求解二维Euler方程的时一空守恒格式

将作者原来得出的一维时－空守恒格式推广到了二维情形,得到了二维Ｅｕｌｅｒ方程的时．空守恒格式,并用几个典型算例进行了检验计算,结果表明：得到的二维时一空守恒格式保留了一维格式所有的优点,格式简单,通用性强,对微波等间断具有很高的分辨率．     

二维时-空守恒格式及其在激波传播计算中的应用

将改进后的一维时－空守恒格式推广到了二维情形,得到了一个新的一般形式的二维Ｅｕｌｅｒ方程时－空守恒格式,并用该格式对几个具有复杂波系的流场进行了数值模拟。结果表明,该格式保留了一维格式通用性好、结构简单的优点,其计算结果精度高,对激波等间断具有很强的分辨率。     

一般坐标系下的二维Euler方程时—空守恒格式

将文「１－３」中的一维时－空守恒格式推广到了二维情形,得到了一般坐标系下的二维Ｅｕｌｅｒ方程时－空守恒格式,并用几个典型算例进行了检验计算,结果表明：本文得到的二维时－空守恒格式保留了一维格式所有的优点,格式简单,通用性强,而且对激波等间断具有很高的分辨率。     

一般形式的二维时—空守恒格式

本文将经作者改进后的一维时－空守恒格式推广到了二维情形，得到了一个一般形式的二维Ｅｕｌｅｒ方程时－空守恒格式，该格式对各种不规则几何区域内的流动问题具有很强的适应性，同时它还保留了一维格式的优点。几个典型算例的计算结果表明，本文格式不仅精度高，通用性好，而且对激波等间断具有很高的分辨率。     

求解双曲型守恒律的半离散三阶中心迎风格式

给出了求解一维双曲型守恒律的一种半离散三阶中心迎风格式,并利用逐维进行计算的方法将格式推广到二维守恒律。构造格式时利用了波传播的单侧局部速度,三阶重构方法的引入保证了格式的精度。时间方向的离散采用三阶TVD Runge—Kutta方法。本文格式保持了中心差分格式简单的优点,即不需用Riemann解算器,避免了进行特征分解过程。用该格式对一维和二维守恒律进行了大量的数值试验,结果表明本文格式是高精度、高分辨率的。     

非线性双曲型守恒律的高精度MmB差分格式

构造了一维非线性双曲型守恒律方程的一个高精度、高分辨率的广义G odunov型差分格式。其构造思想是:首先将计算区间划分为若干个互不相交的小区间,再根据精度要求等分小区间,通过各细小区间上的单元平均状态变量,重构各等分小区间交界面上的状态变量,并加以校正;其次,利用近似R iem ann解算子求解细小区间交界面上的数值通量,并结合高阶R unge-K u tta TVD方法进行时间离散,得到了高精度的全离散方法。证明了该格式的Mm B特性。然后,将格式推广到一、二维双曲型守恒方程组情形。最后给出了一、二维Eu ler方程组的几个典型的数值算例,验证了格式的高效性。     

二维双曲型守恒律的一种五阶松弛格式

松弛格式是Jin和Xin提出的无振荡有限差分方法,其主要思想是将守恒律转化为松弛方程组进行求解.本文用逐维五阶WENO重构和显隐式Runge-Kutta方法对松弛方程组的空间和时间进行离散,得到了一种求解二维双曲型守恒律五阶松弛格式.所得格式保持了松弛格式简单的优点,不用求解Riemann问题和计算通量函数的雅可比矩阵.通过二维Burgers方程和二维浅水方程的数值算例验证了格式的有效性.     

用CE/SE法对弯曲与分叉河道的溃坝洪水波的数值研究

对作者的二维溃坝洪水波的数学模型进一步推广,得到了一般形式的基于任意四边形网格的时空守恒元和解元方法(简称CE/SE法)的新的格式.CE/SE法从守恒积分型浅水方程出发,设立守恒元和解元,严格保证其物理意义上的守恒律,并且构造思想简单,格式通用性好.首先采用CE/SE法计算等宽矩形河道的溃坝洪水波,并与Stoker解析解进行比较,在此基础上,数值模拟了180度强弯曲河道、45度三支分叉河道的二维溃坝洪水波的演进过程,揭示了溃坝洪水波在弯曲河道中内外两岸速度与水位的变化,在分叉河道中自动进行流量与动量的再分配,在分叉点处形成旋涡,水位变化剧烈等复杂的运动特征,算例结果表明基于任意四边形网格的CE/SE法精度高,稳定性好,该格式对各种不规则几何区域内的溃坝问题具有较强的适应性,对溃坝洪水波的间断具有较高的分辨率.     

高效时空同步四阶熵稳定格式

求解双曲守恒律方程的高阶半离散熵稳定方法在时间方向上采用Runge-Kutta型方法时,算法的计算效率较低,Lax-Wendroff型时间离散方法为这一问题的解决提供了新思路．将WENO (Weighted Essentially NonOscillatory)型四阶熵稳定格式与Lax-Wendroff型两步四阶时间离散方法相结合求解双曲守恒律方程,时空同步可达到四阶精度．相较于流行的Runge-Kutta型时间离散方法,Lax-Wendroff型两步四阶方法只需两步就可以达到四阶精度,从而可提高计算效率．多个不同类型双曲型方程数值结果表明：新的耦合算法计算效率有明显提高,一维问题计算效率至少提高35%,二维问题计算效率至少提高39%,且新算法依旧具有熵稳定性,数值结果分辨率高．     

求解双曲守恒律方程的WENO型熵相容格式

通过在单元交界面处进行高阶WENO重构,得到了一种求解双曲型守恒律方程的WENO型熵相容格式。用该格式对一维Burgers方程和Euler方程进行数值模拟,结果表明,该格式具有高精度、基本无振荡性等特点。     

二维CE/SE算法改进及其高阶精度格式

通过提出一种新的守恒元和解元划分方式对二维时-空守恒元解元算法(CE/SE)进行了改进,推导了改进CE/SE算法的一、二阶精度计算格式,并给出了更高阶精度计算格式的构造方法。利用得到的改进CE/SE格式对激波反射问题、后台阶扰流问题及隔墙坑道传播问题进行了数值模拟。数值结果表明,对CE/SE算法的改进是成功的。改进CE/SE算法有诸多优点,值得在数值模拟中推广使用。     

Numerical simulation of oxide nanoparticle growth characteristics under the gas detonation chemical reaction by space-time conservation element–solution element method

Under harsh conditions (such as high temperature, high pressure, and millisecond lifetime chemical reaction), a long-standing challenge remains to accurately predict the growth characteristics of nanosize spherical particles and to determine the rapid chemical reaction flow field characteristics. The growth characteristics of similar spherical oxide nanoparticles are further studied by successfully introducing the space-time conservation element–solution element (CE/SE) algorithm with the monodisperse Kruis model. This approach overcomes the nanosize particle rapid growth limit set and successfully captures the characteristics of the rapid gaseous chemical reaction process. The results show that this approach quantitatively captures the characteristics of the rapid chemical reaction, nanosize particle growth and size distribution. To reveal the growth mechanism for numerous types of oxide nanoparticles, it is very important to choose a rational numerical method and particle physics model.     

时一空守恒元解元（CE／SE）方法综述

时一空守恒元解元方法是近年来兴起的一种全新的高分辨率守恒型方程计算方法．它具有物理概念清晰、计算精度高和格式构造简单等优点,是一种具有广阔发展前景的计算方法．本文详细地介绍了cE／ss方法的基本原理、发展历史、应用情况和最新进展、并指出了当前研究的不足和发展方向．     

The improved space–time conservation element and solution element scheme for two‐dimensional dam‐break flow simulation

A new numerical scheme, namely space–time conservation element and solution element (CE/SE) method, has been used for the solution of the two‐dimensional (2D) dam‐break problem. Distinguishing from the well‐established traditional numerical methods (such as characteristics, finite difference, finite element, and finite‐volume methods), the CE/SE scheme has many non‐traditional features in both concept and methodology: space and time are treated in a unified way, which is the most important characteristic for the CE/SE method; the CEs and SEs are introduced, both local and global flux conservations in space and time rather than space only are enforced; an explicit scheme with a stagger grid is adopted. Furthermore, this scheme is robust and easy to implement. In this paper, an improved CE/SE scheme is extended to solve the 2D shallow water equations with the source terms, which usually plays a critical role in dam‐break flows. To demonstrate the accuracy, robustness and efficiency of the improved CE/SE method, both 1D and 2D dam‐break problems are simulated numerically, and the results are consistent with either the analytical solutions or experimental results. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of Momentum Transfer in a Lid-Driven Cavity Containing a Brinkman–Forchheimer Medium

The CE/SE (the space-time conservation element and solution element method) scheme with the second-order accuracy has been proposed. And the pretreatment method has been introduced to convert the parabolic equations to the hyperbolic equations, which are accurately solved by the CE/SE method. The lid-driven rectangular cavity containing a porous Brinkman–Forchheimer medium is studied in this numerical investigation. The Brinkman–Forchheimer equation is used such that both the inertial and viscous effects are incorporated. The governing equations are solved by the improved CE/SE approach. The characteristics of the flow are analyzed with emphasis on the influence of the Darcy number and the cavity depth. It is found that the porous medium effect decreases both the strength and the number of eddies, especially for deep cavities.     

CE/SE方法在内弹道瞬态两相流中的应用

根据CE/SE方法思想,构造在变换坐标系下内弹道两相流动数值计算的 格式. 采用此格式研究了膛内瞬态二维两相流动点火过程. 数值计算结果反映实际 规律并和试验结果符合. 结果表明,对中心点火方式,在点传火过程初期,膛内压力在 径向和轴向上存在较大的压力梯度,当火药全部着火后,药室内压力在径向上逐渐趋于 一致. 这表明CE/SE方法能够完全模拟瞬态二维两相流动的情况.     

Space–Time Method for Detonation Problems with Finite-rate Chemical Kinetics

The space–time conservation element and solution element (CE/SE) method originally developed for non-reacting flows is extended to accommodate finite-rate chemical kinetics for multi-component systems. The model directly treats the complete conservation equations of mass, momentum, energy, and species concentrations. A subtime-step integration technique is established to handle the stiff chemical source terms in the formulation. In addition, a local grid refinement algorithm within the framework of the CE/SE method is incorporated to enhance the flow resolution in areas of interest. The capability and accuracy of the resultant scheme are validated against several detonation problems, including shock-induced detonation with detailed chemical kinetics and multi-dimensional detonation initiation and propagation.