代数多重网格方法在紊流数值预测中的应用

机械和矿山工程中广泛使用锥形渐扩管。将DLR型k-ε紊流模型中非线性偏微分方程基于全隐式高精度迎风差分格式离散,得到差分方程的系数矩阵为五对角块十三对角带状稀疏矩阵,基于一种"三元组"方式进行压缩存储,节约内存。提出了一种基于DLR型k-ε紊流模型与代数多重网格方法结合的新算法,阐述了代数多重网格方法的实施过程。对具有逆压梯度流动的锥形渐扩管内紊流进行了数值预测。数值实验表明,代数多重网格方法对求解紊流模型离散方程组非常有效,同此前该紊流数值模拟中使用的Point-SOR方法相比,计算效率有了显著提高,计算结果与实验结果吻合较好。     

用混合网格及各向异性多重网格法求解三维可压紊流流动

采用混合网格求解紊流Navier Stokes方程。在物面附近采用柱状网格 ,其他区域则采用完全非结构网格。方程的求解采用Jamson的有限体积法 ,紊流模型采用两层Baldwin Lomax代数紊流模型。用各向异性多重网格法来加速解的收敛。数值算例表明 ,用混合网格及各向异性多重网格求解紊流流动是非常有效的     

预处理方法在低速弹箭流场计算中的应用

基于Weiss-Smith预处理矩阵和全局截断预处理参数,采用有限体积方法对雷诺平均Navier-Stokes方程进行离散。对流项离散采用二阶线性重构和AUSM ＋-up格式,时间推进方法采用多重网格下的LU-SGS方法。结合M PI消息传递方法,建立了一套计算低速流动的并行数值方法。计算了低速椭球体的流场和气动力,压力系数和切应力系数计算结果与文献实验结果对比吻合度较好。生成了末敏弹的流场计算网格,对绕末敏弹流场进行了数值模拟。对多重网格下多进程的加速比和并行效率进行了测试,显示了程序良好的并行效率。计算的气动力结果与实验结果吻合。综合结果表明：本文的数值方法能够用于低速弹箭流场和气动力计算,为新型弹箭的设计和定型提供保证。     

一类网格结构模型的研究

提出了一类适用于大规模二维网格结构计算的离散模型。该模型以网格节点为研究对象，其控制方程仅与跟节点相连的杆件数目及几何形状有关；只要给出几种基本类型的节点控制方程，就可以对具有相应形式节点的各种规模的网格材料组合其控制方程而求解。这种离散模型形式简单，尤便于在计算机上实现。     

基于SIMPLER算法的多重网格方法研究

以二维方腔顶盖驱动流为模型,将多重网格方法和SIMPLER算法进行耦合,对不同雷诺数下多重网格加速SIMPLER算法和SIMPLER算法的计算效率进行了对比,数值计算表明:多重网格加速SIMPLER算法不仅能够解决SIMPLER算法不能准确模拟较高雷诺数流场的问题,而且其计算效率远远高于SIMPLER算法.本文也对松弛因子的选取、多重网格实现形式以及网格层数对多重网格加速SIMPLER算法的影响进行了研究,从而为多重网格加速SIMPLER算法的实施提供了计算技术.     

射流元件控制通道流动的三维数值模拟

针对一种射流元件控制通道的复杂结构 ,采用分块对接技术和网格“融合”技术生成计算网格 ,并运用五步显式格式的 Runge-Kutta法和多重网格法对含全 N-S方程、RNG k-ε湍流模型和两层分区壁面模型的流动模型进行数值求解。通过对控制通道内部流动的数值模拟和流场特性分析 ,提出了改进方案     

k-ε双方程湍流模型对制退机内流场计算的适用性分析

为研究不同双方程湍流模型对制退机内复杂流场计算的适用性,以某火炮制堪机为研究对象,建立了实际结构下的三维计算模型,利用动网格与滑移网格技术.实现了火炮实际后坐速度下的制退机内部三维运动流场的数值计算.分别采用标准k-ε模型、RNGk-ε模型和Realizablek-ε模型计算制退机内部各腔室压力,与实验曲线对比,结果表...     

k-ε双方程湍流模型对制退机内流场计算的适用性分析

为研究不同双方程湍流模型对制退机内复杂流场计算的适用性,以某火炮制退机为研究对象,建立了实际结构下的三维计算模型,利用动网格与滑移网格技术,实现了火炮实际后坐速度下的制退机内部三维运动流场的数值计算。分别采用标准k-ε模型、RNGk-ε模型和Realizable k-ε模型计算制退机内部各腔室压力,与实验曲线对比,结果表明,应用标准k-ε模型对后坐冲击过程的制退机内部压力计算的误差最小,与实验结果吻合最好。     

三维非结构聚合多重网格法数值模拟研究

在三维非结构网格上应用聚合式多重网格技术来加速Euler方程的收敛过程．自行设计了一种高效率的网格聚合方法．采用四重三维非结构网格，在每一层网格上采用有限体积法进行计算．通过对M6翼型的数值求解验证了多重网格加速收敛的高效性．     

一种有效的广义特征值分析方法

提出了一种适合于自适应有限元分析中求解广义特征值问题的多重网格方法．这种方法充分利用了初始网格下的结果，通过插值或最小二乘拟合技术来得到网格变化后的新的近似特征向量，然后由多重网格迭代过程实现对结构广义特征值问题的求解．在多重网格迭代的光滑步中，选择了收敛梯度法以提高其收敛率；在粗网格校正步中，则导出了一种近似求解特征向量误差的方程．这种方法将网格离散过程和数值求解过程很好地相结合，建立了一个网格细分后广义特征值问题的快速重分析方法，与传统有限元方法相比较，具有计算简便、计算量少等特点，可以作为结构动力问题自适应有限元分析的一种十分有效的工具．     

两类网格结构模型的预处理方法

针对参考节点分别为q=3和q=4的网格结构模型,设计了两种预处理方法:以块对角逆为预条件子的共轭梯度法(BPCG)及以块下三角逆为预条件子的PGMRES法。数值结果表明,BPCG法对q=3具有很好的求解效率和鲁棒性,但对q=4的情形,特别是当α很小时,其求解效率将变得很差。当α很小时,以块下三角逆为预条件子的PGMRES法对求解q=4的蜂窝状结构在计算CPU和算法稳定性等方面均全面占优。在这两种预处理方法中,利用了基于标量椭圆问题的GAMG法求各个子块矩阵的逆,以提高内迭代运算效率。近似连续方程的建立为内迭代方法的合理性提供了有效的理论支撑。     

Performance of algebraic multi‐grid solvers based on unsmoothed and smoothed aggregation schemes

A comparison is made of the performance of two algebraic multi‐grid (AMG0 and AMG1) solvers for the solution of discrete, coupled, elliptic field problems. In AMG0, the basis functions for each coarse grid/level approximation (CGA) are obtained directly by unsmoothed aggregation, an appropriate scaling being applied to each CGA to improve consistency. In AMG1 they are assembled using a smoothed aggregation with a constrained energy optimization method providing the smoothing. Although more costly, smoothed basis functions provide a better (more consistent) CGA. Thus, AMG1 might be viewed as a benchmark for the assessment of the simpler AMG0. Selected test problems for D'Arcy flow in pipe networks, Fick diffusion, plane strain elasticity and Navier–Stokes flow (in a Stokes approximation) are used in making the comparison. They are discretized on the basis of both structured and unstructured finite element meshes. The range of discrete equation sets covers both symmetric positive definite systems and systems that may be non‐symmetric and/or indefinite. Both global and local mesh refinements to at least one order of resolving power are examined. Some of these include anisotropic refinements involving elements of large aspect ratio; in some hydrodynamics cases, the anisotropy is extreme, with aspect ratios exceeding two orders. As expected, AMG1 delivers typical multi‐grid convergence rates, which for all practical purposes are independent of mesh bandwidth. AMG0 rates are slower. They may also be more discernibly mesh‐dependent. However, for the range of mesh bandwidths examined, the overall cost effectiveness of the two solvers is remarkably similar when a full convergence to machine accuracy is demanded. Thus, the shorter solution times for AMG1 do not necessarily compensate for the extra time required for its costly grid generation. This depends on the severity of the problem and the demanded level of convergence. For problems requiring few iterations, where grid generation costs represent a significant penalty, AMG0 has the advantage. For problems requiring a large investment in iterations, AMG1 has the edge. However, for the toughest problems addressed (vector and coupled vector–scalar fields discretized exclusively using finite elements of extreme aspect ratio) AMG1 is more robust: AMG0 has failed on some of these tests. However, but for this deficiency AMG0 would be the preferred linear approximation solver for Navier–Stokes solution algorithms in view of its much lower grid generation costs. Copyright © 2001 John Wiley & Sons, Ltd.     

An efficient parallel algebraic multigrid method for 3D injection moulding simulation based on finite volume method

Elapsed time is always one of the most important performance measures for polymer injection moulding simulation. Solving pressure correction equations is the most time-consuming part in the mould filling simulation using finite volume method with SIMPLE-like algorithms. Algebraic multigrid (AMG) is one of the most promising methods for this type of elliptic equations. It, thus, has better performance by contrast with some common one-level iterative methods, especially for large problems. And it is also suitable for parallel computing. However, AMG is not easy to be applied due to its complex theory and poor generality for the large range of computational fluid dynamics applications. This paper gives a robust and efficient parallel AMG solver, A1-pAMG, for 3D mould filling simulation of injection moulding. Numerical experiments demonstrate that, A1-pAMG has better parallel performance than the classical AMG, and also has algorithmic scalability in the context of 3D unstructured problems.     

Algebraic multigrid and incompressible fluid flow

This paper is concerned with the development of algebraic multigrid (AMG) solution methods for the coupled vector–scalar fields of incompressible fluid flow. It addresses in particular the problems of unstable smoothing and of maintaining good vector–scalar coupling in the AMG coarse‐grid approximations. Two different approaches have been adopted. The first is a direct approach based on a second‐order discrete‐difference formulation in primitive variables. Here smoothing is stabilized using a minimum residual control harness and velocity–pressure coupling is maintained by employing a special interpolation during the construction of the inter‐grid transfer operators. The second is an indirect approach that avoids the coupling problem altogether by using a fourth‐order discrete‐difference formulation in a single scalar‐field variable, primitive variables being recovered in post‐processing steps. In both approaches the discrete‐difference equations are for the steady‐state limit (infinite time step) with a fully implicit treatment of advection based on central differencing using uniform and non‐uniform unstructured meshes. They are solved by Picard iteration, the AMG solvers being used repeatedly for each linear approximation. Both classical AMG (C‐AMG) and smoothed‐aggregation AMG (SA‐AMG) are used. In the direct approach, the SA‐AMG solver (with inter‐grid transfer operators based on mixed‐order interpolation) provides an almost mesh‐independent convergence. In the indirect approach for uniform meshes, the C‐AMG solver (based on a Jacobi‐relaxed interpolation) provides solutions with an optimum scaling of the convergence rates. For non‐uniform meshes this convergence becomes mesh dependent but the overall solution cost increases relatively slowly with increasing mesh bandwidth. Copyright © 2006 John Wiley & Sons, Ltd.     

Foreword of the Founding Editor of the Journal Transport in Porous Media,Jacob Bear

The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny–Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.

     

CML模型的时空混沌

提出了一类新的耦合映射格点（ＣＭＬ）模型．数值实验表明这类新的ＣＭＬ模型对于强弱耦合系统均能有效研究其时空复杂性，揭示了非线性、耗散、色散相互作用的非常丰富的时空Ｐａｔｅｒｎ行为     

空间网格结构损伤探测的研究进展

空间网格结构损伤探测技术是目前结构工程领域研究的热点和难点．根据国内外的最新文献信息，讨论了损伤探测技术在空间网格结构中的应用及最新的研究进展，对现有文献中的方法进行了分类和评述．重点介绍了目前比较适用的柔度法和模型修正方法，对该领域中尚存在的问题进行了讨论，对今后的发展方向及趋势进行了展望．