开闭磁场位形中慢激波的传播 *

用一个二维MHD数值模型 ,数值模拟研究了慢激波在近太阳子午面内开磁场和闭磁场中的传播 .结果表明 :开磁场中的慢激波可以保持其慢激波的特性传向行星际空间 ,但闭场中的慢激波在通过盔形电流片向开放形磁场传播时可以转化为中间激波 .     

一种抑制激波计算中数值振荡现象的双重小波收缩方法

在激波数值计算中,容易出现数值振荡的问题,振荡激烈时会掩盖真实解,为此提出了许多高精度复杂计算格式或采用人工粘性抑制数值振荡.从信号处理的角度,提出双重小波收缩方法,它能自适应提取激波数值振荡解中的真实物理解.先用局部微分求积法求解浅水波方程和理想流体Euler运动方程中的激波问题,发现其数值振荡现象严重,然后采用双重小波收缩方法对其处理,获得了无数值振荡解,它能准确捕捉激波的位置并且保持激波结构.相比于复杂的Riemann(黎曼)求解格式,借助小波收缩方法,可以采用相对简单的计算格式如微分求积法求解激波问题.     

计算空气动力学中一个新的激波捕捉法——耗散比拟法

在空气动力学方程的求解时,改进在激波附近数值解的分辨率是一重要研究课题.通常,人们通过差分方程的微分近似来研究差分格式的特性.本文通过启示性的分析方法讨论了在激波附近数值解的行为,分析了在一些格式的数值解中产生振荡的原因.参照差分方程的第一微分近似,定义了耗散比拟系数,构造了耗散比拟方程,给出了克服数值振荡的新方法.耗散比拟法不单启示了在激波附近数值解中产生振荡的原因,还预示了克服的办法.文中给出了四种改造耗散类比系数的方法.与流行的高分辨率格式相比,新发展的方法简单、直观、计算量小和有较强的激波捕捉能力.     

一种治愈强激波数值不稳定性的混合方法

HLLC（Harten-Lax-Leer-contact）格式是一种高分辨率格式,能够准确捕捉激波、接触间断和稀疏波.但是使用HLLC格式计算多维问题时,在强激波附近会出现激波不稳定现象.FORCE（first-order centred）格式在强激波附近表现出很好的稳定性,并且其数值耗散比HLL（Harten-Lax-Leer）格式小.分析了HLLC格式和FORCE格式在特定流动条件下的稳定性,构造了HLLC-FORCE混合格式并且进一步结合开关函数来消除HLLC格式的激波不稳定现象.数值试验表明新构造的混合格式不仅能够消除HLLC格式的激波不稳定现象,还最大程度地保留HLLC格式高分辨率的优点.     

一种改进的Roe格式及其稳定性分析

低耗散的激波捕捉方法,包括流行的Roe格式,在计算多维强激波问题时会遭遇激波不稳定现象的困扰,这会严重影响格式对于高超声速流动问题的精确模拟.对Roe格式进行小扰动分析,结果表明:激波面纵向所有物理量的扰动均会衰减,而横向的密度扰动和剪切速度扰动不会衰减.在横向数值通量上增加与熵波和剪切波相对应的黏性来抑制Roe格式不稳定现象的发生.为了防止不合适的黏性影响格式对于接触间断和剪切层的分辨率,定义两个开关函数,使得黏性仅仅添加在激波层亚声速区的横向数值通量上.数值测试的结果表明:改进的Roe格式不仅保留了原始Roe格式高分辨率的优点,而且具有更好的鲁棒性,消除了激波不稳定现象.     

二维超音速混合层中小激波的存在及其对流场结构的影响

在二维超音速混合层入口处引入T-S波及其亚谐波,对扰动的空间演化进行了数值模拟.研究了由扰动引发的小激波(shocklet)的强度与入口处扰动幅值的关系.分析了激波前后扰动速度剖面的变化,发现小激波的存在对扰动速度剖面有显著影响,而高速层和低速层中激波对扰动速度作用不同.     

凹形双级楔的超音速绕流

讨论均匀的超音速气流对凹形双级楔物体的绕流问题.由于外激波与凹角处产生的内激波的相互干扰,将有一个疏散波在外激波与物面之间无限次反射,且外激波发生弯曲.在弱激波以及双级楔的两个斜率充分小的假定下,证明了整体解的存在性,并对数值计算中常用的关于解的极限性态的事实给出了一个严格的证明.     

带激波的一维非定常两相流动的数值模拟

本文将处理带激波的单相气体非定常流动问题的两种高分辨数值方法(随机取样法和二阶GRP有限差分法)推广应用于气固悬浮体(亦称含灰气体)两相情况,计算了含灰气体激波管中两相激波特性、波后流场结构及气固两相流动参数随时间的变化.数值结果表明:这两种方法均能给出带有尖锐间断阵面的两相激波松弛结构.二阶GRP方法在计算精度和机时耗用等方面优于随机取样法.     

基于第二粘性用局部微分求积法计算激波

考虑第二粘性效应,采用局部微分求积法数值求解激波问题．首先解释了在激波计算时,有必要考虑第二粘性,然后基于粘性模型,对一维和二维激波进行了数值模拟,还分别考察了剪切粘性力和第二粘性力对数值结果的影响．结果表明,采用粘性模型加上局部微分求积法能够模拟出激波特征,具有客观、简单的优点．     

内机械激波——海洋激流的一种解释

采用Lagrange坐标和Hamilton原理,推导了二维两层浅水系统的位移法内波方程,并在此基础上研究了二维内机械激波.通过具体的数值算例分析发现内机械激波具有流速大、持续时间短、空间范围狭小、水面存在突变的特点,指出海洋激流就是内机械激波.内机械激波同样也为海洋断崖提供了一种解释.     

求解浅水波方程的熵相容格式

提出了一种求解浅水波方程组的熵相容格式．在熵稳定通量中添加特征速度差分绝对值的项来抵消解在跨过激波时所产生的熵增,从而实现熵相容．新的数值差分格式具有形式简单、计算效率高、无需添加任何的人工数值粘性的特点．数值算例充分说明了其显著的优点．利用新格式成功地模拟了不同类型溃坝问题的激波、稀疏波传播及溃坝两侧旋涡的形成,是求解浅水波方程组较为理想的方法.     

A HIGHLY ACCURATE NUMERICAL METHOD FOR FLOW PROBLEMS WITH INTERACTIONS OF DISCONTINUITIES

1. IntroductionCompared with the widely used shock capturing methods for the compressible flows, theshock fitting methods have the main advantage of accuracy. The shock fitting methods areusually very accurate wherever it can be applied. Several kinds of shock fitting methods havebeen developed il1 the last tl1ree decades. Glimrn and his coworkers have worked extensively onthe front tracking methods and applied them to many complicated problems with shocks andother types of singularities [1]-[…     

时间空间均为二阶的新型NND差分格式

张涵信的研究表明,为了避免激波前后差分解的波动,在差分格式的改型方程中三阶导数的系数在激波上游必须是正的,而在激波下游则必须是负的.据此提出了一种新型的无波动、无自由参数耗散性的差分格式,它对时间和空间都是二阶的.证明了此格式是TVD的,而且是推广的二阶Годунов格式.在处理有激波的流场时,此格式是Lax-Wendroff格式的改进和推广.给出了若干算例,计算结果表明,此格式不仅无波动,而且具有形式紧凑、应用方便、分辨率高、稳定性准则中的Courant数较大的优点.     

The arbitrary order implicit multistep schemes of exponential fitting and their applications

We develop the arbitrary order implicit multistep schemes of exponential fitting (EF) for systems of ordinary differential equations. We use an explicit EF scheme to predict an approximation, and then use an implicit EF scheme to correct this prediction. This combination is called a predictor–corrector EF method. We demonstrate the accuracy and efficiency of the new predictor–corrector methods via application to a variety of test cases and comparison with other analytical and numerical results. The numerical results show that the schemes are highly accurate and computationally efficient.     

A composite semi-conservative scheme for hyperbolic conservation laws

In this work a first order accurate semi-conservative composite scheme is presented for hyperbolic conservation laws. The idea is to consider the non-conservative form of conservation law and utilize the explicit wave propagation direction to construct semi-conservative upwind scheme. This method captures the shock waves exactly with less numerical dissipation but generates unphysical rarefaction shocks in case of expansion waves with sonic points. It shows less dissipative nature of constructed scheme. In order to overcome it, we use the strategy of composite schemes. A very simple criteria based on wave speed direction is given to decide the iterations. The proposed method is applied to a variety of test problems and numerical results show accurate shock capturing and higher resolution for rarefaction fan.     

激波捕捉差分方法研究

在迎风型格式和矢通量分裂技术的基础之上,对捕捉激波方法进行一种新的尝试．该方法首先对原始格式在特征方向上进行投影,然后用限制器对这些特征分量的变化幅值进行限制以抑止非物理波动,最后再把它转换成守恒形式,得到了基本上无振荡的激波捕捉格式．用该方法对两种迎风显示格式(二阶和三阶)和3种迎风紧致格式(三阶、五阶和七阶)进行处理,并在一维和二维的情况下进行了应用测试．通过与高阶WENO、MP、Compact-WENO等格式的比较,表明该方法在光滑捕捉激波的前提下仍有较高精度和分辨率．     

Numerical experiments on a hybrid WENO5 filter for shock‐capturing

In the present paper, a hybrid filter is introduced for high accurate numerical simulation of shock‐containing flows. The fourth‐order compact finite difference scheme is used for the spatial discretization and the third‐order Runge–Kutta scheme is used for the time integration. After each time‐step, the hybrid filter is applied on the results. The filter is composed of a linear sixth‐order filter and the dissipative part of a fifth‐order weighted essentially nonoscillatory scheme (WENO5). The classic WENO5 scheme and the WENO5 scheme with adaptive order (WENO5‐AO) are used to form the hybrid filter. Using a shock‐detecting sensor, the hybrid filter reduces to the linear sixth‐order filter in smooth regions for damping high frequency waves and reduces to the WENO5 filter at shocks in order to eliminate unwanted oscillations produced by the nondissipative spatial discretization method. The filter performance and accuracy of the results are examined through several test cases including the advection, Euler and Navier–Stokes equations. The results are compared with that of a hybrid second‐order filter and also that of the WENO5 and WENO5‐AO schemes.     

Pressure‐based adaption indicator for compressible euler equations

We consider the Euler equations of gas dynamics and develop a new adaption indicator, which is based on the weak local residual measured for the nonconservative pressure variable. We demonstrate that the proposed indicator is capable of automatically detecting discontinuities and distinguishing between the shock and contact waves when they are isolated from each other. We then use the developed indicator to design a scheme adaption algorithm, according to which nonlinear limiters are used only in the vicinity of shocks. The new adaption algorithm is realized using a second‐order limited and a high‐order nonlimited central‐upwind scheme. We demonstrate robustness and high resolution of the designed method on a number of one‐ and two‐dimensional numerical examples. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1844–1874, 2015     

Combined Monotone Bicompact Scheme of Higher Order Accuracy in Domains of Influence of Nonstationary Shock Waves

Doklady Mathematics - A new method is proposed for constructing a combined shock-capturing scheme that monotonically localizes shock wave fronts and, at the same time, has increased accuracy in...     

一个求解双曲型守恒律方程的高分辨率GVC格式

1　引　　言本文研究双曲型方程:ut+fx=0,　t>0,-∞相似文献