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。

基于CE/SE方法的二维Euler型多物质流体弹塑性问题计算

将CE/SE方法推广到二维固体流体弹塑性问题的数值计算,同时结合杂交粒子水平集方法追踪物质界面和合适的边界条件,提出一套完整的二维Euler型流体弹塑性计算方案.通过长钨杆侵彻装甲钢实验的数值模拟,对方法的精度和有效性进行验证.

3D Finite Volume Scheme for Czochralski Crystal Growth

A general three-dimensional model is developed for simulation of the growth process of silicon single crystals by Czochralski technique. The numerical scheme is based on the curvilinear non-orthogonal finite volume discretization. Numerical solutions show that the flow and temperature fields in the melt are asymmetric and unsteady for 8’’ silicon growth. The effects of rotation of crystal on the flow structure are studied. The rotation of crystal forms the Ekman layer in which the temperature gradient along solid/melt surface is small.

3D Finite Volume Scheme for Czochralski Single Crystal Growth

Czochralski (Cz) technique, which is used for growing single crystals, has dominated the production of single crystals for electronic applications. The Cz growth process involves multiple phases, moving interface and three-dimensional behavior. Much has been done to study these phenomena by means of numerical methods as well as experimental observations. A three-dimensional curvilinear finite volume based algorithm has been developed to model the Cz process. A body-fitted transformation based approach is adopted in conjunction with a multizone adaptive grid generation (MAGG) technique to accurately handle the three-dimensional problems of phase-change in irregular geometries with free and moving surfaces. The multizone adaptive model is used to perform a three-dimensional simulation of the Cz growth of silicon single crystals.Since the phase change interface are irregular in shape and they move in response to the solution, accurate treatment of these interfaces is important from numerical accuracy point of view. The multizone adaptive grid generation (MAGG) is the appropriate scheme for this purpose. Another challenge encountered is the moving and periodic boundary conditions, which is essential to the numerical solution of the governing equations. Special treatments are implemented to impose the periodic boundary condition in a particular direction and to determine the internal boundary position and shape varying with the combination of ambient physicochemical transport process and interfacial dynamics. As indicated above that the applications and processes characterized by multi-phase, moving interfaces and irregular shape render the associated physical phenomena three-dimensional and unsteady. Therefore a generalized 3D model rather than a 2D simulation, in which the governing equations are solved in a general non-orthogonal coordinate system, is constructed to describe and capture the features of the growth process. All this has been implemented and validated by using it to model the low pressure Cz growth of silicon. Accuracy of this scheme is demonstrated by agreement of simulation data with available experimental data. Using the quasi-steady state approximation, it is shown that the flow and temperature fields in the melt under certain operating conditions become asymmetric and unsteady even in the absence of extrinsic sources of asymmetry. Asymmetry in the flow and temperature fields, caused by high shear initiated phenomena, affects the interface shape in the azimuthal direction thus results in the thermal stress distribution in the vicinity, which has serious implications from crystal quality point of view.

时-空守恒元解元(CE/SE)数值方法及其应用

<正>时-空守恒元解元方法(space-timeconservationelementandsolutionelementmethod,CE/SE)是近年来兴起的一种全新的守恒方程型方程计算方法。它最早由NASALewis研究中心的Chang于1995年提出来的。这种方法从根本上区别于传统的方法:它将时间和空间统一起来同等对待;利用守恒

时—空守恒元解元(CE/SE)方法简述

时-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方程型方程计算方法。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流体力学方法。本文介绍了CE/SE方法的基本理论、格式构造、发展历史、应用情况和最新进展,并指出了应解决的问题和发展方向。

An Improved Ce/Se Scheme For Multi-Material Elastic-Plastic Flows And Its Applications

In this paper, a new definition of SE and CE, which is based on the hexahedron mesh and simpler than Chang's original CE/SE method (the space-time Conservation Element and Solution Element method), is proposed and an improved CE/SE scheme is constructed. Furthermore, the improved CE/SE scheme is extended in order to solve the elastic-plastic flow problems. The hybrid particle level set method is used for tracing the interfaces of materials. Proper boundary conditions are presented in interface tracking. Two high-velocity impact problems are simulated numerically and the computational results are carefully compared with the experimental data, as well as the results from other literature and LS-DYNA software. The comparisons show that the computational scheme developed currently is clear in physical concept, easy to be implemented and high accurate and efficient for the problems considered. (C) 2008 Elsevier Ltd. All rights reserved.

SUPER CE/SE的新算法及其在爆炸力学中的应用

研究了SUPER CE/SE的新算法及其在爆炸力学中的应用. 算法和模型方面, 主要包括改进CE/SE算法、快速杂交粒子水平集方法、常用化学反应模型和两流体模型. 使用上述算法和模型, 对激波楔面反射、爆炸焊接、爆轰波胞格结构和气液两相爆轰问题进行了数值模拟. 数值结果表明, 该文采用的算法具有计算精度高、应用范围广和兼容性强等优点, 可广泛应用于爆炸力学的数值研究.

An Improved CE/SE Scheme for Numerical Simulation of Gaseous and Two-Phase Detonations

A new structure of solution elements and conservation elements based on rectangular mesh was pro- posed and an improved space-time conservation element and solution element (CE/SE) scheme with sec- ond-order accuracy was constructed. Furthermore, the application of improved CE/SE scheme was extended to detonation simulation. Three models were used for chemical reaction in gaseous detonation. And a two-fluid model was used for two-phase (gas–droplet) detonation. Shock reflections were simu- lated by the improved CE/SE scheme and the numerical results were compared with those obtained by other different numerical schemes. Gaseous and gas–droplet planar detonations were simulated and the numerical results were carefully compared with the experimental data and theoretical results based on C–J theory. Mach reflection of a cellular detonation was also simulated, and the numerical cellular pat- terns were compared with experimental ones. Comparisons show that the improved CE/SE scheme is clear in physical concept, easy to be implemented and high accurate for above-mentioned problems.

New Numerical Algorithms in SUPER CE/SE and Their Applications in Explosion Mechanics

The new numerical algorithms in SUPER/CESE and their applications in explosion mechanics are studied. The researched algorithms and models include an improved CE/SE (space-time Conservation Element and Solution Element) method, a local hybrid particle level set method, three chemical reaction models and a two-fluid model. Problems of shock wave reflection over wedges, explosive welding, cellular structure of gaseous detonations and two-phase detonations in the gas-droplet system are simulated by using the above-mentioned algorithms and models. The numerical results reveal that the adopted algorithms have many advantages such as high numerical accuracy, wide application field and good compatibility. The numerical algorithms presented in this paper may be applied to the numerical research of explosion mechanics.

高阶精度CE/SE算法及其应用

对时-空守恒元解元算法(CE/SE)的网格设置做较大改进,提出一种新的六面体解元和元定义;同时在解元中对物理量进行高阶Taylor展开,给出一种在时间和空间上均具有高阶精度CE/SE算法.在此基础上,把新型的高阶精度CE/SE算法推广应用于高速流动捕捉激波间断、气相化学反应流动、计及固体动态效应的流体-弹塑性流动和非稳态多相不可压缩粘性流动中.数值实践表明,提出的新型网格结构上的高阶精度CE/SE算法具有算法简单、计算精度高、计算效率和计算效果好的优点,并大大改进和拓展了CE/SE算法的应用范围.

A CE/SE Scheme for Flows in Porous Media and Its Applications

In this paper, a new computational scheme for solving flows in porous media was proposed. The scheme was based on an improved CE/SE method (the space-time Conservation Element and Solution Element method). We described porous flows by adopting DFB (Brinkman-Forchheimer extended Darcy) equation. The comparison between our computational results and Ghia's confirmed the high accuracy, resolution, and efficiency of our CE/SE scheme. The proposed first-order CE/SE scheme is a new reliable way for numerical simulations of flows in porous media. After investigation of effects of Darcy number on porous flow, it shows that Darcy number has dominant influence on porous flow for the Reynolds number and porosity considered.

Study On Buoyancy Convection Phenomenon In The Crystal Growth Process

Real-time phase shift Mach-Zehnder interference technique, imaging technique, and computer image processing technique were combined to perform a real-time diagnosis of NaClO3 crystal, which described both the dissolution process and the crystallization process of the NaClO3 crystal in real-time condition. The dissolution fringes and the growth fringes in the process were obtained. Moreover, a distribution of concentration field in this process was obtained by inversion calculation. Finally, the buoyancy convection phenomenon caused by gravity in the crystal growth process was analyzed. The results showed that this convection phenomenon directly influences the growth rate of each crystal face in the crystal.

Influence Of Gravity On Structure Of Colloidal Crystal Using Simulated Microgravity

Liquid mixtures of water and deuterium oxide as the liquid phase, were used to match the density of charged colloidal particles. Kossel diffraction method was used to detect the crystal structures. The experiments under the density-matched (g=0) and unmatched (g=1) conditions are compared to examine the influence of gravity on the crystal structures formed by self-assembly of 110 nm (in diameter) polystyrene microspheres. The result shows that die gravity tends to make the lattice constants of colloidal crystals smaller at lower positions, which indicates that the effect of gravity should be taken into account in the study of the colloidal crystals.