通过大量的数值比较实验表明,这种高阶三对角OCI差分格式能很好地求解奇异性问题,固有不稳定性问题,奇异摄动问题,对生不稳定性问题和振荡性问题。     

杂质扩散方程的数值解法

研究杂质在等离子体中的扩散(非定态)时,提出了求解二阶非线性抛物型偏微分方程组的问题。对于这类方程组的数值求解,不少人进行过研究,但是在理论上至今还不够完善。仅就常用的差分方法而言,对于具体问题仍有采用哪种差分格式、如何线性化以及如何迭代等问题。这些问题的解决带有一定的经验性质。     

黏性水波振荡型行波解的存在性

利用追赶法技巧,研究了倾度为常数的宽矩形通道中黏性水波振荡型行波解的存在性,证明了当黏性系数、摩擦系数、倾度和高度比满足一定关系时,存在唯一的振荡型行波解.由于解析求解的困难,通过数值计算,给出了部分结果,最后进一步讨论了可能存在的振荡型行波解的结构. 关键词： 追赶法 黏性水波 振荡型行波解     

二维翼型跨音速绕流的数值模拟

本文结合高精度TVD格式的数值通量和时间进展多步法给出了一种求解定常流问题的数值方法。同时给出一些特殊处理来加快数值解的收敛速度。本文用以上方法计算了翼型跨音速绕流问题,结果表明此方法具有分辨率高,收敛速度较快之性质。     

两点边值问题解的一种有效算法

本文讨论非线性微分方程边值问题的数值解。对非线性项在局部予以线性化后,再应用打靶方法求解,可加快收敛过程;同时对线性化的函数值采取插值逼近,进一步减少了计算量。本文算法格式简便、编程容易。若辅助内、外存交换技术,利用本文算法,可在微机上完成较大规模复杂问题的分析。算例表明,本文算法大大快于用牛顿法求解一些差分格式方程的收敛速度。     

粒子输运方程的线性间断有限元方法

将空间线性间断有限元方法应用于动态粒子输运方程的求解.数值算例表明,空间线性间断有限元方法在网格边界的数值精度方面明显高于指数格式和菱形格式,并且通量在时间上的微分曲线相对光滑,避免了指数格式、菱形格式数值解的非物理振荡现象.     

MUSCL格式TV性质的非线性分析

分析求解非线性双曲型守恒律的MUSCL类格式的TV性质。首先从该类格式的一般形式出发,提出和证明了该类格式实现TVD的需求。所提TVD需求直接表示为对变量变差符号和量值限制,体现了双曲型方程解的依赖域原理,为分析MUSCL格式的TV性质提供了理论工具。同时提出了基于TVD需求再构数值解分布,以降低数值耗散从而提高接触面及膨胀波头/波尾分辨率的基本思路。     

Splitting based finite volume schemes for ideal MHD equations

We design finite volume schemes for the equations of ideal magnetohydrodynamics (MHD) and based on splitting these equations into a fluid part and a magnetic induction part. The fluid part leads to an extended Euler system with magnetic forces as source terms. This set of equations are approximated by suitable two- and three-wave HLL solvers. The magnetic part is modeled by the magnetic induction equations which are approximated using stable upwind schemes devised in a recent paper [F. Fuchs, K.H. Karlsen, S. Mishra, N.H. Risebro, Stable upwind schemes for the Magnetic Induction equation. Math. Model. Num. Anal., Available on conservation laws preprint server, submitted for publication, URL: <http://www.math.ntnu.no/conservation/2007/029.html>]. These two sets of schemes can be combined either component by component, or by using an operator splitting procedure to obtain a finite volume scheme for the MHD equations. The resulting schemes are simple to design and implement. These schemes are compared with existing HLL type and Roe type schemes for MHD equations in a series of numerical experiments. These tests reveal that the proposed schemes are robust and have a greater numerical resolution than HLL type solvers, particularly in several space dimensions. In fact, the numerical resolution is comparable to that of the Roe scheme on most test problems with the computational cost being at the level of a HLL type solver. Furthermore, the schemes are remarkably stable even at very fine mesh resolutions and handle the divergence constraint efficiently with low divergence errors.     

高强度大动态范围高效率三倍频转换的数值模拟

 对高强度大动态范围基频光入射以及偏振态发生部分变化的条件下,Ⅰ/Ⅱ角度失谐和Ⅱ/Ⅱ偏振失配（双倍频和双混频）两种高效三倍频方案的转换特性进行了数值模拟,结果表明在上述条件下Ⅰ/Ⅱ角度失谐方案优于Ⅱ/Ⅱ偏振失配方案。     

大动态范围高效率三次谐波转换的特性研究

根据激光核聚变(ICF)物理实验中整形脉冲对倍频器的要求,对高功率密度下的KDP晶体Ⅰ/Ⅱ角度失谐和Ⅱ/Ⅱ偏振失配双倍频双混频两种高效三倍频方案进行了详细的模拟计算和对比分析.结果表明:该方案具有动态范围大、调节精度降低等优点,对工程设计具有参考价值.     

Two schemes of teleportation one-particle state by a three-particle GHZ state

In accordance with transformation operator, we give two schemes for teleporting an unknown one-particle state via a general GHZ state, Two Von Neumann type measurements are given for teleporting an unknown one-particle state. The first Von Neumann type measurement use four orthogonal states and the second Von Neumann type measurement is eight orthogonal states. For maximally entangled GHZ state, the successful probability and fidelity of two schemes both reach 1.     

Hybrid Flux-Splitting Schemes for a Two-Phase Flow Model

In this paper we deal with the construction of hybrid flux-vector-splitting (FVS) schemes and flux-difference-splitting (FDS) schemes for a two-phase model for one-dimensional flow. The model consists of two mass conservation equations (one for each phase) and a common momentum equation. The complexity of this model, as far as numerical computation is concerned, is related to the fact that the flux cannot be expressed in terms of its conservative variables. This is the motivation for studying numerical schemes which are not based on (approximate) Riemann solvers and/or calculations of Jacobian matrix. This work concerns the extension of an FVS type scheme, a Van Leer type scheme, and an advection upstream splitting method (AUSM) type scheme to the current two-phase model. Our schemes are obtained through natural extensions of corresponding schemes studied by Y. Wada and M.-S. Liou (1997, SIAM J. Sci. Comput.18, 633–657) for Euler equations. We explore the various schemes for flow cases which involve both fast and slow transients. In particular, we demonstrate that the FVS scheme is able to capture fast-propagating acoustic waves in a monotone way, while it introduces an excessive numerical dissipation at volume fraction contact (steady and moving) discontinuities. On the other hand, the AUSM scheme gives accurate resolution of contact discontinuities but produces oscillatory approximations of acoustic waves. This motivates us to propose other hybrid FVS/FDS schemes obtained by removing numerical dissipation at contact discontinuities in the FVS and Van Leer schemes.     

Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number

We propose a theoretical framework to clearly explain the inaccuracy of Godunov type schemes applied to the compressible Euler system at low Mach number on a Cartesian mesh. In particular, we clearly explain why this inaccuracy problem concerns the 2D or 3D geometry and does not concern the 1D geometry. The theoretical arguments are based on the Hodge decomposition, on the fact that an appropriate well-prepared subspace is invariant for the linear wave equation and on the notion of first-order modified equation. This theoretical approach allows to propose a simple modification that can be applied to any colocated scheme of Godunov type or not in order to define a large class of colocated schemes accurate at low Mach number on any mesh. It also allows to justify colocated schemes that are accurate at low Mach number as, for example, the Roe–Turkel and the AUSM⁺-up schemes, and to find a link with a colocated incompressible scheme stabilized with a Brezzi–Pitkäranta type stabilization. Numerical results justify the theoretical arguments proposed in this paper.     

On <Emphasis Type="Bold">Λ</Emphasis> −<Emphasis Type="Bold">ϕ</Emphasis> generalized synchronization of chaotic dynamical systems in continuous–time

In this paper, a new type of chaos synchronization in continuous-time is proposed by combining inverse matrix projective synchronization (IMPS) and generalized synchronization (GS). This new chaos synchronization type allows us to study synchronization between different dimensional continuous-time chaotic systems in different dimensions. Based on stability property of integer-order linear continuous-time dynamical systems and Lyapunov stability theory, effective control schemes are introduced and new synchronization criterions are derived. Numerical simulations are used to validate the theoretical results and to verify the effectiveness of the proposed schemes.     

DGM-FD: A finite difference scheme based on the discontinuous Galerkin method applied to wave propagation

In this paper we formulate a numerical method that is high order with strong accuracy for numerical wave numbers, and is adaptive to non-uniform grids. Such a method is developed based on the discontinuous Galerkin method (DGM) applied to the hyperbolic equation, resulting in finite difference type schemes applicable to non-uniform grids. The schemes will be referred to as DGM-FD schemes. These schemes inherit naturally some features of the DGM, such as high-order approximations, applicability to non-uniform grids and super-accuracy for wave propagations. Stability of the schemes with boundary closures is investigated and validated. Proposed scheme is demonstrated by numerical examples including the linearized acoustic waves and solutions of non-linear Burger’s equation and the flat-plate boundary layer problem. For non-linear equations, proposed flux finite difference formula requires no explicit upwind and downwind split of the flux. This is in contrast to existing upwind finite difference schemes in the literature.