Analysis of super compact finite difference method and application to simulation of vortex-shock interaction

Turbulence and aeroacoustic noise high-order accurate schemes are required, and preferred, for solving complex flow fields with multi-scale structures. In this paper a super compact finite difference method (SCFDM) is presented, the accuracy is analysed and the method is compared with a sixth-order traditional and compact finite difference approximation. The comparison shows that the sixth-order accurate super compact method has higher resolving efficiency. The sixth-order super compact method, with a three-stage Runge-Kutta method for approximation of the compressible Navier-Stokes equations, is used to solve the complex flow structures induced by vortex-shock interactions. The basic nature of the near-field sound generated by interaction is studied.

Scheme Construction with Numerical Flux Residual Correction (NFRC) and Group Velocity Control (GVC)

For simulating multi-scale complex flow fields like turbulent flows, the high order accurate schemes are preferred. In this paper, a scheme construction with numerical flux residual correction (NFRC) is presented. Any order accurate difference approximation can be obtained with the NFRC. To improve the resolution of the shock, the constructed schemes are modified with group velocity control (GVC) and weighted group velocity control (WGVC). The method of scheme construction is simple, and it is used to solve practical problems.

Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Routing scheme, permutation properties, and optical implementation of a four-shuffle-exchange-based Omega network

The routing scheme and some permutation properties of a four-shuffle-exchange-based Omega network are discussed. The corresponding optical setup, which is composed of 2-D phase spatial light modulators and calcite plates, is proposed and demonstrated through mapping the inputs to a 2-D array. Instead of one shuffle-exchange followed by one switching operation as in ordinary Omega networks, in our presented system, the shuffle interconnection embraced in the switches is accomplished simply by varying the switching structure of each stage. For the proposed polarization-optical modules, the system is compact in structure, efficient in performance, and insensitive to the environment. (C) 1997 Society of Photo-Optical Instrumentation Engineers.

Design of a compact polarizing beam splitter based on a photonic crystal ring resonator with a triangular lattice

We propose and simulate a new kind of compact polarizing beam splitter (PBS) based on a photonic crystal ring resonator (PCRR) with complete photonic bandgaps. The two polarized states are separated far enough by resonant and nonresonant coupling between the waveguide modes and the microring modes. Some defect holes are utilized to control the beam propagation. The simulated results obtained by the finite-difference time-domain method show that high transmission (over 95%) is obtained and the polarization separation is realized with a length as short as 3.1 mu m. The design of the proposed PBS can be flexible, thanks to the advantages of PCRRs.

Design of a compact polarization beam splitter based on a deformed photonic crystal directional coupler

In this paper a compact polarization beam splitter based on a deformed photonic crystal directional coupler is designed and simulated. The transverse-electric (TE) guided mode and transverse-magnetic (TM) guided mode are split due to different guiding mechanisms. The effect of the shape deformation of the air holes on the coupler is studied. It discovered that the coupling strength of the coupled waveguides is strongly enhanced by introducing elliptical airholes, which reduce the device length to less than 18.5 mu m. A finite-difference time-domain simulation is performed to evaluate the performance of the device, and the extinction ratios for both TE and TM polarized light are higher than 20 dB.

Resonant cavity based compact efficient antireflection structures for photonic crystals

We propose an effective admittance ( EA) method to design antireflection structures for two-dimensional photonic crystals (PCs). We demonstrate that a compact and efficient antireflection structure, which is difficult to obtain by the conventional admittance matching method, can be readily designed by the EA method. The antireflection structure consists of an air slot resonant cavity that is constructed only with the materials that constitute the PC. Compared with a bare PC, the reflection from a PC with an antireflection structure is reduced by two orders of magnitude over a wide bandwidth. To confirm the presented EA method, finite-difference time-domain (FDTD) simulations are performed, and the results from the FDTD and the EA method are in good agreement.

A Compact Direct Digital Frequency Synthesizer for System-on-chip

A compact direct digital frequency synthesizer (DDFS) for system-on-chip (SoC) is developed in this paper. For smaller chip size and lower power consumption, the phase to sine mapping data is compressed by using sine symmetry technique, sine-phase difference technique, quad line approximation (QLA) technique and quantization and error read only memory (QE-ROM) technique. The ROM size is reduced by 98 % using the techniques mentioned above. A compact DDFS chip with 32-bit phase storage depth and a 10-bit on-chip digital to analog converter(DAC) has been successfully implemented using standard 0.35um CMOS process. The core area of the DDFS is 1.6mm(2). It consumes 167 mW at 3.3V, and its spurious free dynamic range (SFDR) is 61dB.

Compact and efficient triple-pass optical parametric chirped pulse amplification

Compact and efficient triple-pass optical parametric chirped pulse amplification in a single crystal has been demonstrated. The signal was triple-pass amplified in a single nonlinear crystal by a nanosecond pump pulse. The first-pass optical parametric amplification is completely phase matched in the plane of the maximum effective nonlinearity, and the other two passes work symmetrically near to the first-pass optical parametric amplification plane. This architecture efficiently increases the overall gain, overcomes the optical parametric fluorescence, and clearly simplifies the amplification scheme.

A Compact Direct Digital Frequency Synthesizer for the Rubidium Atomic Frequency Standard

A compact direct digital frequency synthesizer （DDFS） for system-on-chip implementation of the high precision rubidium atomic frequency standard is developed. For small chip size and low power consumption, the phase to sine mapping data is compressed using sine symmetry technique, sine-phase difference technique, quad line approximation technique,and quantization and error read only memory （QE-ROM） technique. The ROM size is reduced by 98% using these techniques. A compact DDFS chip with 32bit phase storage depth and a 10bit on-chip digital to analog converter has been successfully implemented using a standard 0.35μm CMOS process. The core area of the DDFS is 1.6mm^2. It consumes 167mW at 3.3V,and its spurious free dynamic range is 61dB.

对流扩散方程的变步长摄动有限差分格式

摄动有限差分(PFD)方法是构造高精度差分格式的一种新方法。变步长摄动有限差分方法是等步长摄动有限差分方法的发展和推广。对需要局部加密网格的计算问题，变步长PFD格式不需要对自变量进行数学变换，且和等步长PFD格式一样，具有如下的共同特点：从变步长一阶迎风格式出发，通过把非微商项(对流系数和源项)作变步长摄动展开，展开幂级数系数通过消去摄动格式修正微分方程的截断误差项求出，由此获得高精度变步长PFD格式。该格式在一、二和三维情况下分别仅使用三、五和七个基点，且具有迎风性。文中利用变步长PFD格式对对流扩散反应模型方程，变系数方程及Burgers方程等进行了数值模拟，并与一阶迎风和二阶中心格式及其问题的精确解作了比较。数值试验表明，与一阶迎风和二阶中心格式相比，变步长PFD格式具有精度高，稳定性与收敛性好的特点。变步长PFD格式与等步长PFD格式相比，变步长PFD解在薄边界层型区域的分辨率得到了明显的提高。

Perturbational Finite Volume Method For The Solution of 2-D Navier-Stokes Equations on Unstructured and Structured Colocated Meshes

Based on the first-order upwind and second-order central type of finite volume( UFV and CFV) scheme, upwind and central type of perturbation finite volume ( UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from 0.3 to 0. 8 and convergence perform excellent with Reynolds number variation from 102 to 104.

六阶精度的群速度直接控制紧致格式及其应用

差分数值解产生非特殊振荡的直接原因是在于非均一的波群的群速度，因此本文利用直接群速度控制的方法重新构造具有六阶精度的紧致型差分格式，以达到改善激波数值解的目的。对所构造的格式的精度及数值解随控制参数变化的行为进行了分析。最后文中给出了一些典型算例，证明了文中所构造的格式具有方法简便，物理含义清楚，精度高，网格基架点小，和捕捉激波能力较强的优点。

Difference in Enzyme Activity and Conformation of Glucose Oxidase Before and After Purification

EEnzyme activity of commercial glucose oxidase was enhanced after purification through a strong anionic exchange resin. In order to get a better insight into this phenomenon, surface pressure–area ( –A) isotherms and surface pressure–time ( –t) isotherms was used to study the interaction and the absorption at different pH values of the subphases between octadecylamine and glucose oxidase purified by a styrene system quaternary ammonium type strongly basic anionic exchange resin. Circular dichroism (CD), electrophoresis and enzyme activity measurements were conducted to study these phenomena. A preliminary hypothesis has been suggested to explain why the enzyme activity of purified glucose oxidase was higher than that of the commercial one. © 2002 Elsevier Science B.V. All rights reserved.

An incremental micromechanical scheme for nonlinear particulate composites

A general incremental micromechanical scheme for the nonlinear behavior of particulate composites is presented in this paper. The advantage of this scheme is that it can reflect partly the effects of the third invariant of the stress on the overall mechanical behavior of nonlinear composites. The difficulty involved is the determination of the effective compliance tensors of the anisotropic multiphase composites. This is completed by making use of the generalized self-consistent Mori-Tanaka method which was recently developed by Dai et al. (Polymer Composites 19(1998) 506-513; Acta Mechanica Solida 18 (1998) 199-208). Comparison with existing theoretical and numerical results demonstrates that the present incremental scheme is quite satisfactory. Based on this incremental scheme, the overall mechanical behavior of a hard-particle reinforced metal matrix composite with progressive particle debonding damage is investigated.