一种部分连续复合网格生成方法

本文描述了一种构造部分连续复合网络的偏微分方程的数值生成方法，该方法以泊松方程为变换控制方程，构造特定的边界条件，对复杂的蜗尾船型的横剖面进行了变换，变换出来的复合网格与单一区域网格相比，生成的网格质量有明显提高，并计算了另外一个例子，证明了该方法的通用性。     

一种三维表面网格自动生成方法

提出了一种改进的区域分解法,用于三维表面三角形和四边形网格的自动生成。基于区域分解法的三维表面网格生成的主要技术包括三维表面三角形面片拓扑关系的建立,表面三角形面片的分组及特征面的确定,空间曲线上网格节点的生成,区域内外边界的合并,最佳剖分面的确定,以及网格的光滑处理等。本文对这些技术进行了详细的介绍。本文提出的表面网格生成方法具有算法可靠、生成网格效率高以及生成网格质量高等优点。最后给出三维表面网格生成实例验证了本文提出方法的可靠性。     

一种新的准结构网格生成方法

在有限元分析中,高质量的结构网格可以有效地提高有限元分析的精度,但结构网格的几何适应性差,针对复杂边界的二维计算模型,现有的方法很难自动生成高质量的结构网格;而非结构网格几何适应性很好,但存在计算效率低和精度差等问题。提出了一种新的准结构网格生成方法,能够实现复杂区域的网格自动生成并且具有高网格质量。该方法首先对计算区域运用Delaunay三角剖分技术生成粗背景网格;然后利用背景网格,使用优化的Voronoi图生成过渡的蜂巢网格;最后,通过中心圆方法对蜂巢网格单元进行结构网格剖分。分析NACA0012翼型数值模拟结果表明,提出的新准结构网格生成方法能够对边界复杂的模型自动生成高质量的网格,并且通过三种不同拓扑类型网格计算结果相互对比及与实验结果对比,证明准结构网格具有高计算精度。     

一种新的全四边形网格快速生成方法─—模板法

本文提出了一种正方形亲单元上实现网格在二个坐标方向均能过渡的全四边形单元生成方法．该方法允许正方形周边节点任意分布，并可以对单元密度进行控制，将该方法和映射法结合解决了用映射单元法对结构进行四边形单元划分时存在的网格过渡的这一关键问题。该方法计算量少，运算速度快，生成单元的形状良好。     

一种新的钢筋薄膜组合单元及其网格自动生成

提出了一种新的钢筋薄膜组合单元模型和薄膜单元结点信息生成技术。该模型能考虑任意方向的钢筋薄膜,使得单元网格的划分不必考虑钢筋的方位,克服了现有钢筋薄膜组合单元所存在的缺陷。应用本文提出的薄膜结点生成技术,只要给出钢筋薄膜四个角点的坐标,即可自动形成薄膜单元在组合单元中的信息。算例表明该模型方便可行,单元划分效率高,且能达到相当的精度。     

一种全四边形网格生成方法——改进模板法

首先对全四边形单元网格自动剖分算法中的模板法进行了探讨，并提出了相应的改进方法。在此基础上提出了一种新的全四边形单元网格自动生成方法。该方法允许在两个方向上存在网格疏密过渡，并可以提高单元的密度要求自动计算亲单元每条边上的结点数，有效地对局部实施加密处理。     

一种简单快速的多块网格生成方法

利用有限元中的形函数进行网格插值映射分块生成网格,构造了一种块网格拓扑结构,使得块与相邻块之间自动组合,并利用该方法对二维、三维复杂区域进行分块网格生成,说明该方法生成的网格质量较好,适合于复杂区域分块求解。     

一种新的全四边形网格快速生成方法——模板法

本文提出了一种正方形亲单元上实现网格在二个坐标方向均能过渡的全四边形单元生成方法，该方法允许正方形周边节点任意分布，并可以对单元密度进行控制，将该方法和映射法结合解决了用映射单元法对结构进行的四边形单元划分时存在的网格过渡的这一关键问题，该方法计算量少，运算速度快，生成单元的形状良好。     

基于贴体网格的VOF方法数模流场研究

提出了一种基于VOF方法的模拟具有复杂边界形状结构物附近流场的新算法,BFC—SIMPLE—VOF算法。采用坐标变换方法实现了任意复杂区域的结构化网格划分,在贴体网格下对二维不可压缩粘性流体的控制方程进行了离散。提出了基于交错网格的修正SIMPLE算法来迭代求解压力一速度场,修正了贴体坐标下的界面跟踪方法（VOF方法）...     

一种基于双前沿推进的边界层网格生成算法

高雷诺数粘性流动模拟对边界层内的网格正交性有特殊要求.对于复杂外形,这类问题的网格自动化生成十分困难.面向该问题,提出一种双前沿推进思想,并形成一种面向复杂几何外形的边界层网格全自动生成算法.结合多种网格技术处理局部几何特征以保证边界层网格的质量.双前沿推进思想同时适用于多块结构网格和混合网格的边界层网格生成.多个模型...     

An algorithm of finite element grid generation for three-dimensional complex connected domain

An automated quasi three-dimensional finite element grid generation method is presented for particular three-dimensional complex connected domain, across which some are simply connected two-dimensional.regions and some are multiply connected two-dimensional regions. A subdivision algorithm based on the variational principle has been developed to ascertain the smoothness and orthogonality of the generated grid in any cross sections. Smooth transition between the simply and multiply connected regions is maintained. For illustration, the method is applied to generate a finite element three-dimensional grid for human above knee stump.     

A finite volume method for numerical grid generation

A novel method to generate body‐fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables ξ, η and ζ is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re‐zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid‐correction procedure. The scalar variables are re‐mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet–Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local‐boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point‐by‐point and whole‐field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright © 1999 National Research Council of Canada.     

子域精细积分及偏微分方程数值解

对于偏微分方程半解析法的方程，精细时程积分虽然能求出高度准确的解，但往往面临矩阵尺度太大的困难；另一方面差分法虽然有带宽小的优点，但有稳定性及精度方面的问题．本文提出子域精细积分法，既可利用精细积分的数值优点，又有带宽小的好处．数值例题表明了子域精细积分法的效能．     

A composite grid approach for the Euler equations

A zonal grid methodology has been developed for the calculation of compressible fluid flows. The domain subdivision is based on patched grid systems composed of zones or blocks within which a distinct curvilinear grid is generated. The flow simulation is then carried out with a modified scheme based on the Euler finite volume solver of Ni. This scheme uses a distribution procedure that provides an easy and accurate way for the transfer of information from one block to another. This method results in a naturally conservative computation at the interfaces. It is analysed and developed for the treatment of embedded grids with a grid point common to more than four blocks.     

A large-scale parallel hybrid grid generation technique for realistic complex geometry

High-Performance Computing (HPC) systems and Computational Fluid Dynamics (CFD) have made significant progress in recent years; however, as the basis of the large-scale parallel computing, the massive grid generation of billions of cells has become a bottleneck problem. In this study, a parallel grid generation technique is proposed to generate large-scale mixed grids with arbitrary cell types and scales. The basic idea of our method is analogous to the global mesh refinement technique. An initial coarse grid with arbitrary cell types is regarded as a background mesh which is partitioned into subzones, and subzones are assigned onto different CPU cores. After the cells and faces in each subzone are split, the inserted new points of the solid wall are projected onto the original CAD entities to preserve the geometry accurately. Finally, the tangled cells caused by the projection in the boundary layer are untangled by a local Radial Basis Function mesh deformation technique. Furthermore, a parallel partition approach and an efficient wall distance computing technique for massive grids are developed also to shorten the preprocessing time. The tests show that the preprocessing efficiency has been increased by two or three orders compared with traditional methods. Billions of grids are generated for the AIAA JSM high-lift model and the Chinese CHN-T1 transport model to test the ability of the parallel grid generation technique. The maximum scale up to 19 billion mixed elements is generated using 16 384 CPU cores in parallel, and the mesh quality is acceptable for CFD simulations.     

The boundary layer method for the solution of singular perturbation problem for the parabolic partial differential equation

In this paper, we discuss the singular perturbation problem of the parabolic partial differential equation. As usual, we must reduce the mesh size in the neighbourhood of the boundary layer so that typical feature of the boundary layer will not be lost. Then we need very large operational quantity when mesh sizes are getting too small. Now we propose the boundary layer scheme, which need not take very fine mesh size in the neighbourhood of the boundary layer. Numerical examples show that the accuracy can be satisfied with moderate step size.     

Numerical residual elimination method of finite differential equations

In this paper,a new elimination of finite differential equations has been discussed.It applies the numerical direct iteration to obtain the residual equations,in which the number of unknowns has been reduced greatly.The solution process is simple and efficient,and the solution is exact     

基于非结构/混合网格的高阶精度格式研究进展

尽管以二阶精度格式为基础的计算流体力学(CFD) 方法和软件已经在航空航天飞行器设计中发挥了重要的作用, 但是由于二阶精度格式的耗散和色散较大, 对于湍流、分离等多尺度流动现象的模拟, 现有成熟的CFD 软件仍难以给出满意的结果, 为此CFD 工作者发展了众多的高阶精度计算格式. 如果以适应的计算网格来分类, 一般可以分为基于结构网格的有限差分格式、基于非结构/混合网格的有限体积法和有限元方法,以及各种类型的混合方法. 由于非结构/混合网格具有良好的几何适应性, 基于非结构/混合网格的高阶精度格式近年来备受关注. 本文综述了近年来基于非结构/混合网格的高阶精度格式研究进展, 重点介绍了空间离散方法, 主要包括k-Exact 和ENO/WENO 等有限体积方法, 间断伽辽金(DG) 有限元方法, 有限谱体积(SV) 和有限谱差分(SD) 方法, 以及近来发展的各种DG/FV 混合算法和将各种方法统一在一个框架内的CPR (correctionprocedure via reconstruction) 方法等. 随后简要介绍了高阶精度格式应用于复杂外形流动数值模拟的一些需要关注的问题, 包括曲边界的处理方法、间断侦测和限制器、各种加速收敛技术等. 在综述过程中, 介绍了各种方法的优势与不足, 其间介绍了作者发展的基于"静动态混合重构" 的DG/FV 混合算法. 最后展望了基于非结构/混合网格的高阶精度格式的未来发展趋势及应用前景.     

A vertically moving grid finite‐element modelling of tidal flow in the Changjiang Estuary,China

An estuarine two‐dimensional vertical finite‐element model of tidal flow has been established by laterally integrating Navier–Stokes equation. To this end, a moving grid finite‐element method has been used. An arbitrarily shaped quadrilateral element has been selected. This model has been validated by using field data from two monitoring stations at the North Passage of the Changjiang Estuary. Using this numerical model, two types of modelled results were obtained: (1) vertical distributions of tidal current velocities at the North Passage of the Changjiang Estuary; (2) longitudinal distributions of tidal current velocities at maximum flood tide, at high slack water, at maximum ebb tide and at low slack water tide at the North Passage of the Changjiang Estuary. The conclusion is that the model provides a reasonable agreement with observed data. Copyright © 2003 John Wiley & Sons, Ltd.