基于重叠划分的自由网格四边形单元计算方法

提出了一种基于重叠划分的自由网格四边形单元计算方法。这一方法将四边形单元引入到自由网格计算方法中，不仅提高了计算的精度，同时还保留了自由网格计算方法的特点。方法首先对分析域内自动生成的每一个节点建立一套临时三角形单元，利用这些临时三角形单元组合生成四边形单元，以节点为单位进行计算。由于各矩阵的计算与组集均以节点为中心进行处理，因而特别适合于并行计算环境。在详细介绍自由网格四边形单元计算方法的基础上，利用数值算例证实了这一方法改善计算精度方面的有效性。     

求解对流扩散方程的一种高效的有限体积法

考虑无结构三角网格上求解对流扩散方程的有限体积法.引入一种梯度函数的计算方法,将现有方法中计算解变量在网格单元中心和网格单元边界的梯度的两个独立过程改造成一个过程来完成,发展了一种求解对流扩散方程的高效的有限体积法.数值实验结果表明,该方法完全达到了已有方法同样的精度,而在计算速度上有明显的提高.     

非连续问题中单元分割的模板方法

扩展有限元法 (extended finite element method, XFEM) 因具有裂纹几何独立于模拟网格、裂纹扩展时无需网格重分重映、计算精度高等优点,成为裂纹分析的主流数值方法之一. 但该方法在工程实践中存在单元被裂纹分割的几何困难 —— 现有精确几何分割方法实现复杂、计算量大、鲁棒性差. 为克服这一困难, 本文提出一种基于单元水平集的模板分割方法, 用于非连续单元子剖分和数值积分. 首先, 遍历单元水平集值所有形态并建立标准单元分割模板库; 然后, 根据单元水平集值, 对非标准单元进行形态查询和模板插值; 最后, 套用标准单元分割模板实现单元高效分割和子剖分. 将该方法与常规XFEM、改进型XFEM进行结合,从而应用于孔洞、夹杂、裂纹等非连续问题分析中. 算例分析表明, 本文提出的模板分割方法具有较高计算精度. 由于不引入复杂几何操作, 该模板分割方法同时具有较高计算效率和鲁棒性, 故可为XFEM类方法在实际工程应用中提供有效支撑.      

板壳畸变单元的无网格和有限元自动耦合方法

板壳大变形时单元的严重畸变会使计算精度降低。无网格局部Petrov-Galerkin法是一种真正的无网格方法,能够消除网格畸变,但比有限元法计算效率低。根据板壳网格畸变的局部性特点,利用过渡单元法,基于板壳网格质量,建立了板壳的网格严重畸变区域由有限元分析切换为无网格分析的自动耦合算法,实现了有限元法和无网格局部彼得罗夫．迦辽金法的耦合。应用实例表明：通过自适应耦合,既能发挥有限元法计算效率高的特点,又能发挥无网格法适合大变形分析、没有网格畸变造成计算困难的特点。     

非结构网格二阶有限体积法中黏性通量离散格式精度分析与改进

非结构网格二阶有限体积离散方法广泛应用于计算流体力学工程实践中,研究非结构网格二阶精度有限体积离散方法的计算精度具有现实意义. 计算精度主要受到网格和计算方法的影响,本文从单元梯度重构方法、黏性通量中的界面梯度计算方法两个方面考察黏性流动模拟精度的影响因素. 首先从理论上分析了黏性通量离散中的“奇偶失联”问题,并通过基于标量扩散方程的制造解方法验证了“奇偶失联”导致的精度下降现象,进一步通过引入差分修正项消除了“奇偶失联”并提高了扩散方程计算精度;其次,在不同类型、不同质量的网格上进行基于扩散方程的制造解精度测试,考察单元梯度重构方法、界面梯度计算方法对扩散方程计算精度的影响,结果显示,单元梯度重构精度和界面梯度计算方法均对扩散方程计算精度起重要作用;最后对三个黏性流动算例(二维层流平板、二维湍流平板和二维翼型近尾迹流动)进行网格收敛性研究,初步验证了本文的结论,得到了计算精度和网格收敛性均较好的黏性通量计算格式.      

非结构网格二阶有限体积法中黏性通量离散格式精度分析与改进

非结构网格二阶有限体积离散方法广泛应用于计算流体力学工程实践中,研究非结构网格二阶精度有限体积离散方法的计算精度具有现实意义.计算精度主要受到网格和计算方法的影响,本文从单元梯度重构方法、黏性通量中的界面梯度计算方法两个方面考察黏性流动模拟精度的影响因素.首先从理论上分析了黏性通量离散中的"奇偶失联"问题,并通过基于标量扩散方程的制造解方法验证了"奇偶失联"导致的精度下降现象,进一步通过引入差分修正项消除了"奇偶失联"并提高了扩散方程计算精度;其次,在不同类型、不同质量的网格上进行基于扩散方程的制造解精度测试,考察单元梯度重构方法、界面梯度计算方法对扩散方程计算精度的影响,结果显示,单元梯度重构精度和界面梯度计算方法均对扩散方程计算精度起重要作用;最后对三个黏性流动算例(二维层流平板、二维湍流平板和二维翼型近尾迹流动)进行网格收敛性研究,初步验证了本文的结论,得到了计算精度和网格收敛性均较好的黏性通量计算格式.     

无单元Galerkin法和边界元耦合法

无网格方法与有限元法或边界元法耦合是无网格方法处理边界条件的方法之一,在无网格方法中研究无网格方法与有限元法或边界元法耦合的研究显得非常重要.本文在无单元Galerkin法和边界元法的基础上,基于无单元Galerkin法子域和边界元法子域的界面上位移连续和面力平衡条件,提出了一种新的无单元Galerkin法和边界元法的直接耦合方法,对弹性力学问题详细推导了在整个求解域上的耦合公式.与以往的耦合法相比,这种方法简单直观,不需要增加新的耦合区域,也不需要建立新的逼近函数来保证界面位移的连续性.算例结果表明,该方法具有较好的计算精度.     

基于单元相交的混合网格精确守恒插值方法

基于网格切割思想,发展了二维/三维混合网格条件下的单元相交算法,可精确计算任意两个多边形/多面体的交集。在此基础上,实现了基于单元相交(CIB/DC)的精确守恒插值算法。二维和三维验证算例表明,该方法能够保证插值过程中计算域内物理量的严格守恒,且具有比常规二阶插值更高的精度。     

三维弹塑性自然单元法算法实现

自然单元法是一种新兴的无网格数值计算方法,其实质是基于自然相邻插值(C∞)的伽辽金法。该方法计算精度与四边形或六面体单元有限元法相当,自然相邻插值函数比其他无网格法插值函数的计算速度快。由于自然相邻插值在凸域的边界上的相邻点之间是严格线性的,所以自然单元法在边界面的处理也相当简单。本文研究了在自然单元法中采用Von.Mises,Mohr-Coulomb和Drucker-Prager屈服准则解决三维弹塑性问题,并编制了相应计算程序,最后通过算例验证算法的正确性。     

中厚板弯曲问题的自然单元法

自然单元法是一种新兴的无网格数值计算方法,基于Reissner-Mindlin板弯曲理论,将自然单元法应用于平板弯曲问题的计算中,给出了相关的公式,推导了总体刚度矩阵和荷载列阵的计算列式.算例分析表明,自然单元法应用于中厚板的弯曲问题具有较高的计算精度,并可用于Winkler地基上基础板的计算.同时指出,对于厚跨比较小的薄板,由于对挠度和中面法线转角采用相同的插值形式,当板厚变薄时夸大了虚假的剪切变形影响,因而表现出剪切自锁现象.对进一步开发厚薄板通用的计算程序作了初步探讨.     

一种强耦合预估-校正浸入边界法

为克服传统浸入边界法的质量不守恒缺陷,提出了一种用于可压缩流固耦合问题的强耦合预估-校正浸入边界法。通过阐述一般流固耦合系统的矩阵表示,推导了流固耦合系统的强耦合Gauss-Seidel迭代格式,进一步导出预估-校正格式,提出了预估-校正浸入边界法。该方法使用无耦合边界模型对流体进行预估,将流固耦合边界视为自由面,固体原本占据的空间初始化为零质量的单元,允许流体自由穿过耦合边界。对于流体的计算,使用带有minmod限制器的二阶MUSCL有限体积格式和基于Zha-Bilgen分裂的AUSM+-up方法,配合三阶Runge-Kutta格式推进时间步。在校正步骤中,通过一组质量守恒的输运规则来实现输运过程。输运算法可概括为将边界内侧的流体进行标记,根据标记顺序以均匀方式分割和移动流体,产生一个指向边界外侧的流动,最后在边界附近施加速度校正保证无滑移条件。标记和输运算法避免了繁琐的对截断单元的几何处理,确保了算法易于实现。对于固体的计算,分别采用一阶差分格式和隐式动力学有限元格式求解刚体和线弹性体,并利用高斯积分获得固体表面的耦合力。使用预估-校正浸入边界法计算了一维问题和二维问题。在一维活塞问题中,获得了压力分布、相对质量历史和误差曲线,并与其他方法进行了对比。在二维的激波冲击平板问题中,获得了数值模拟纹影和平板结构的挠度历史,并与实验结果进行了对比。研究表明,该方法区别于传统的虚拟网格方法和截断单元方法,能够精确地维持流场的质量守恒并易于实现,且具有一阶收敛精度,能够较准确地预测激波绕射后的流场以及平板在激波作用下的挠度,为开发流固耦合算法提供了一种新的思路。     

A dissipation‐free numerical method to solve one‐dimensional hyperbolic flow equations

In this paper, a numerical method to capture the shock wave propagation in 1‐dimensional fluid flow problems with 0 numerical dissipation is presented. Instead of using a traditional discrete grid, the new numerical method is built on a range‐discrete grid, which is obtained by a direct subdivision of values around the shock area. The range discrete grid consists of 2 types: continuous points and shock points. Numerical solution is achieved by tracking characteristics and shocks for the movements of continuous and shock points, respectively. Shocks can be generated or eliminated when triggering entropy conditions in a marking step. The method is conservative and total variation diminishing. We apply this new method to several examples, including solving Burgers equation for aerodynamics, Buckley‐Leverett equation for fractional flow in porous media, and the classical traffic flow. The solutions were verified against analytical solutions under simple conditions. Comparisons with several other traditional methods showed that the new method achieves a higher accuracy in capturing the shock while using much less grid number. The new method can serve as a fast tool to assess the shock wave propagation in various flow problems with good accuracy.     

Euler analysis of transonic stator-rotor interaction using a finite volume method

A generalized finite volume method that can solve the Euler equations for the stator and rotor parts of stage flow in similar formulations is presented. The method consists of a new moving grid finite volume formulation applied to the rotor region and the existing fixed grid finite volume method used in the stator region, with the data transfer made by an interpolation procedure at the sliding surface in between. The accuracy of the method has been demonstrated on a simple cascade flow before the time-dependent compressor stage flow is fully investigated. The transonic stator-rotor flow interaction is elucidated within the inviscid and rotational flow limit.     

A new numerical algorithm for viscoelastic fluid flows : The grid-by-grid inversion method

We present a new algorithm for solving viscoelastic flows with a general constitutive equation. In our approach the hyperbolic constitutive equation is split such that the term for the convective transport of stress tensor is treated as a source. This allows the stress tensor at each grid point to be expressed mainly in terms of the velocity gradient tensor at the same point. Then, the set of six stress tensor components is found after inverting a six by six matrix at each grid point. Thus we call this algorithm the grid-by-grid inversion method. The convective transport of stress tensor in the constitutive equation, which has been treated as a source, is updated iteratively. The present algorithm can be combined with finite volume method, finite element method or the spectral methods. To corroborate the accuracy and robustness of the present algorithm we consider viscoelastic flow past a cylinder placed at the center between two plates, which has served as a benchmark problem. Also considered is the investigation of the pattern and strength of the secondary flows in the viscoelastic flows through a rectangular pipe. It is found that the present method yields accurate results even for large relaxation times.     

多相流局部混合型质点网格法

提出模拟多相流的局部混合型质点网格法，该方法能稳定地模拟高浓度流体颗粒两相 流. 在每一个颗粒团尺度的欧拉网格下(本文称之为欧拉微元)，基于Lagrangian 追踪原理，可直接估计体积内颗粒的总量，从而准确求出欧拉微元和控制容积内颗粒的 浓度(即颗粒在容积内的体积含量). 同时，假设在新的时间步下，颗粒在欧拉微元里充分 混合，形成新颗粒团. 作者对竖直和倾斜容器中单粒径颗粒沉降和竖直容器中双粒径颗粒双 峰悬浮液沉降过程进行了计算，结果与实测数据相符.     

A sliding interface method for unsteady unstructured flow simulations

The objective of this work is to develop a sliding interface method for simulations involving relative grid motion that is fast and efficient and involves no grid deformation, remeshing, or hole cutting. The method is implemented into a parallel, node‐centred finite volume, unstructured viscous flow solver. The rotational motion is accomplished by rigidly rotating the subdomain representing the moving component. At the subdomain interface boundary, the faces along the interface are extruded into the adjacent subdomain to create new volume elements forming a one‐cell overlap. These new volume elements are used to compute a flux across the subdomain interface. An interface flux is computed independently for each subdomain. The values of the solution variables and other quantities for the nodes created by the extrusion process are determined by linear interpolation. The extrusion is done so that the interpolation will maintain information as localized as possible. The grid on the interface surface is arbitrary. The boundary between the two subdomains is completely independent from one another; meaning that they do not have to connect in a one‐to‐one manner and no symmetry or pattern restrictions are placed on the grid. A variety of numerical simulations were performed on model problems and large‐scale applications to examine conservation of the interface flux. Overall solution errors were found to be comparable to that for fully connected and fully conservative simulations. Excellent agreement is obtained with theoretical results and results from other solution methodologies. Copyright © 2006 John Wiley & Sons, Ltd.     

岩石、混凝土类材料断裂破坏有限元数值模拟中的有效方法

岩石、混凝土类材料断裂破坏有限元数值模拟中的网格重划,依据单元畸变和裂缝介质间的单元干涉作为网格重划判据,采用几何体重构技术把几何实体分解成能在ANSYS上实现六面体网格划分的几个部分,利用体积判断法确定新结点在旧单元的单元编号,在场量传递上采用基于解析性质的等参有限元逆变换,把旧网格场量信息传递到新网格中。本文对ANSYS进行二次开发,实现了三维网格重划,网格重划采用单元畸变和界面干涉两个判据,在网格再划分前进行几何体重构,提取变形后的点线面信息重新生成实体,充分利用AN-SYS的函数和体积判断法找到新结点在旧网格中的位置,在新旧网格间的场量传递中采用基于解析逆等参单元法。在平台上实现了三维有限元网格重划技术,最后利用方料的单轴压缩断裂模拟计算检验了传递前后等效塑性应变分布用载荷信息的变化,证明了所开发系统的正确性。     

多介质流体力学计算的谱体积方法

针对高维及多物理耦合计算耗费大等困难,设计适合多介质流动模拟的模板紧致、易于并行、高阶精度、计算耗费小的谱体积方法。该方法是求解双曲型守恒率谱体积方法的直接推广,针对多介质流动物质界面捕捉的困难,利用拟守恒格式的思想避免物质界面处的非物理振荡。数值模拟结果表明,本方法具有高阶精度、高分辨率,且节约计算量,并且可以有效避免物质界面处非物理振荡。     

计算气动弹性力学中的界面映射方法研究

非线性气动弹性体振动研究中,涉及到非线性的结构动力学和非线性的流体动力学耦合问题,在耦合边界上要满足两个系统的连续性相容条件,必须在边界处进行数据的交换。本文针对非线性气动弹性问题的计算流体动力学(CFD)和计算结构动力学(CSD)的耦合计算方法,在常体积转换法(CVT)的基础上,发展了一种耦合界面的数据映射矩阵(IMM)。该方法仅需要局部的网格信息,将耦合边界上载荷信息和位移信息的转换放在同一个映射矩阵中来处理,并且该矩阵可以通用求解CFD/CSD的耦合问题,克服了占用大量CPU时间和内存的弊端。最后将该界面映射方法应用于柔性大展弦比机翼的气动弹性计算和AGARD445.6机翼的颤振预测中,结果表明该方法能够高效、高精度地处理不同网格体系间的数据交换,并具有处理复杂非规则几何体信息转换的能力。     

A projection method for solving incompressible viscous flows on domains with moving boundaries

In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary‐Lagrangian–Eulerian (ALE) co‐ordinates are used. The unsteady incompressible Navier–Stokes equations on the ALE co‐ordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov‐projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier–Stokes equations. Multi‐block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving‐grid projection method. Copyright © 2004 John Wiley Sons, Ltd.