Structured mesh generation with smoothness controls

In geometrically complex domains, the Ryskin and Leal (RL) orthogonal mesh generation system may cause mesh distortion and overlapping problems when using the ‘weak constraint’ method with specified boundary point distribution for all boundaries. To resolve these problems, an improved RL system with automatic smoothness control is proposed. In this improved RL system, the automatic smoothness control mechanism is based on five types of smoothness conditions and includes the self‐adjustment mechanism and the auto‐evaluation mechanism for an empirical parameter. The proposed system is illustrated using several test examples. Several applications to natural domains are also demonstrated. It is shown that the improved RL system is capable of resolving the above problems at little cost of orthogonality. Copyright © 2006 John Wiley & Sons, Ltd.     

Two‐dimensional adaptive mesh generation

In this paper, a two‐dimensional adaptive elliptic mesh generation system, derived from the Ryskin and Leal (RL) orthogonal mesh generation system based on the orthogonal condition (orthogonality) and the cell area equal‐distribution principle (adaptivity), is presented. The proposed generation system takes into account not only the mesh orthogonality and adaptivity but also the mesh smoothness by adopting a method that the distortion functions is determined by both the scale factors and the averaged scale factors of the constant mesh lines. Examples and application show that the proposed generation system is effective and easy to use. Copyright © 2007 John Wiley & Sons, Ltd.     

A simple quality triangulation algorithm for complex geometries

This paper presents a simple algorithm for quality triangulation in domains with complex geometries. Based on the fact that the equilateral triangles (regular meshes) are ideal for numerical computations in computational fluids dynamics (CFD) analysis, the proposed algorithm starts with an initial equilateral triangle mesh covering the whole domain. Nodes close to the boundary edges satisfy the so‐called non‐encroaching criterion, the distance from any inserted node to any boundary vertices and the midpoints of any boundary edge is greater than a given characteristic length. Both nearly uniform and non‐uniform triangle meshes can be generated using a mesh size reduction technique. Local refinement is achieved by using transition layers. More regular meshes can be generated in the interior of the domain and all angles of the triangle mesh produced by this algorithm are proven to be bounded in a reasonable range (19.5–141°). Copyright © 2010 John Wiley & Sons, Ltd.     

一类面向高阶精度自适应流动计算的流场插值方法

网格自适应技术和高阶精度数值方法是提升计算流体力学复杂问题适应能力的有效技术途径. 将这两项技术结合需要解决一系列技术难题, 其中之一是高阶精度流场插值. 针对高阶精度自适应流动计算, 提出一类高精度流场插值方法, 实现将前一迭代步网格中流场数值解插值到当前迭代步网格中, 以延续前一迭代步中的计算状态. 为实现流场插值过程中物理量守恒, 该方法先计算新旧网格的重叠区域, 然后将物理量从重叠区域的旧网格中转移到新网格中. 为满足高阶精度要求, 先采用k-exact最小二乘方法对旧网格上的数值解进行重构, 获得描述物理量分布的高阶多项式, 随后采用高阶精度高斯数值积分实现物理量精确地转移到新网格单元上. 最后, 通过一个具有精确解的数值算例和一个高阶精度自适应流动计算算例验证了本文算法的有效性. 第一个算例结果表明当网格规模固定不变时, 插值精度阶数越高, 插值误差越小; 第二个算例显示本文方法可以有效缩短高精度自适应流动计算的迭代收敛时间.      

面向复杂几何模型的并行四面体网格生成方法

面向大规模工程计算等数值模拟领域,提出了一种支持复杂几何模型的大规模四面体网格并行生成方法。该方法以复杂几何模型作为输入,首先采用串行网格生成方法生成初始四面体网格,然后通过两级区域分解方法将初始网格分解为多个子网格并分配到相应的进程中,进程间并行地提取出子网格的表面网格,并基于几何模型对面网格进行贴体加密,最后对加密后的面网格采用Delaunay方法重新生成四面体网格,该方法可以更好地适应高性能计算机体系结构,较好地克服了并行方法中并行性能和网格质量不能兼顾的问题。对三峡大坝模型进行测试和验证,证明该方法具有良好的并行效率和可扩展性,可以在数万处理器核上并行生成数十亿高质量四面体网格。     

A coupled finite volume method for the solution of flow processes on complex geometries

CFD modelling of ‘real‐life’ thermo‐fluid processes often requires solutions in complex three‐dimensional geometries, which can result in meshes containing aspects that are badly distorted. Cell‐centred finite volume methods (CC‐FV), typical of most commercial CFD tools, are computationally efficient, but can lead to convergence problems on meshes that feature cells with highly non‐orthogonal shapes. The control volume‐finite element method (CVFE) uses a vertex‐based approach and handles distorted meshes with relative ease, but is computationally expensive. A combined vertex‐based—cell‐centre technique (CFVM), detailed in this paper, allows solutions on distorted meshes where purely cell‐centred solutions procedures fail. The method utilizes the ability of the vertex‐based approach to resolve the flow field on a distorted mesh, enabling well established cell‐centred physical models to be employed in the solution of other transported quantities. The vertex‐based flow code is verified against a manufactured 3D solution and error norms are compared on meshes with various degrees of distortion. The CFVM method is validated with benchmark solutions for thermally driven flow and turbulent flow. Finally, the method is illustrated on three‐dimensional turbulent flow over an aircraft wing on a distorted mesh where purely cell‐centred techniques fail. The CFVM is relatively straightforward to embed within generic CC based CFD tools allowing it to be employed in a wide variety of processing applications. Copyright © 2006 John Wiley & Sons, Ltd.     

A study on the extension of a VOF/PLIC based method to a curvilinear co-ordinate system

The conventional volume-of-fluid method has the potential to deal with large free surface deformation on a fixed Cartesian grid. However, when free-surface flows are within or over complex geometries of industrial relevance, such as free-surface flows over offshore oil platforms, it is advantageous to extend the method originally written in Cartesian forms into non-Cartesian forms. In the present study, an algorithm similar to the algorithm described by Rudman in 1997 is proposed for use with curvilinear co-ordinates. This extension results in the ability to model complex geometries which could not be modelled using the original algorithm. Excellent agreement between the solutions obtained on both orthogonal and non-orthogonal meshes is achieved, although in general the L ₁ error, based on the exact solution, on the non-orthogonal mesh is slightly higher than that on the orthogonal mesh. The extended fluid flow solving capacity of the present method is demonstrated through its application to a non-orthogonal Rayleigh–Taylor instability problem.     

多特征几何体的全六面体网格自动生成方法

有限元分析的精度和效率与网格划分的质量有直接关系.目前尚缺乏一种普适性的自动网格划分方法,尤其是对于具有多种几何特征的复杂模型,现有的六面体网格自动划分算法存在不同几何特征间的网格兼容性较差以及孔状特征周围网格质量不高的问题.对此本文提出一种基于映射法的六面体网格自动生成方法,在映射法的基本框架下,将物理空间中的复杂几何体映射为计算空间中的规则几何体,引入边界顶点分类,将复杂几何体边界进行简化,将子域约束进行连接,寻找贯穿边界,以使映射网格在约束特征间兼容;对圆弧特征进行等效转化,降低曲率过大对于网格过渡的影响.实例验证表明,本方法稳定可靠,生成的六面体网格质量较高,能够解决多特征复杂几何体六面体网格自动划分问题.     

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...     

Nouvelle approche pour la discrétisation de flux diffusifs en volumes finis à forte obliquité

We propose a new approach for the discretization of diffusive flux on a non orthogonal mesh based on the Deferred correction introduced by Peric. This new method is applied successfully to the solution of a Poisson problem in quadrangular domains meshed with very distorted control volumes. The interest of this approach lies in the fact that the precision of the used schemes is conserved despite meshes distortion level. The comparative study of the value of the spectral radius of iteration matrix enables us to explain why our Deferred correction approach is better than that of Peric, which diverges on highly skewed meshes. To cite this article: Y.M. Ahipo, Ph. Traore, C. R. Mecanique 334 (2006).     

基于人工神经网络的非结构网格尺度控制方法

网格自动化生成和自适应是制约计算流体力学发展的瓶颈问题之一, 网格生成质量、效率、灵活性、自动化程度和鲁棒性是非结构网格生成的关键问题. 在非结构网格生成中, 网格空间尺度分布控制至关重要, 直接影响网格生成质量、效率和求解精度. 采用传统的背景网格法进行空间尺度分布控制需要在背景网格上求解微分方程得到背景网格上的尺度分布, 再将网格尺度从背景网格插值到真实空间点, 过程十分繁琐且耗时. 本文从效率和自动化角度提出两种网格尺度控制方法, 首先发展了基于径向基函数(RBF)插值的网格尺度控制方法, 通过贪婪算法实现边界参考点序列的精简, 提高了RBF插值的效率. 同时, 还采用人工神经网络进行网格尺度控制, 初步引入相对壁面距离和相对网格尺度作为神经网络输入输出参数, 建立人工神经网络训练模型, 采用商业软件生成二维圆柱和二维翼型非结构三角形网格作为训练样本, 通过训练和学习建立起相对壁面距离和相对网格尺度的神经网络关系. 进一步实现了二维圆柱、不同的二维翼型的尺度预测, RBF方法和神经网络方法的效率与传统背景网格法相比提高了5~10倍, 有助于提高网格生成的效率. 最后, 将方法推广应用于各向异性混合网格尺度预测, 得到的网格质量满足要求.      

黏性边界层网格自动生成

高雷诺数黏性流动在壁面附近存在边界层,在计算模拟中自动生成可靠且有效的计算网格仍然是计算流体力学存在的瓶颈.三棱柱/四面体混合网格技术在一定程度上缓解了这个困难.然而,对于复杂外形的情况,在边界层内自动高效生成高质量的三棱柱单元仍然十分困难.常用的层推进法在凹凸区域及角点处生成的边界层网格单元质量较差,边界层网格最外层尺寸不均匀.针对这些问题,发展了一种黏性边界层网格自动生成方法,通过顶点周围边的二面角识别物面网格特征确定多生长方向,预估并调整生长高度处理相交情况.同时提出一种三维前沿尺寸调节方式,提高了边界层网格单元的正交性,保证了边界层网格与远场网格尺寸的光滑过渡.通过ONERA M6翼型以及带发动机短舱的DLR-F6翼身组合体等外形的网格生成实例及绕流数值模拟,将计算值与标准实验值进行对比,结果表明:该方法能够自动高效地生成满足数值计算需求的混合网格.     

Improving the robustness of the control volume finite element method with application to multiphase porous media flow

Control volume finite element methods (CVFEMs) have been proposed to simulate flow in heterogeneous porous media because they are better able to capture complex geometries using unstructured meshes. However, producing good quality meshes in such models is nontrivial and may sometimes be impossible, especially when all or parts of the domains have very large aspect ratio. A novel CVFEM is proposed here that uses a control volume representation for pressure and yields significant improvements in the quality of the pressure matrix. The method is initially evaluated and then applied to a series of test cases using unstructured (triangular/tetrahedral) meshes, and numerical results are in good agreement with semianalytically obtained solutions. The convergence of the pressure matrix is then studied using complex, heterogeneous example problems. The results demonstrate that the new formulation yields a pressure matrix than can be solved efficiently even on highly distorted, tetrahedral meshes in models of heterogeneous porous media with large permeability contrasts. The new approach allows effective application of CVFEM in such models.     

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。     

A novel Cartesian cut cell solver for incompressible viscous flow in irregular domains

A Cartesian cut cell solver with solution‐based adaptive mesh refinement is developed for simulating viscous, incompressible flows with arbitrary complex geometries. The cut cells are automatically generated using Volume CAD (VCAD), a framework for storing geometric and material attribute data. Unlike earlier cut cell methods, this solver organizes the cutting patterns into only six categories and further subdivides the resulting pentagon into two quadrilaterals, such that mesh data can be stored by uniform data structure and the post‐processing of flow data can be handled conveniently. A novel method is proposed to treat minuscule cut cells without the process of cell merging. A collocated finite volume method, which can be used even when multiple cell shapes and orthogonal and non‐orthogonal grids exist in the decomposition, is employed to discretize the Navier–Stokes equations. A modified SIMPLE‐based smoothing pressure correction scheme is applied in this cut cell method to suppress checkerboard pressure oscillations caused by collocated arrangement. The solver is first used to simulate a channel flow to demonstrate its calculation accuracy expressed with L₁ and L_∞ norm errors and then the method is utilized to solve three benchmark problems of flow and heat transfer within irregular domains to verify its feasibility, efficiency, accuracy and potential in engineering applications. Copyright © 2010 John Wiley & Sons, Ltd.     

Semi‐structured meshes for axial turbomachinery blades

This paper describes the development and application of a novel mesh generator for the flow analysis of turbomachinery blades. The proposed method uses a combination of structured and unstructured meshes, the former in the radial direction and the latter in the axial and tangential directions, in order to exploit the fact that blade‐like structures are not strongly three‐dimensional since the radial variation is usually small. The proposed semi‐structured mesh formulation was found to have a number of advantages over its structured counterparts. There is a significant improvement in the smoothness of the grid spacing and also in capturing particular aspects of the blade passage geometry. It was also found that the leading‐ and trailing‐edge regions could be discretized without generating superfluous points in the far field, and that further refinements of the mesh to capture wake and shock effects were relatively easy to implement. The capability of the method is demonstrated in the case of a transonic fan blade for which the steady state flow is predicted using both structured and semi‐structured meshes. A totally unstructured mesh is also generated for the same geometry to illustrate the disadvantages of using such an approach for turbomachinery blades. Copyright © 2000 John Wiley & Sons, Ltd.     

格子玻尔兹曼法多块网格的交界结构优化研究

基于格子玻尔兹曼方法LBM(Lattice Boltzmann Method)对多块网格方法(Multi-Block)的粗细网格交界结构进行了研究,提出了一种新的优化处理方案。解决了原有网格交界结构存在的三个问题,即两套插值运算造成的程序结构复杂的问题,存储前几个时间步的节点流场数据以备插值运算造成内存浪费的问题和基于时间插值结果进行空间插值计算造成插值误差积累的问题。用一次多点二维空间插值的方式,将原方法的空间和时间双插值,简并成一次空间插值。通过对经典的非定常的圆柱绕流算例和定常的标准顶盖方腔驱动流算例的仿真模拟,验证了交界面处质量、动量及应力的连续性以及网格交界面数据过渡的流畅度,最终验证了改进方法的正确性。数值模拟结果表明,改进后多块算法可实现局部网格细化,进一步推动LBM方法在实际工程问题中的应用。     

A Runge-Kutta–based WENO reconstruction on moving mesh for compressible fluids

In this paper, we construct a high-order moving mesh method based on total variation diminishing Runge-Kutta and weighted essential nonoscillatory reconstruction for compressible fluid system. Beginning with the integral form of fluid system, we get the semidiscrete system with an arbitrary mesh velocity. We use weighted essential nonoscillatory reconstruction to get the space accuracy on moving meshes, and the time accuracy is obtained by modified Runge-Kutta method; the mesh velocity is determined by moving mesh method. One- and two-dimensional numerical examples are presented to demonstrate the efficient and accurate performance of the scheme.     

A method for computing three dimensional flows using non-orthogonal boundary-fitted co-ordinates

For three-dimensional fluid flows in complex geometries, it is convenient to make predictions using a non-orthogonal boundary-fitted mesh. The present paper describes an economical method of solving the equations of motion for two and three dimensional problems using such meshes. The locations on the mesh at which the depenent variables are calculated, and the methods used to solve the equations, are key issues in the development of a successful algorithm; these are discussed in the present paper. Results obtained when the proposed method is applied to several problems are also described. The method is intended for flows in which compressibility effects do not dominate.     

平面区域四边形网格自动生成技术

本文分析和综述了四边形网格自动生成的各种算法,给出了三角形网格向四边形网格转换的局部算法,以及有FCT思想直接生成四边形和三角形网格算法。详细分析了此法之下生成网格的几何拓朴性质,最后给出实例验证了算法的有效性。