源于G.I.Taylor工作的现代经典物理学

一位科学家的工作提供了一门完整课程的素材，涉及从流体动力学稳定性、湍流到流体电动力学、微生物的运动．

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.

Perturbational finite volume scheme for the one-dimensional Navier-Stokes equations

Starting from the second-order finite volume scheme,though numerical value perturbation of the cell facial fluxes, the perturbational finite volume (PFV) scheme of the Navier-Stokes (NS) equations for compressible flow is developed in this paper. The central PFV scheme is used to compute the one-dimensional NS equations with shock wave.Numerical results show that the PFV scheme can obtain essentially non-oscillatory solution.

Development of a Cell Size Relaxed Scheme for the Direct Simulation Monte Carlo Method

The conventional direct simulation Monte Carlo (DSMC) method has a strong restriction on the cell size because simulated particles are selected randomly within the cell for collisions. Cells with size larger than the molecular mean free path are generally not allowed in correct DSMC simulations. However, the cell-size induced numerical error can be controlled if the gradients of flow properties are properly involved during collisions. In this study, a large cell DSMC scheme is proposed to relax the cell size restriction. The scheme is applied to simulate several test problems and promising results are obtained even when the cell size is greater than 10 mean free paths of gas molecules. However, it is still necessary, of course, that the cell size be small with respect to the flow field structures that must be resolved.

液氮温区G-M制冷机的数值分析及新型结构制冷机的研制

G-M制冷机是回热式的小型低温制冷机，它利用绝热放气膨胀原理（又称为西蒙膨胀法）获得低温，具有振动小、运行稳定、寿命长、操作方便等特点，在对效率、重量、尺寸等没有太高要求的场合应用非常广泛。在八十年代末，G-M制冷机已经突破了液氦温度，非常适合在液氦温区为超导器件或电子元件提供冷量，在低温真空泵、MRI超导磁体冷却系统、SQUID再冷凝系统等方面有良好的应用前景，推广其应用已属当务之急。本文围绕着探索氦温区G-M制冷机工作机理、提高低温蓄冷器性能及新型结构G-M制冷机的研制等方面，进行了系统地理论分析和纳归纳，以及初步地实验研究：一. 首次比较完善地建立了液氦温区G-M型制冷机整机数值模拟方法，数值模拟方法给出了制冷机内工质参数瞬态分布及动态变化曲线，为分析制冷机独特的循环特性提供了直观的依据，为探讨运行及结构参数对制冷性能的影响机理提供了强有力的工具。模型中考虑了制冷机中的阻力、实际进排气角、物性变化及蓄冷器内空隙率的存在等多种实际因素：解决了一、二级耦合及部件交界处物性变化不连续对计算影响等问题；采取网格非均匀化、牛顿迭代法以及负反馈原理等措施，提高了计算精度和收敛性。在微机上成功地模拟了液氦温区G-M制冷机的工作过程，程序采用模块化编程，具有一定通用性。二. 运用液氦温区整套机数值模拟方法，计算了制冷机内工质参数（氦流温度、压力、流速等）周期性变化和空间分布，采用一级蓄冷器与低温蓄冷器工作特性对比法，从整机内工质参数动态变化规律分析的角度，验证了液氦温区G-M制冷机工质氦的循环主要分为两部分：常规循环、低温循环。并详细地讨论了运行参数（频率、工作压力）及一级制冷机结构参数对整机内工数动态变化的影响规律以及制冷机性能的影响机理。三. 首次建立了较完善的液氦温区多层混合填料型低温蓄冷器的数值模拟方法，运用数值模拟方法，首次详细地研究了常用填料的不同组合、一定组合下填料比例以及蓄冷器结构对制冷机性能的影响机理，提出了不同填料的最佳节组合及一定组合下填料最佳比例的确定和低温蓄冷器结构和填料优化的原则，为合理有效地设计高性能液氦温区低温蓄冷器提供了依据。四. 提出并设计、加工了一种新型结构的液氦温区双级G-M型制冷机，该机结构在国内外属于首创。其具有以下主要结构特点：一、二级分别独立驱动；一、二级之间通过热桥连接；二级蓄冷器外置于汽缸等。同时建立了新型结构液氦温区双级G-M型制冷机实验系统，为今后整机性能和内部动态过程的研究奠定了基础。五. 新型结构双级G-M型制冷机二级单机动转频率为0.6Hz时，制冷温度为13.6K，且在20K时有4.4W的制冷量；制冷机已达到液氦温区，f = 0.4Hz时，最低温度为4.6K；f = 1Hz，制冷温度为10K时，制冷量大于6W，上述结果目前均未见有文献报道。在新型G-M制冷机上，初步进行了低温蓄冷器性能测试实验及运行参数对制冷机性能影响的实验研究。

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.

A Hybrid Scheme Based on Finite Element/Volume Methods for Two Immiscible Fluid Flows

We have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

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.

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.

Parallel Fully-Implicit Computation of MHD Acceleration Experiments

A three-dimensional MHD solver is described in the paper. The solver simulates reacting flows with nonequilibrium between translational-rotational, vibrational and electron translational modes. The conservation equations are discretized with implicit time marching and the second-order modified Steger-Warming scheme, and the resulted linear system is solved iteratively with Newton-Krylov-Schwarz method that is implemented by PETSc package. The results of convergence tests are plotted, which show good scalability and convergence around twice faster when compared with the DPLR method. Then five test runs are conducted simulating the experiments done at the NASA Ames MHD channel, and the calculated pressures, temperatures, electrical conductivity, back EMF, load factors and flow accelerations are shown to agree with the experimental data. Our computation shows that the electrical conductivity distribution is not uniform in the powered section of the MHD channel, and that it is important to include Joule heating in order to calculate the correct conductivity and the MHD acceleration.

Electronic entanglement purification scheme enhanced by charge detections

We present an entanglement purification scheme for the mixed entangled states of electrons with the aid of charge detections. Our scheme adopts the electronic polarizing beam splitters rather than the controlled-NOT (CNOT) operations, but the total successful probability of our scheme can reach the quantity as large as that of the the CNOT-operation-based protocol and twice as large as that of linear-optics-based protocol for the purification of photonic entangled states. Thus our scheme can achieve a high successful prabability without the usage of CNOT operations.

Enhancement of Kerr nonlinearity with vanishing absorption in a tripod scheme

The giant enhancement of Kerr nonlinearity in a four-level tripod type system is investigated theoretically. By tuning the value of the Rabi frequency of the coherent control field, owing to the double dark resonances, the giant-enhanced Kerr nonlinearity can be achieved within the right transparency window. The in fluence of Doppler broadening is also discussed.