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。     

基于AFT-Delaunay的二维解耦并行网格生成算法

面向平面任意几何区域网格生成,提出了一种将波前法AFT(Advancing Front Technique)与Delaunay法相结合的解耦并行网格生成算法。算法主要思想是沿着求解几何区域惯性轴,采用扩展的AFT-Delaunay算法生成高质量三角形网格墙,递归地将几何区域动态划分成多个彼此解耦的子区域;采用OpenMP多线程并行技术,将子区域分配给多个CPU并行生成子区域网格;子区域内部的网格生成复用AFT-Delaunay算法,保证了生成网格的质量、效率和一致性要求。本算法优先生成几何边界与交界面网格,有利于提高有限元计算精度;各个子区域的网格生成彼此完全解耦,因此并行网格生成过程无需通信。该方法克服了并行交界面网格质量恶化难题,且具有良好的并行加速比,能够全自动、高效率地并行生成高质量的三角网格。     

复杂三维组合曲面的有限元网格生成方法

提出一种基于映射法的复杂三维组合曲面的有限元网格全自动生成方法。通过引入虚边界解决了闭合曲面在参数域中边界不完整的问题；通过调节虚边界提高了复杂组合曲面网格生成的质量。改进二维多边形区域的裁减算法，解决了闭合曲面在参数空间中的边界环形成问题。对曲面片公共边界进行统一离散化处理，以满足有限元网格的相容性要求。以边界表示(B—Rep)数据结构为基础，实现了组合曲面全自动网格剖分的总成算法．改进了曲面网格剖分布点算法，并结合局部连接、诊断交换等技术，优化了网格的整体质量。     

复杂无粘流场数值模拟的矩形/三角形混合网格技术

建立了一套模拟复杂无粘流场的矩形／三角形混合网格技术，其中三角形仅限于物面附近，发挥非结构网格的几何灵活性，以少量的网格模拟复杂外型；同时在以外的区域采用矩形结构网格，发挥矩形网格计算简单快速的优势，有效地克服全非结构网格计算方法需要较大内存量和较长ＣＰＵ时间的不足．混合网格系统由修正的四分树方法生成．将ＮＮＤ有限差分与ＮＮＤ有限体积格式有机地融合于混合网格计算，消除了全矩形网格模拟曲边界的台阶效应，同时保证了网格间的通量守恒．数值实验表明本方法在模拟复杂无粘流场方面的灵活性和高效性．     

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.     

大量椭球颗粒随机分布三维区域的模拟及其四面体网格快速生成算法

针对颗粒为椭球形状并且随机分布的多相复合材料给出了三维情形下的计算机模拟方法,并对此复杂区域提供了一种四面体网格快速生成算法。此方法的基本思想:首先是根据材料的要求,给出随机颗粒材料的计算机模拟,然后对模拟后的颗粒边界初始化,得到一些初始剖分点,并给出剖分区域的初始网格(正四面体),接着把颗粒的初始边界点投入到剖分区域中,替换区域中靠此点近的点,并且采用加点寻找边界的方法和修正初始点方法来解决四面体穿刺边界问题,从而得到整个区域的四面体网格。最后用实例说明了算法的有效性。     

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。     

自适应多重网格有限元网格生成器研制

基于协调三角形剖分算法、分子表数据结构和Ｚｉｅｎｋｉｅｗｉｃｚ－Ｚｈｕ误估计方法，本文研制出适用于自适应多重网格有限元的网格生成器，该网格生成器可对复杂的区域进行自适应加密。当荷载作用边界随时间变及在动力荷载作用下，网格生成器可退化与再加密网格。     

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。     

高质量点集的快速局部网格生成算法

高效及高质量的局部网格生成算法是基于节点有限元并行方法设计的关键。泡泡布点算法能够在复杂区域上不经过人工干预生成高质量的节点集,本文提出了基于该方法所生成的节点集的快速局部网格生成算法。该算法充分利用泡泡布点方法提供的节点集及节点邻接链表信息,避免了桶数据结构的建立以及节点的局部搜索过程,只需应用Delaunay三角剖分的外接圆准则从中心节点的邻接链表中去除极少数的非卫星点,可快速地生成局部网格,比现有的局部网格生成算法更为快捷。算例结果表明,该算法高效可靠,生成网格与Delaunay三角剖分网格一致。     

Adaptive Runge–Kutta discontinuous Galerkin method for complex geometry problems on Cartesian grid

A Cartesian grid method using immersed boundary technique to simulate the impact of body in fluid has become an important research topic in computational fluid dynamics because of its simplification, automation of grid generation, and accuracy of results. In the frame of Cartesian grid, one often uses finite volume method with second order accuracy or finite difference method. In this paper, an h‐adaptive Runge–Kutta discontinuous Galerkin (RKDG) method on Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is developed. A ghost cell immersed boundary treatment with the modification of normal velocity is presented. The method is validated versus well documented test problems involving both steady and unsteady compressible flows through complex bodies over a wide range of Mach numbers. The numerical results show that the present boundary treatment to some extent reduces the error of entropy and demonstrate the efficiency, robustness, and versatility of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

直接控制网格节点分布的曲线网格生成技术研究

指出了Thompson与Thomas曲线网格生成方法中控制网格分布的调节函数的问题所在,克服了Thomas曲线网格生成法中边界处局部线性化近似假定的缺陷,经过严格推导得出一组新的调节函数P、Q的表达式,并给出了曲线网格生成实例.实例检验表明,该调节函数能够对复杂边界的单连通域或多连通域生成理想的曲线网格,即边界处网格正交,内部网格分布能够适应物理量场变化的情形.在实际水利工程流场数值模拟中,该方法能够准确地使用边界条件,提高求解的精确度.     

三维非均匀介质中弹性波传播的数值模拟

提出了一种三维非均匀介质中弹性波传播数值模拟的方法,文中称为三维格子法。该算法是二维格子法（一种二维非均匀介质中P－SV波传播的数值模拟算法）向三维非均匀介质情况的推广。在空间离散上该文方法与有限元方法类似,容许根据连续体的形状和介质分界面任意剖面网格,且自然满足自由表面边界条件。不同于常规有限差分法在各个节点上满足动力学微分方程,该算法通过满足各节点周围格子的整体平衡（积分平衡方程）来对问题进行求解,三维格子法所需的计算机内存及计算耗时与同阶精度的规则网格有限差分法相当。算例表明,该文提出的三维格子法具有较高的精度且可很好地模拟三维复杂形状地表对弹性波的反射和绕射。     

An adaptive Cartesian grid generation method for ‘Dirty’ geometry

Traditional structured and unstructured grid generation methods need a ‘water‐tight’ boundary surface grid to start. Therefore, these methods are named boundary to interior (B2I) approaches. Although these methods have achieved great success in fluid flow simulations, the grid generation process can still be very time consuming if ‘non‐water‐tight’ geometries are given. Significant user time can be taken to repair or clean a ‘dirty’ geometry with cracks, overlaps or invalid manifolds before grid generation can take place. In this paper, we advocate a different approach in grid generation, namely the interior to boundary (I2B) approach. With an I2B approach, the computational grid is first generated inside the computational domain. Then this grid is intelligently ‘connected’ to the boundary, and the boundary grid is a result of this ‘connection’. A significant advantage of the I2B approach is that ‘dirty’ geometries can be handled without cleaning or repairing, dramatically reducing grid generation time. An I2B adaptive Cartesian grid generation method is developed in this paper to handle ‘dirty’ geometries without geometry repair. Comparing with a B2I approach, the grid generation time with the I2B approach for a complex automotive engine can be reduced by three orders of magnitude. Copyright © 2002 John Wiley & Sons, Ltd.     

各向异性介质中弹性波的数值模拟

提出了一种非均匀各向异性介质中弹性波传播的数值模拟算法。该方法可以灵活地运用于具有任意地表形状、内部孔洞、固液边界和不规则内部交界面的介质情况,另外,该方法自然满足复杂几何边界的自由表面条件。这种基于三角形和四边形离散网格的算法使用的是围绕每个节点的积分平衡方程,而不是其它有限差分法中使用的各个节点满足的弹性动力学的微分方程。该文工作是非均匀各向同性介质中弹性波传播格子法研究的继续。除了研究各向异性介质中波的传播以外,还给出了一种能够省时的四边形网格的格子法。     

A virtual boundary method with improved computational efficiency using a multi‐grid method

The flow around spherical, solid objects is considered. The boundary conditions on the solid boundaries have been applied by replacing the boundary with a surface force distribution on the surface, such that the required boundary conditions are satisfied. The velocity on the boundary is determined by extrapolation from the flow field. The source terms are determined iteratively, as part of the solution. They are then averaged and are smoothed out to nearby computational grid points. A multi‐grid scheme has been used to enhance the computational efficiency of the solution of the force equations. The method has been evaluated for flow around both moving and stationary spherical objects at very low and intermediate Reynolds numbers. The results shows a second order accuracy of the method both at creeping flow and at Re=100. The multi‐grid scheme is shown to enhance the convergence rate up to a factor 10 as compared to single grid approach. Copyright © 2004 John Wiley & Sons, Ltd.     

NUMERICAL SIMULATION OF ELASTIC WAVE PROPAGATION IN ANISOTROPIC MEDIA

A new numerical simulation algorithm is presented for the elastic wave propagation in heterogeneous anisotropic media. We make discretization of the computational domain by using triangular and quadrangular grids. The scheme is based on integral equilibrium at each node to simulate the elastic wave propagation in heterogeneous anisotropic media. The scheme is very flexible in dealing with arbitrary surface topography, inner openings, liquid-solid boundaries and irregular interfaces. Moreover, the free-surface condition of complex geometrical boundaries can be satisfied naturally. This work is an extension of the grid method for the elastic wave propagation in heterogeneous isotropic media, and a quadrangular grid with low computational cost is also introduced. Project supported by the National Natural Science Foundation of China(19672016).     

A hybrid building‐block and gridless method for compressible flows

A hybrid building‐block Cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries. In this method, a Cartesian mesh based on a building‐block grid is used as a baseline mesh to cover the computational domain, while the boundary surfaces are represented using a set of gridless points. This hybrid method combines the efficiency of a Cartesian grid method and the flexibility of a gridless method for the complex geometries. The developed method is used to compute a number of test cases to validate the accuracy and efficiency of the method. The numerical results obtained indicate that the use of this hybrid method leads to a significant improvement in performance over its unstructured grid counterpart for the time‐accurate solution of the compressible Euler equations. An overall speed‐up factor from six to more than one order of magnitude and a saving in storage requirements up to one order of magnitude for all test cases in comparison with the unstructured grid method are demonstrated. Copyright © 2008 John Wiley & Sons, Ltd.     

A simplified adaptive Cartesian grid system for solving the 2D shallow water equations

This paper presents a new simplified grid system that provides local refinement and dynamic adaptation for solving the 2D shallow water equations (SWEs). Local refinement is realized by simply specifying different subdivision levels to the cells on a background uniform coarse grid that covers the computational domain. On such a non‐uniform grid, the structured property of a regular Cartesian mesh is maintained and neighbor information is determined by simple algebraic relationships, i.e. data structure becomes unnecessary. Dynamic grid adaptation is achieved by changing the subdivision level of a background cell. Therefore, grid generation and adaptation is greatly simplified and straightforward to implement. The new adaptive grid‐based SWE solver is tested by applying it to simulate three idealized test cases and promising results are obtained. The new grid system offers a simplified alternative to the existing approaches for providing adaptive mesh refinement in computational fluid dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

CFD多块网格生成新进展

网格生成是计算流体力学的重要组成部分,多块网格在CFD实践中获得了广泛的应用．结合对网格生成技术规范和网格生成系统的讨论,综述了多块网格近年来的新进展,重点评述了网格拓扑和网格拼接技术（包括所谓的连续拼接、非结构拼接和广义拼接）,完整飞机外形多块网格生成策略,自动分块技术以及相应的块合井技术,CAD和CFD之间的数据交换技术和基于NURBS的曲面网格生成技术,网格质量分析和控制技术,若干网格生成新方法,以及多块网格在航空气动力数值模拟中的应用．