福建海岸带地质环境背景与海水入侵的形成条件探讨

提出一种新的网格自适应方法：在需要加密的网格单元中心加入新结点,并对加密后的相邻 三角形网格单元进行公共边变换, 构成新的网格单元. 与传统的在网格边界中点加入新节点的自 适应方法相比,新方法可以更加灵活地控制网格密度,加密后的网格继承原先的网格质量不 发生畸变,并且算法编程简便,容易实现. 将自适应网格生成方法和基于特征线方程的分离 算法相结合,对空腔内不可压缩黏性流动进行了计算. 在特征线方向上进行时间步离散,动 量方程求解过程中采用非增量型分离算法. 计算中,把求解变量梯度值作为判定准则,在 变化剧烈的区域进行网格局部加密. 计算结果表明该组合算法有很好的计算精度,并有效减 少了计算时间和存储量.     

结合自适应网格的基于特征线方程的分离算法

提出一种新的网格自适应方法:在需要加密的网格单元中心加入新结点,并对加密后的相邻三角形网格单元进行公共边变换, 构成新的网格单元. 与传统的在网格边界中点加入新节点的自适应方法相比,新方法可以更加灵活地控制网格密度,加密后的网格继承原先的网格质量不发生畸变,并且算法编程简便,容易实现. 将自适应网格生成方法和基于特征线方程的分离算法相结合,对空腔内不可压缩黏性流动进行了计算. 在特征线方向上进行时间步离散,动量方程求解过程中采用非增量型分离算法. 计算中,把求解变量梯度值作为判定准则,在变化剧烈的区域进行网格局部加密. 计算结果表明该组合算法有很好的计算精度,并有效减少了计算时间和存储量.      

基于参数曲面三维势问题的边界面法

提出了边界元法(BEM)的一种新的实现方法——边界面法(BFM)。在传统的边界元法中,单元不仅用来进行边界积分和函数插值,而且用来近似几何体。当离散网格较稀疏时,会引起较大几何误差,因而影响计算精度。本文基于参数曲面,将几何实体的边界曲面离散为参数空间里的曲面单元,边界积分和场变量的插值都是在曲面参数空间里进行。积分点...     

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。     

计算含动边界非定常流动的无网格算法

在无网格算法中考虑了含动边界的流动问题,研究了可以计算处理包含一定位移及扭转动边界非定常流动的算法.创建了无网格算法的动点法则,并引入抗扭方法对弹簧方法进行改进来处理离散点运动,提高了方法的可用度及精度.发展了求解基于无网格的ALE方程组的算法,在点云离散的基础上采用曲面逼近计算空间导数及HLLC格式计算数值通量,运用四步龙格-库塔法进行时间推进.在跨、超音速条件下,计算模拟了典型翼型简谐振动流场,计算结果与实验结果及文献对比吻合,验证了该算法的正确性.     

基于实体造型的三维有限元网格自动剖分

本文叙述了用八叉树法对三维实体进行有限元网格自动剖分算法的设计和实现。本文的算法对传统的八叉树法进行了一系列的改进，包括新型数据结构的建立，对八叉树结点属性判断算法的改进，边界结点体处理方法的改进等。使得本文的算法既保持了传统算法中自动化程度高、层次结构分明、适于再进行网格加密等特点，又克服了其所需存贮空间大、执行速度慢、边界处理复杂、边界单元形状质量不好等缺点，使算法的实现取得了令人满意的结果     

基于OPS和拓扑交换的离心泵网格质量提高算法

针对OPS算法本身固有的无法提高"全边界单元"质量的缺陷,提出了一种结合OPS和拓扑优化的网格质量提高算法。该方法通过判别"全边界单元"中边(或面)受到相邻单元共享的形式,采用不同的拓扑交换策略,且在拓扑交换过程中仅考虑网格的拓扑相关性,并不考虑网格的质量,保证将"全边界单元"转化为OPS算法提高其质量的其他类型边界单元。算例分析表明,本文算法相比Freitag的组合算法在消除极端二面角方面更具优势,相比OPS算法对提高离心泵边界网格及整体网格质量也具有较好的优势。     

三维约束Delaunay三角化的边界恢复和薄元消除方法

提出一种有效的三维约束Delaunay三角剖分的边界恢复算法，该算法综合了P．L．George算法和N．P．Weatherill算法的优点，通过将约束边和约束面加以恢复，保持了实体边界的完整性，解决了经典Delaunay算法不能剖分凹域的问题，从而实现了复杂三维实体的网格剖分。提出了一种简易而有效的消除薄元方法——薄元分解法，彻底解决了三维Delaunay三角剖分过程中所产生的薄元问题。实践证明，本文提出的边界恢复算法和薄元消除算法健壮有效，生成网格的质量高，并且易于实现。     

基于实体造型的三维有限元网格自动剖分

本文叙述了用八叉树法对三维实体进行有限元网络自动剖分算法的设计和实现。本文的算法对传统的八叉树法进行了一系列的改进，包括新型数据结构的建立，对八叉树结点属性判断算法的改进，边界结点体处理方法的改进等。使得本文的算法既保持了传统算法中自动化程度高、层次结构分明、适于再进行网格加密等特点，又克服了其所需存贮空间大、执行速度慢、边界处理复杂，边界单元形状质量不好等缺点，使算法的实现取得了令人满意的结果。     

前沿推进曲面四边形网格生成算法

将一类前沿推进三角形曲面网格生成算法拓展到曲面四边形网格生成。新算法逐个单元推进前沿,避免了铺路法（Paving）逐排推进方式的鲁棒性问题,针对四边形算法在理想点计算、候选点列表构建和新单元生成等环节存在的特殊技术问题给出了系统的解决方案。数值实验表明,本文算法能针对复杂的组合参数曲面自动生成全四边形网格,网格质量优于...     

Mesh adaptation for simulation of unsteady flow with moving immersed boundaries

In this work, an approach for performing mesh adaptation in the numerical simulation of two‐dimensional unsteady flow with moving immersed boundaries is presented. In each adaptation period, the mesh is refined in the regions where the solution evolves or the moving bodies pass and is unrefined in the regions where the phenomena or the bodies deviate. The flow field and the fluid–solid interface are recomputed on the adapted mesh. The adaptation indicator is defined according to the magnitude of the vorticity in the flow field. There is no lag between the adapted mesh and the computed solution, and the adaptation frequency can be controlled to reduce the errors due to the solution transferring between the old mesh and the new one. The preservation of conservation property is mandatory in long‐time scale simulations, so a P1‐conservative interpolation is used in the solution transferring. A nonboundary‐conforming method is employed to solve the flow equations. Therefore, the moving‐boundary flows can be simulated on a fixed mesh, and there is no need to update the mesh at each time step to follow the motion or the deformation of the solid boundary. To validate the present mesh adaptation method, we have simulated several unsteady flows over a circular cylinder stationary or with forced oscillation, a single self‐propelled swimming fish, and two fish swimming in the same or different directions. Copyright © 2012 John Wiley & Sons, Ltd.     

基于双重自适应的六面体网格再生成方法

提出了一种以栅格法为基本方法,基于几何特征和物理场量双重自适应的六面体网格再生成方法。首先,依据旧网格的表面曲率和几何特征,采用基于栅格法的几何自适应网格再生成方法,生成密度受控的基础网格;然后,将旧网格的物理场量传递到基础网格中;最后,采用有限元误差估计方法对新网格单元的计算误差进行估计,对误差较大的单元进行加密,减...     

An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved.     

Mesh Deformation Method Based on Mean Value Coordinates Interpolation

Mesh deformation technique is widely used in many application fields, and has received a lot of attentions in recent years. This paper focuses on the methodology and algorithm of algebraic type mesh deformation for unstructured mesh in numerical discretization. To preserve mesh quality effectively, an algebraic approach for two and three dimensional unstructured mesh is developed based on mean value coordinates interpolation combined with node visibility analysis.The proposed approach firstly performs node visibility analysis to find out the visible boundary for each grid point to be moved, then evaluates the mean value coordinates of each grid point with respect to all vertices on its visible boundary. Thus the displacements of grid points can be calculated by interpolating the boundary movement by the mean value coordinates. Compared with other methods, the proposed method has good deformation capability and predictable computational cost, with no need to select parameters or functions. Applications of mesh deformation in different fields are presented to demonstrate the effectiveness of the proposed approach. The results of numerical experiments exhibit not only superior deformation capability of the method in traditional applications of fluid dynamic grid, but also great potential in modeling for large deformation analysis and inverse design problems.     

Implementation of Convergence in Adaptive Global Digital Image Correlation

In FE based global digital image correlation (DIC) a finite element mesh is used to describe the deformation of the region of interest (ROI). However, the identification of an optimal mesh is a difficult problem and is often obtained by using “mechanical” pre-knowledge of the solution. In Finite Element Analysis (FEA) an optimal mesh can be found without any pre-knowledge of the solution by using mesh adaptivity, where an initial (non optimal) mesh is refined until the optimal solution is obtained. Refinement of the mesh can be based on error and/or convergence estimators. Despite the fundamental differences between FEA and DIC, in the present article the convergence procedure is successfully used in a recently published global FE based DIC method. In the used global DIC method elements can receive higher order shape functions, also known as p-elements. Using the aforementioned algorithm, also called p-DIC, refinement to a non-uniform higher order mesh is possible. Using the non-uniform mesh, an optimal mesh can be obtained for each section of the ROI. The presented study shows that a convergence scheme can be used to automatically control the mesh refinement in a global DIC approach. The convergence boundary, in percentage, is a more intuitive boundary than the absolute error boundary used in the original p-DIC approach. The procedure is validated using numerical examples and the robustness to experimental variables is investigated. Finally, the complete procedure is tested against a wide range of practical examples.     

An adaptive boundary element approach to transient free surface flow as applied to injection molding

An adaptive (Lagrangian) boundary element approach is proposed for the general two‐dimensional simulation of confined moving‐boundary flow of viscous incompressible fluids. Only the quasi‐steady creeping (Stokes) flow of a Newtonian fluid is examined. The method is stable as it includes remeshing capabilities of the deforming moving boundary, and thus it can handle large deformations. An algorithm is developed for mesh refinement of the deforming moving‐boundary mesh. Several flow problems are presented to illustrate the utility of the approach, with particular emphasis on cavity filling and viscous fingering, as applied to conventional and gas‐assisted injection molding. The accuracy of the method is assessed through the problem of jet flow and the transient fountain flow between two flat plates. Copyright © 2000 John Wiley & Sons, Ltd.     

基于二重网格的动网格松弛法改进

相比传统的弹簧法等方法,基于球松弛算法的动网格松弛法在复杂边界大变形条件下可以得到质量更高的边界网格以及更大的极限变形量,但该方法在时间效率上还有提升的空间.引入二重网格,采用动网格松弛法进行稀疏网格的网格变形,将边界位移传递到整个网格计算域;再利用二重网格映射,将稀疏网格位移映射到原有计算网格的节点上.算例表明,改进...     

An immersed boundary method for fluid flows around rigid objects

In this paper, we present an immersed boundary method for solving fluid flow problems in the presence of static and moving rigid objects. A FEM is used starting from a base mesh that does not represent exactly rigid objects (non?body?conforming mesh). At each time step, the base mesh is locally modified to provide a new mesh fitting the boundary of the rigid objects. The mesh is also locally improved using edge swapping to enhance the quality of the elements. The Navier–Stokes equations are then solved on this new mesh. The velocity of moving objects is imposed through standard Dirichlet boundary conditions. We consider a number of test problems and compare the numerical solutions with those obtained on classical body?fitted meshes whenever possible. Copyright © 2014 John Wiley & Sons, Ltd.     

Considerations on the spring analogy

This paper presents an investigation on the spring analogy. The spring analogy serves for deformation in a moving boundary problem. First, two different kinds of springs are discussed: the vertex springs and the segment springs. The vertex spring analogy is originally used for smoothing a mesh after mesh generation or refinement. The segment spring analogy is used for deformation of the mesh in a moving boundary problem. The difference between the two methods lies in the equilibrium length of the springs. By means of an analogy to molecular theory, the two theories are generalized into a single theory that covers both. The usual choice of the stiffness of the spring is clarified by the mathematical analysis of a representative one‐dimensional configuration. The analysis shows that node collision is prevented when the stiffness is chosen as the inverse of the segment length. The observed similarity between elliptic grid generation and the spring analogy is also investigated. This investigation shows that both methods update the grid point position by a weighted average of the surrounding points in an iterative manner. The weighting functions enforce regularity of the mesh. Based on these considerations, several improvements on the spring analogy are developed. The principle of Saint Venant is circumvented by a boundary correction. The prevention of inversion of triangular elements is improved by semi‐torsional springs. The numerical results show the superiority of the segment spring analogy over the vertex one for a small rotation of an NACA0012 mesh. The boundary correction allows for large deformation of the mesh, where the standard spring analogy fails. The final test is performed on a Navier–Stokes mesh. This mesh contains high aspect ratio mesh cells near the boundary. Large deformation of this mesh shows that the semi‐torsional spring improvement is imperative to retain the validity of this mesh. Copyright © 2000 John Wiley & Sons, Ltd.     

A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion

Computational fluid mechanics techniques for examining free surface problems in two‐dimensional form are now well established. Extending these methods to three dimensions requires a reconsideration of some of the difficult issues from two‐dimensional problems as well as developing new formulations to handle added geometric complexity. This paper presents a new finite element formulation for handling three‐dimensional free surface problems with a boundary‐fitted mesh and full Newton iteration, which solves for velocity, pressure, and mesh variables simultaneously. A boundary‐fitted, pseudo‐solid approach is used for moving the mesh, which treats the interior of the mesh as a fictitious elastic solid that deforms in response to boundary motion. To minimize mesh distortion near free boundary under large deformations, the mesh motion equations are rotated into normal and tangential components prior to applying boundary conditions. The Navier–Stokes equations are discretized using a Galerkin–least square/pressure stabilization formulation, which provides good convergence properties with iterative solvers. The result is a method that can track large deformations and rotations of free surface boundaries in three dimensions. The method is applied to two sample problems: solid body rotation of a fluid and extrusion from a nozzle with a rectangular cross‐section. The extrusion example exhibits a variety of free surface shapes that arise from changing processing conditions. Copyright © 2000 John Wiley & Sons, Ltd.