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One method was unstructured grid transformed from structured grid, which was created by numerically solving the elliptic partial differential equation.

提出两种非结构化网格生成方法，一种是由结构网格转化为非结构网格，结构化网格的生成是用椭圆型偏微方程法。

The influences of the shock thickness and Alfven waves on the particle acceleration by diffusive shock waves are numerically studied through solving one-dimensional diffusive equation including the second-order Fermi effect. It is shown that the spectral index of the energetic particles strongly depends on the shock thickness. For example, the spectral index increases from 2.1 to 3.7 in the low energy range of 3-10 MeV and from 2.5 to 5.0 in the high energy range of 20-60 MeV as the thickness increases. The spectral index decreases from 4.3 to 3.1 as the particle injection energy increases. The spectral index decreases from 4.0 to 1.8 at the quasi-steady stage with the enhancement of the compression ratio from 2 to 4. The results indicate that under the influence of Alfven waves, the energetic particle spectrum at lower energy becomes flat and the spectral index decreases from 2.5 to 0.6 in the low energy range of 3-10 MeV and from 11.6 to 5.0 in the high energy range of 20-60 MeV. At the same time, the rollover energy reaches 19.6 MeV. The spectral index decreases from 5.8 to 2.9 as the energy density of Alfven waves increase. All these results are basically consistent with the theoretical models, as well as the observations of typical energetic particle events.

通过数值求解包含二阶费米加速的一维扩散方程，探讨在准平行激波条件下激波厚度和级联阿尔芬波对粒子加速的影响，研究粒子分布函数的演化与激波厚度和阿尔芬波强度的内禀关系，计算结果表明：(1)考虑激波厚度时，谱指数明显依赖于激波厚度，随着厚度从0.32增大到2.56，低能端(3-10MeV)谱指数逐渐从2.1增加到3.7，高能端(20-60MeV)谱指数从2.4增大到5.0，能谱逐渐变软；当初始注入粒子动量增大1.3倍，质子能谱指数从4.3减小到3.1，且与零厚度激波加速的谱指数差值缩小；厚度不变时，随着压缩比从2增加到4，准稳态分布时低能端(3-10MeV)粒子能谱指数逐渐从4.0减小到1.8谱变硬；(2)在级联阿尔芬波的影响下，随着时间的增大，粒子在低能处(3-10MeV)的谱指数从2.5减小到0.6高能端(20-60MeV)谱指数从11.6减小到5.0，能谱变硬，拐点能量值从7.5MeV增大到为19.6MeV；随着波的能量密度增大，谱指数从5.8减小到2.9，这表明阿尔芬波强度越大，加速效率越高，通过与激波厚度解析结果和高能粒子事件的观测能谱比较发现两者是一致的，说明数值模拟结果是可靠的。

The effect of switching modes on the entrancement,combustion and billet heating process in furnace were analyzed numerically,and the computational results were compared with production records and onsite measurement,which verified the practicability of this CFD system.

结果表明：采用分段同侧换向控制的HTAC加热炉能获得很好的流场和温度场分布，基本满足高质量的钢坯加热需要，但该炉在生产条件下的温度制度存在不合理之处，在今后设计和操作中应进一步优化和改进；全同侧换向控制的火焰布置方式不利于钢坯的均匀、快速加热；而采用交叉换向控制的火焰布置方式可以改善加热炉内的流场和温度分布，更有利于满足钢坯的加热工艺要求。

When the masses of the two balls are unequal, we numerically found that ergodicity still preserves.

对于质量不相等的情形，我们数值证明了系统的遍历性。

For the long composite cylindrical panels, including the influences of the transverse shear deformation, rotatory inertia and initial geometric imperfections, the nonlinear dynamic equations of the long composite cylindrical panels were derived from Hamilton's philosophy. The nonlinear partial differential equations were transformed to ordinary differential equations by expansion in series and solved numerically by fourthorder Runge-Kutta method.

针对含初始几何缺陷的复合材料圆柱曲板，考虑横向剪切变形、转动惯量、初始几何缺陷以及非扁壳等诸多因素，利用Hamilton原理导出复合材料长圆柱曲板的非线性动力方程；用级数展开把非线性偏微分方程组转化为二阶常微分方程组，并由四阶Runge-Kutta方法数值求解。

The one-dimensional time-dependent Schrdinger equation was numerically solved with the symmetric splitting of the short-time exponential propagator and the fast Fourier transformation, and influence of intensity and pulse with on ionization of linear multi-ation molecular ion in two-color laser fields was researched.

利用短时指数传播子对称分割法和快速傅里叶变换技术，数值求解了一维含时Schrodinger方程，探讨了双色激光场中激光的基波和谐波强度之间的不同配比以及脉宽对线性多原子分子离子电离的影响。

Three dimensional unsteady flow field around a simplified fastback car in process of accelerating was simulated numerically with computational fluid dynamicsmethod.

用CFD方法对直背式轿车加速过程中非定常外流场进行了数值模拟，计算出不同速度及加速度情况下汽车的气动阻力。

The flow field around a simplified fastback car with rear view mirrors and aerodynamic noise at some receiving point were numerically simulated and analyzed using CFD software FLUENT.

应用计算流体力学软件FLUENT对带后视镜简化直背式轿车外部流场及车外某接收点处的气动噪声进行了数值计算和分析。

The absorbing performance of one dimensional PML is theoretically analyzed and numerically simulated in view of the error caused by finite difference approximation, respectively, whose results show that this theoretical analysis can exactly indicate practical circumstances.

在计及有限差分近似造成的误差下，理论分析和数值模拟了一维理想匹配层的吸收性能，结果表明这种理论分析能完全反映实际情况。

Using numerical simulation technology and method of orthogonal experiment design and single factor rotating optimization, this thesis makes a study of "lost core injection ", thus achieve the optimization of the parameters of molding process, to offer basic reference when developing production technology and mould of the plastics intake manifold. Based on the study of the status in quo and development trend of weight reduction on automobile, the application of plastics to automobile and intake manifold, then under the guidance of theory model and numerical simulation technology in the process of high polymer material, this thesis launches flowing main research work: First of all, on the basis of the three-dimensional model of the part and finite element net model, several designs of gating and running system are numerically simulated and analyzed via MPA of Moldflow.

本文在对当今汽车轻量化、零部件塑料化以及的汽车进气歧管塑料化的发展现状和发展趋势进行了研究和简要介绍，然后在高分子材料成型过程中的理论模型和数值计算方法的指导下，展开主要的研究工作：首先，在零件三维模型和有限元网格模型的基础上，使用Moldflow 的MPA模块对塑料进气歧管的多个浇注系统设计方案进行数值模拟，通过分析各个方案的充填质量、熔接线位置及数量等指标，得到了综合质量较高的4 个进料口的浇口位置及半限制型浇口大小的浇注系统。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。