迎风紧致格式的混淆误差分析及其同谱方法的比较

对运用迎风紧致格式求解非线性方程时混淆误差产生的机理进行了研究，通过算例对五阶迎风紧致格式与谱方法进行了比较，发现在混淆误差的处理上迎风紧致格式优于谱方法。

粘性可压混合层时间稳定性对称紧致差分求解

基于可压扰动方程组的一阶改型，将高精度对称紧致格式引入边值法数值线性稳定分析。对所获非线性离散特征值问题给出了一个通用形式二阶迭代局部算法，实现了时间模式和空间模式的统一求解，并将扰动特征及其特征函数同时得到。据此分析了可压平面自由混合层时间稳定性，涉及二维/三维扰动波、粘性/无粘扰动波、第一/第二模态、特征函数、伪特征值谱等。研究表明，压缩性效应和粘性效应对最不稳定扰动波数和增长率呈相似的减抑作用；在Mc = 1附近，从高波数段开始，粘性效应可强化二维不稳定扰动波由第一模态向第二模态的过渡。

若干流体力学问题的数学性质研究

该文利用高智的扩散抛物化方程组理论及流体力学基本方程组的特征次特征理论,流体大小尺度（LSS）方程组理论以及摄动有限差分（PFD）方法,研究若干流体力学问题的数学性质.该文得到的主要结论有：1.利用湍流大小尺度（LSS）方程组推导出湍流大小尺度涡量（LSSV）方程组,并证明两个关于湍流大小尺度涡量的命题,从而得到湍流封闭大小尺度涡量（CLSSV）方程组,并对已有的近程相互作用命题进行推广.2.根据扩散抛物化方程组理论和流体力学层次结构方程组的特征和次特征方法,研究了抛物化稳定性方程组（PSE）的特征和次特征以及消除PSE的剩余椭圆特性的问题.3.利用摄动有限差分（PFD）方法得到对流扩散反应方程的变步长摄动有限差分格式,是等步长摄动有限差分格式的推广.

槽道湍流的直接数值模拟

通过直接数值模拟(DNS)研究槽道湍流的性质和机理。包含五个部分：1）湍流直接数值模拟的差分方法研究。2）求解不可压N－S方程的高效算法和不可压槽道湍流的直接数值模拟。3）可压缩槽道湍流的直接数值模拟和压缩性机理分析。4）“二维湍流”的机理分析。5）槽道湍流的标度律分析。1．针对壁湍流计算网格变化剧烈的特点，构造了基于非等距网格的的迎风紧致格式。该方法直接针对计算网格构造格式中的系数，克服了传统方法采用 Jacobian 变换因网格变化剧烈而带来的误差。针对湍流场的多尺度特性分析了差分格式的精度、网格尺度与数值模拟能分辨的最小尺度的关系，给出不同差分格式对计算网格步长的限制。同时分析了计算中混淆误差的来源和控制方法，指出了迎风型紧致格式能很好地控制混淆误差。2．将上述格式与三阶精度的Adams半隐格式相结合，构造了不可压槽道湍流直接数值模拟的高效算法。该算法利用基于交错网格的离散形式的压力Poisson方程求解压力项，避免了压力边界条件处理的困难。利用FFT对方程中的隐式部分进行解耦，解耦后的方程采用追赶法（LU分解法）求解，大大减少了计算量。为了检验该方法，进行了三维不可压槽道湍流的直接数值模拟，得到了Re＝2800的充分发展不可压槽道湍流，并对该湍流场进行了统计分析。包括脉动速度偏斜因子在内的各阶统计量与实验结果及Kim等人的计算结果吻合十分理想，说明本方法是行之有效的。3．进行了三维充分发展的可压缩槽道湍流的直接数值模拟。得到了 Re=3300，Ma=0.8的充分发展可压槽道湍流的数据库。流场的统计特征（如等效平均速度分布，“半局部”尺度无量纲化的脉动速度均方根）和他人的数值计算结果吻合。得到了可压槽道湍流的各阶统计量，其中脉动速度的偏斜因子和平坦因子等高阶统计量尚未见其他文献报道。同时还分析了压缩性效应对壁湍流影响的机理，指出近壁处的压力－膨胀项将部分湍流脉动的动能转换成内能，使得可压湍流近壁速度条带结构更加平整。4．模拟了二维不可压槽道流动的饱和态（所谓“二维湍流”），分析了“二维槽道湍流”的非线性行为特征。分析了流场中的上抛－下扫和间歇现象，研究了“二维湍流”与三维湍流的区别。指出“二维湍流”反映了三维湍流的部分特征，同时指出了展向扰动对于湍流核心区发展的重要性。5．首次对可压缩槽道湍流及“二维槽道湍流”标度律进行了分析，得出了以下结论：a）槽道湍流中，在槽道中心线附近较宽的区域，存在标度律。b）该区域流场存在扩展自相似性（ESS）。c）在Mach数不是很高时，压缩性对标度指数影响不大。本文结果同SL标度律的理论值吻合较好，有效支持了该理论。对“二维槽道湍流”也有相似的结论，但与三维湍流不同的是，“二维槽道湍流”存在标度律的区域更宽，近壁处的标度指数比中心处有所升高。

A highly efficient beam propagation method for modeling step-index waveguides with tilt interface

Based on a new finite-difference scheme and Runge-Kutta method together with transparent boundary conditions (TBCs), a novel beam propagation method to model step-index waveguides with tilt interfaces is presented. The modified scheme provides an precies description of the tilt interface of the nonrectangular waveguide structure, showing a much better efficiency and accuracy comparing with the previously presented formulas.

A High-Efficiency Fiber-to-Waveguide Coupler with Low Polarization Dependence Using a Diluted Waveguide in InP Substrate with a 1.55μm Wavelength

We propose a fiber-to-waveguide coupler for side-illuminated p-i-n photodiodes to obtain high responsivity and low polarization dependence that is grown on InP substrate and is suitable for surface hybrid integration in low cost modules. The fiber-to-waveguide coupler is based on a diluted waveguide,which is composed of ten periods of undoped 120nm InP/80nm InGaAsP （1.05μm bandgap） multiple layers. Using the semi-vectorial three dimensional beam propagation method （BPM） with the central difference scheme,the coupling efficiency of fiber-to-waveguide under different conditions is simulated and studied,and the optimized conditions for fiber-to-waveguide coupling are obtained. For TE-like and TM-like modes,the calculated maximum coupling efficiency is higher than 94% and 92% ,respectively. The calculated polarization dependence is less than 0. ldB,showing good polarization independence.

Effects of Magnetohydrodynamic Interaction-Zone Position on Shock-Wave/Boundary-Layer Interaction

A third-order weighted essentially nonoscillatory and non-free-parameter difference scheme magnetohydrodynamic solver has been established to investigate the mechanisms of magnetohydrodynamics controlling separation induced by an oblique shock wave impinging on a flat plate. The effects of magnetohydrodynamic interaction-zone location on the separation point, reattachment point, separation-bubble size, and boundary-layer velocity profiles are analyzed. The results show that there exists a best location for the magnetohydrodynamic zone to be applied, where the separation point is delayed the farthest, and the separation bubble is decreased up to about 50% in size compared to the case without magnetohydrodynamic control, which demonstrated the promising of magnetohydrodynamics suppressing the separation induced by shock-wave/boundary-layer interactions.

地震波模拟：非规则网格离散的数值解法、吸收边界及其实际应用

This dissertation presents a series of irregular-grid based numerical technique for modeling seismic wave propagation in heterogeneous media. The study involves the generation of the irregular numerical mesh corresponding to the irregular grid scheme, the discretized version of motion equations under the unstructured mesh, and irregular-grid absorbing boundary conditions. The resulting numerical technique has been used in generating the synthetic data sets on the realistic complex geologic models that can examine the migration schemes. The motion equation discretization and modeling are based on Grid Method. The key idea is to use the integral equilibrium principle to replace the operator at each grid in Finite Difference scheme and variational formulation in Finite Element Method. The irregular grids of complex geologic model is generated by the Paving Method, which allow varying grid spacing according to meshing constraints. The grids have great quality at domain boundaries and contain equal quantities of nodes at interfaces, which avoids the interpolation of parameters and variables. The irregular grid absorbing boundary conditions is developed by extending the Perfectly Matched Layer method to the rotated local coordinates. The splitted PML equations of the first-order system is derived by using integral equilibrium principle. The proposed scheme can build PML boundary of arbitrary geometry in the computational domain, avoiding the special treatment at corners in a standard PML method and saving considerable memory and computation cost. The numerical implementation demonstrates the desired qualities of irregular grid based modeling technique. In particular, (1) smaller memory requirements and computational time are needed by changing the grid spacing according to local velocity; (2) Arbitrary surfaces and interface topographies are described accurately, thus removing the artificial reflection resulting from the stair approximation of the curved or dipping interfaces; (3) computational domain is significantly reduced by flexibly building the curved artificial boundaries using the irregular-grid absorbing boundary conditions. The proposed irregular grid approach is apply to reverse time migration as the extrapolation algorithm. It can discretize the smoothed velocity model by irregular grid of variable scale, which contributes to reduce the computation cost. The topography. It can also handle data set of arbitrary topography and no field correction is needed.

离散裂缝诱导各向异性粘弹性地震波模拟与特征分析

The real media always attenuate and distort seismic waves as they propagate in the earth. This behavior can be modeled with a viscoelastic and anisotropic wave equation. The real media can be described as fractured media. In this thesis, we present a high-order staggered grid finite-difference scheme for 2-D viscoelastic wave propagation in a medium containing a large number of small finite length fractures. We use the effective medium approach to compute the anisotropic parameters in each grid cell. By comparing our synthetic seismogram by staggered-grid finite-difference with that by complex-ray parameter ray tracing method, we conclude that the high-order staggered-grid finite-difference technique can effectively used to simulate seismic propagation in viscoelastic-anisotropic media. Synthetic seismograms demonstrate that strong attenuation and significant frequency dispersion due to viscosity are important factors of reducing amplitude and delaying arrival time varying with incidence angle or offset. On the other hand, the amount of scattered energy not only provides an indicator of orientation of fracture sets, but can also provide information about the fracture spacing. Analysis of synthetic seismograms from dry- and fluid-filled fractures indicates that dry-filled fractures show more significant scattering on seismic wavefields than fluid-filled ones, and offset-variations in P-wave amplitude are observable. We also analyze seismic response of an anticlinal trap model that includes a gas-filled fractured reservoir with high attenuation, which attenuates and distorts the so-called bright spot.

Fully developed laminar flow and heat transfer in smooth trapezoidal microchannel

Numerical analysis of fully developed laminar slip flow and heat transfer in trapezoidal micro-channels has been studied with uniform wall heat flux boundary conditions. Through coordinate transformation, the governing equations are transformed from physical plane to computational domain, and the resulting equations are solved by a finite-difference scheme. The influences of velocity slip and temperature jump on friction coefficient and Nusselt number are investigated in detail. The calculation also shows that the aspect ratio and base angle have significant effect on flow and heat transfer in trapezoidal micro-channel. (c) 2005 Elsevier Ltd. All rights reserved.

Fourth order accurate compact scheme with group velocity control (GVC)

For solving complex flow field with multi-scale structure higher order accurate schemes are preferred. Among high order schemes the compact schemes have higher resolving efficiency. When the compact and upwind compact schemes are used to solve aerodynamic problems there are numerical oscillations near the shocks. The reason of oscillation production is because of non-uniform group velocity of wave packets in numerical solutions. For improvement of resolution of the shock a parameter function is introduced in compact scheme to control the group velocity. The newly developed method is simple. It has higher accuracy and less stencil of grid points.

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.

Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

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.

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.