Description of a radially polarized Laguerre-Gauss beam beyond the paraxial approximation

Fifth-order corrected expressions for the fields of a radially polarized Laguerre-Gauss (R-TEMn1) laser beams are derived based on perturbative Lax series expansion. When the order of Laguerre polynomial is equal to zero, the corresponding beam reduces to the lowest-order radially polarized beam (R-TEM01). Simulation results show that the accuracy of the fifth-order correction for R-TEMn1 depends not only on the diffraction angle of the beam as R-TEM01 does, but also on the order of the beam. (c) 2007 Optical Society of America.

Exact description of a cylindrically symmetrical complex-argument Laguerre-Gauss beam

Based on the perturbative series representation of a complex-source-point spherical wave an expression for cylindrically symmetrical complex-argument Laguerre-Gauss beams of radial order n is derived. This description acquires the accuracy up to any order of diffraction angle, and its first three corrected terms are in accordance with those given by Seshadri [Opt. Lett. 27, 1872 (2002)] based on the virtual source method. Numerical results show that on the beam axis the number of orders of nonvanishing nonparaxial corrections is equal to n. Meanwhile a higher radial mode number n leads to a smaller convergent domain of radius. (C) 2008 Optical Society of America.

三维油藏数值模拟正反演算法研究

The dynamic prediction of complex reservoir development is one of the important research contents of dynamic analysis of oil and gas development. With the increase development of time, the permeabilities and porosities of reservoirs and the permeability of block reservoir at its boundaries are dynamically changing. How to track the dynamic change of permeability and porosity and make certain the permeability of block reservoir at its boundary is an important practical problem. To study developing dynamic prediction of complex reservoir, the key problem of research of dynamic prediction of complex reservoir development is realizing inversion of permeability and porosity. To realize the inversion, first of all, the fast forward and inverse method of 3-dimension reservoir simulation must be studied. Although the inversion has been widely applied to exploration and logging, it has not been applied to3-dimension reservoir simulation. Therefore, the study of fast forward and inverse method of 3-dimension reservoir simulation is a cutting-edge problem, takes on important realistic signification and application value. In this dissertation, 2-dimension and 3-dimension fluid equations in porous media are discretized by finite difference, obtaining finite difference equations to meet the inner boundary conditions by Peaceman's equations, giving successive over relaxation iteration of 3-dimension fluid equations in porous media and the dimensional analysis. Several equation-solving methods are compared in common use, analyzing its convergence and convergence rate. The alternating direction implicit procedure of 2-dimension has been turned into successive over relaxation iteration of alternating direction implicit procedure of 3-dimension fluid equations in porous media, which possesses the virtues of fast computing speed, needing small memory of computer, good adaptability for heterogeneous media and fast convergence rate. The geological model of channel-sandy reservoir has been generated with the help of stochastic simulation technique, whose cross sections of channel-sandy reservoir are parabolic shapes. This method makes the hard data commendably meet, very suit for geological modeling of containing complex boundary surface reservoir. To verify reliability of the method, theoretical solution and numerical solution are compared by simplifying model of 3-dimension fluid equations in porous media, whose results show that the only difference of the two pressure curves is that the numerical solution is lower than theoretical at the wellbore in the same space. It proves that using finite difference to solve fluid equations in porous media is reliable. As numerical examples of 3-dimension heterogeneous reservoir of the single-well and multi-well, the pressure distributions have been computed respectively, which show the pressure distributions there are clearly difference as difference of the permeabilities is greater than one order of magnitude, otherwise there are no clearly difference. As application, the pressure distribution of the channel-sandy reservoir have been computed, which indicates that the space distribution of pressure strongly relies on the direction of permeability, and is sensitive for space distributions of permeability. In this dissertation, the Peaceman's equations have been modified into solving vertical well problem and horizontal well problem simultaneously. In porous media, a 3D layer reservoir in which contain vertical wells and horizontal wells has been calculated with iteration. For channel-sandy reservoir in which there are also vertical wells and horizontal wells, a 3D transient heterogeneous fluid equation has been discretized. As an example, the space distribution of pressure has been calculated with iteration. The results of examples are accord with the fact, which shows the modification of Peaceman's equation is correct. The problem has been solved in the space where there are vertical and horizontal wells. In the dissertation, the nonuniform grid permeability integration equation upscaling method, the nonuniform grid 2D flow rate upscaling method and the nonuniform grid 3D flow rate upscaling method have been studied respectively. In those methods, they enhance computing speed greatly, but the computing speed of 3D flow rate upscaling method is faster than that of 2D flow rate upscaling method, and the precision of 3D flow rate upscaling method is better than that of 2D flow rate upscaling method. The results also show that the solutions of upscaling method are very approximating to that of fine grid blocks. In this paper, 4 methods of fast adaptive nonuniform grid upscaling method of 3D fluid equations in porous media have been put forward, and applied to calculate 3D heterogeneous reservoir and channel-sandy reservoir, whose computing results show that the solutions of nonuniform adaptive upscaling method of 3D heterogeneous fluid equations in porous media are very approximating to that of fine grid blocks in the regions the permeability or porosity being abnormity and very approximating to that of coarsen grid blocks in the other region, however, the computing speed of adaptive upscaling method is 100 times faster than that of fine grid block method. The formula of sensitivity coefficients are derived from initial boundary value problems of fluid equations in porous media by Green's reciprocity principle. The sensitivity coefficients of wellbore pressure to permeability parameters are given by Peaceman's equation and calculated by means of numerical calculation method of 3D transient anisotropic fluid equation in porous media and verified by direct method. The computing results are in excellent agreement with those obtained by the direct method, which shows feasibility of the method. In the dissertation, the calculating examples are also given for 3D reservoir, channel-sandy reservoir and 3D multi-well reservoir, whose numerical results indicate: around the well hole, the value of the sensitivity coefficients of permeability is very large, the value of the sensitivity coefficients of porosity is very large too, but the sensitivity coefficients of porosity is much less than the sensitivity coefficients of permeability, so that the effect of the sensitivity coefficients of permeability for inversion of reservoir parameters is much greater than that of the sensitivity coefficients of porosity. Because computing the sensitivity coefficients needs to call twice the program of reservoir simulation in one iteration, realizing inversion of reservoir parameters must be sustained by the fast forward method. Using the sensitivity coefficients of permeability and porosity, conditioned on observed valley erosion thickness in wells (hard data), the inversion of the permeabilities and porosities in the homogeneous reservoir, homogeneous reservoir only along the certain direction and block reservoir are implemented by Gauss-Newton method or conjugate gradient method respectively. The results of our examples are very approximating to the real data of permeability and porosity, but the convergence rate of conjugate gradient method is much faster than that of Gauss-Newton method.

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.

Saltation in wind blown sand

The Boltzmann equation of the sand particle velocity distribution function in wind-blown sand two-phase flow is established based on the motion equation of single particle in air. And then, the generalized balance law of particle property in single phase granular flow is extended to gas-particle two-phase flow. The velocity distribution function of particle phase is expanded into an infinite series by means of Grad's method and the Gauss distribution is used to replace Maxwell distribution. In the case of truncation at the third-order terms, a closed third-order moment dynamical equation system is constructed. The theory is further simplified according to the measurement results obtained by stroboscopic photography in wind tunnel tests.

风沙两相流中的跃移运动

从单个跃移沙粒在气流中的运动方程出发导出了风沙两相流中沙粒相速度分布函数的Ｂoltzmann方程；并以此将单相颗粒流理论中的广义平衡方程推广到气固两相流的情形。提出用Grad方法将粒子相速度分布函数展成无穷级数，并引入Gauss分布取代单相颗粒流中传统的Maxwell分布。在保留到3次项的情况下，建立了气体－颗粒两相湍流边界层三阶矩封闭理论的动力学方程组。并在风洞频闪摄影实验的基础上，对理论进行简化，得到便于工程应用的简化方程。

一个推广Virial定理的数学方法和应用

本文在提出广义Gauss定理的思路下,提出了广义Stokes定理和一个推广Virial定理的新方法,后者应用于天体磁流体力学和引力平衡问题时得到的结果有:(1)气体具有运动时的平衡系统的判据,(2)磁场对气团形态的影响。应用于实验室等离子体平衡问题时,其结果有:(1)包围在气体中孤立磁场的特性,(2)发现内包无力场必须外包一有力场,(3)无力场的形态,应用于Tokmak等离子体环时的结果有:(1)环的胖瘦对环表面磁压的影响,(2)两个外加磁场分量分别和气压、环的胖瘦,截面形态、环电流分布和逆磁或顺磁的平衡关系,搞清楚了外加磁场约束等离子体总体平衡的物理机制。

气流与化学激光中的碰撞和非均匀加宽效应——理论分析模型

本文把用于气流与化学激光性能计算的理论模型作了分析比较,包括常用的Lorentz-Gauss谱线形因子近似、本文提出的矩形谱线形因子近似以及文献[5]的理论。对气流化学激光的简化扩散混合模型,文中简要地导出了与上述诸理论相对应的具体结果。分析和计算表明:在碰撞与非均匀加宽同时起作用,特别是非均匀加宽占优势的情况下,两种谱线形因子近似以及文献[5]理论的结果三者之间存在显著的差异;矩形谱线形因子近似要比常用的Lorentz-Gauss谱线形因子近似精确,而矩形谱线形因子近似的计算量要比Lorentz-Gauss谱线形因子近似的计算量少。

分析金属熔滴快速凝固过程的双倒易边界元方法

本文发展了非线性边界条件相变传热过程的轴对称双倒易边界元方法，数值模拟了金属熔滴在快速冷却条件下的快速凝固过程。分别研究了在微重力落管和落塔中及喷射成形过程中金属熔滴的快速凝固过程，得到了过冷度，再辉时间，温度变化及相变界面随时间的变化等数值结果。

Numerical Analyses of Transonic Fluid/Structure interaction in Aircraft Engineering

Through the coupling between aerodynamic and structural governing equations, a fully implicit multiblock aeroelastic solver was developed for transonic fluid/stricture interaction. The Navier-Stokes fluid equations are solved based on LU-SGS (lower-upper symmetric Gauss-Seidel) Time-marching subiteration scheme and HLLEW (Harten-Lax-van Leer-Einfeldt-Wada) spacing discretization scheme and the same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Transfinite interpolation (TFI) is used for the grid deformation of blocks neighboring the flexible surfaces. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between fluid and structure. The developed code was fort validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. In the subsonic and transonic range, the calculated flutter speeds and frequencies agree well with experimental data, however, in the supersonic range, the present calculation overpredicts the experimental flutter points similar to other computations. Then the flutter character of a complete aircraft configuration is analyzed through the calculation of the change of structural stiffness. Finally, the phenomenon of aileron buzz is simulated for the weakened model of a supersonic transport wing/body model at Mach numbers of 0.98 and l.05. The calculated unsteady flow shows, on the upper surface, the shock wave becomes stronger as the aileron deflects downward, and the flow behaves just contrary on the lower surface of the wing. Corresponding to general theoretical analysis, the flow instability referred to as aileron buzz is induced by a stronger shock alternately moving on the upper and lower surfaces of wing. For the rigid structural model, the flow is stable at all calculated Mach numbers as observed in experiment

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.

计算流体力学

基于图像处理的陶瓷基复合材料的微结构表征

本文综述了目前边界元法研究现状和进展，分析了边界元法长期以来存在着超奇异积分和几乎超奇异积分的计算难题，该问题一直困扰着边界元法的应用范围和效率。文中针对二维边界积分方程中几乎奇异积分问题，取用二节点线性单元，剖析了边界积分方程中出现几乎奇异积分的根源。提出了接近度概念，定量地度量了单元上积分发生几乎奇异性的程度。作者寻找到一些积公式，采用分部积分法将几乎奇异积分转化为无奇异积分和解析积分之和，从而获得正则化算法。针对三维边界元法中几乎奇异面积分问题，取用三角形线性单元，在三角形平面内采用极坐标（ρ，θ），建立一种半解析算法，对变量ρ施用分部积分法将几乎强奇异和超奇异面积分转化为沿单元围道的一系列线积分，然后Gauss数值积分能够胜任这些线积的计算。对于高阶单元，提出将高阶单元细分为若干线性单元策略进行处理。对二、三维问题的几乎奇异积分分别给出了数值实验，即使接近度非常小，本文方法计算值与精确值非常一致。本文将正则化算法和半解析算法运用于二、三维弹性力学问题边界元法中，直接地计算出单元上的几乎强奇异和超奇异积分，成功地求解了近边界点的位移和应力。与已有算法比较，本文方法简单，易于施行，精度高。同样，本文方法在边界方法计算位势问题中几乎超奇异积分也获得成功。另则，因为几乎奇异积分的障碍，一种观点认为边界元法无力求解薄壁弱性体问题，本文的正则化算法同样成功地计算了源点在边界时的边界积分方程中几乎奇异积分，显示了边元法能够有效地分析薄壁结构及组合结构。导数场边界积分方程中存在着超奇异主值积分的计算屏障。对于弹性力学平面问题，本文提出以符号算子δ_(ij)和∈_(ij)（排列张量）分别作用于位移导数边界积分方程，运用一系列数学技巧将边界位移、面力和位移导数变换为新的边界变量，从而获得一个新的导数场边界积分方程－自然边界积分方程。自然边界积分方程仅存在Cauchy主值积分，文中导出了相应的主值积分列式和奇性系数。自然边界积分方程与位移边界积分方程联合可直接获取边界应力，并且精度与位移相当。自然边界积分方程的一个优点是可以仅在我们感兴趣的局部边界段建立求解。文中提出联合位移边界积分方程和自然边界积分方程计算二维弹性裂纹体的位移场、应力场和应力强度因子，结合几乎奇异积分的正则化算法，求解了含狭窄孔洞的高度应力集中问题。若干算例显示了本文方法计算结果与分析解吻合的很好。因为位移边界积分方程在裂纹面上是不适定的，本文建议采用位移边界积分方程、自然边界积分方程和差分关系联立求解一般的二维断裂力学问题的位移场和应力场，由此求得应力强的因子。