二维自适应网格生成的改进AFT与背景网格法

在基于重生成的自适应有限元网格生成算法研究中,将推进波前法（AFT）与背景网格法结合并提出改进方法,有效地解决了网格生成和单元尺寸计算这两个关键问题。改进的AFT方法,将前沿区分为活跃前沿和非活跃前沿两类,在选取目标前沿时既考虑前沿尺寸又考虑前沿分类。改进的背景网格法,利用结构化栅格对背景网格进行管理,在栅格中直接存放背景网格中的单元,既提高了新单元尺寸的计算速度,又从数值上保证了新生成网格中单元之间尺寸合理过渡。     

Drapage géométrique des compositesGeometrical draping of composite fabrics

This paper presents a study devoted to the composite fabric shaping simulation in finite strain analysis. We introduce a new geometrical approach based on the fishnet method for which the deformation of a fabric mesh element consists in a pure trellis effect. Such a fabric mesh element is then defined by a curved quadrilateral whose edges are geodesic lines with the same length plotted onto the surface to drape. Given three vertices of the fabric mesh element on the surface, we propose an optimization algorithm to define the fourth vertex of the fabric mesh element. This algorithm allows us to drape the surface using an advancing front approach from the data of an initial impact point between the fabric and the surface and the initial fibre directions at this point. A numerical draping simulation example using this approach is given. To cite this article: H. Borouchaki, A. Cherouat, C. R. Mecanique 331 (2003).     

复杂区域非结构化四边形网格全自动生成方法

针对多介质平面复杂区域，本文建议了一种基子推进网阵法的全四边形网格自动生成方法。其特点是对不规则区域适应能力强，考虑了节理单元自动生成。文中提出了网格质量改进方法，并给出了三个工程算例。     

并行有限元网格生成方法及其应用

大型工程数值仿真中,在前处理阶段需要生成千万甚至亿量级的网格,传统的串行网格生成方法由于内存和时间的限制,难以处理如此规模的网格。针对此问题,本文提出了一种大规模网格并行生成方法。首先基于推进波前法对几何模型进行初始体网格划分,接着利用图论理论进行区域分解,并通过表面单元恢复保持其几何精度,然后通过分裂法进行网格的并行生成。将所述方法应用到实际大型工程数值仿真前处理阶段,结果表明所述方法可以获得较好的并行效率,同时所产生的网格质量可以满足后续计算需要。     

基于点球弹簧修匀法的混合网格变形并行算法

针对二维/三维混合网格,提出基于点球弹簧修匀法的并行网格变形算法。按特定模板将混合网格中的非三角形/四面体单元分解成三角形/四面体单元。针对每个内部节点及其相邻节点建立相应的子弹簧系统,并通过增加Ball-Vertex弹簧避免弹簧系统的塌陷问题。由于点球弹簧法在计算中逐点对网格内部节点进行计算,在计算过程中具有良好的弱耦合性质,因此有利于算法并行化。在并行化时仅需对网格进行虚拟分区操作,不必进行复杂的几何分区操作,同时避免了混合网格不同单元之间的兼容性问题。该方法适用于具有复杂外形的大规模混合网格的变形问题,能够显著提高网格变形的效率,同时具有良好的适应性。     

黏性不可压缩流体流动前沿的数值模拟

提出了模拟注射成型中黏性、不可压缩流体流动前沿的新方法. 将Hele-Shaw流动应用于非 等温条件下的黏性、不可压缩流体，建立了流动分析模型，用充填因子的输运方程描述流动 前沿. 应用高阶Taylor展开式计算每一时间步长的充填因子，用Galerkin方法导出了计算 充填因子各阶导数的递推公式. 给出了时间增量的选取方法，证明了它的稳定性. 针对Han 设计的试验模具，用相同的材料及工艺条件模拟充填过程，比较了传统方法和该方法的模 拟结果与实验结果的差异. 算例分析表明，该方法可以有效地提高注射成型中流动前沿的 模拟精度和计算效率.     

二维稳定流形的自适应推进算法

稳定和不稳定流形是研究动力系统全局特性的重要工具. 一般系统的稳定和不稳定流形的曲率在全局范围内会有明显变化,应根据流形曲率的变化采用不同尺寸的网格单元计算全局流形. 然而在现有二维流形算法中,流形网格单元的尺寸在全局范围内是统一的. 为持续有效地计算全局稳定流形,提高计算网格对流形曲率变化的适应性. 本文在偏微分方程算法的基础上提出一种二维稳定流形的自适应推进算法. 该算法的基本思想是根据稳定流形曲率的变化自适应地调整网格单元的尺寸. 该算法首先在系统的稳定特征子空间中确定稳定流形的一个初始估计,该初始估计的网格单元尺寸设置为初始大小. 然后根据稳定流形网格前沿的曲率特点自适应地产生新的备选网格单元,继而根据相切性条件更新备选点的坐标,并将距离平衡点最近的备选点接受为已知点,最后更新稳定流形网格的前沿并自适应地产生新的备选网格单元,通过这个迭代过程使流形网格自适应地向前推进. 本文算法通过引入流形单元尺寸自适应,成功实现了洛伦兹流形和类球面流形的计算,并与偏微分方程算法进行了对比,结果表明自适应推进算法的流形计算单元的尺寸可在全局范围内根据流形曲率自适应地调整. 利用自适应推进算法计算二维稳定流形,可实现稳定流形的自适应推进.      

High‐order time integrators for front‐tracking finite‐element analysis of viscous free‐surface flows

This paper proposes implicit Runge–Kutta (IRK) time integrators to improve the accuracy of a front‐tracking finite‐element method for viscous free‐surface flow predictions. In the front‐tracking approach, the modeling equations must be solved on a moving domain, which is usually performed using an arbitrary Lagrangian–Eulerian (ALE) frame of reference. One of the main difficulties associated with the ALE formulation is related to the accuracy of the time integration procedure. Indeed, most formulations reported in the literature are limited to second‐order accurate time integrators at best. In this paper, we present a finite‐element ALE formulation in which a consistent evaluation of the mesh velocity and its divergence guarantees satisfaction of the discrete geometrical conservation law. More importantly, it also ensures that the high‐order fixed mesh temporal accuracy of time integrators is preserved on deforming grids. It is combined with the use of a family of L‐stable IRK time integrators for the incompressible Navier–Stokes equations to yield high‐order time‐accurate free‐surface simulations. This is demonstrated in the paper using the method of manufactured solution in space and time as recommended in Verification and Validation. In particular, we report up to fifth‐order accuracy in time. The proposed free‐surface front‐tracking approach is then validated against cases of practical interest such as sloshing in a tank, solitary waves propagation, and coupled interaction between a wave and a submerged cylinder. Copyright © 2015 John Wiley & Sons, Ltd.     

A stabilized Nitsche‐type extended embedding mesh approach for 3D low‐ and high‐Reynolds‐number flows

This paper presents a stabilized extended finite element method (XFEM) based fluid formulation to embed arbitrary fluid patches into a fixed background fluid mesh. The new approach is highly beneficial when it comes to computational grid generation for complex domains, as it allows locally increased resolutions independent from size and structure of the background mesh. Motivating applications for such a domain decomposition technique are complex fluid‐structure interaction problems, where an additional boundary layer mesh is used to accurately capture the flow around the structure. The objective of this work is to provide an accurate and robust XFEM‐based coupling for low‐ as well as high‐Reynolds‐number flows. Our formulation is built from the following essential ingredients: Coupling conditions on the embedded interface are imposed weakly using Nitsche's method supported by extra terms to guarantee mass conservation and to control the convective mass transport across the interface for transient viscous‐dominated and convection‐dominated flows. Residual‐based fluid stabilizations in the interior of the fluid subdomains and accompanying face‐oriented fluid and ghost‐penalty stabilizations in the interface zone stabilize the formulation in the entire fluid domain. A detailed numerical study of our stabilized embedded fluid formulation, including an investigation of variants of Nitsche's method for viscous flows, shows optimal error convergence for viscous‐dominated and convection‐dominated flow problems independent of the interface position. Challenging two‐dimensional and three‐dimensional numerical examples highlight the robustness of our approach in all flow regimes: benchmark computations for laminar flow around a cylinder, a turbulent driven cavity flow at Re = 10000 and the flow interacting with a three‐dimensional flexible wall. Copyright © 2016 John Wiley & Sons, Ltd.     

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...     

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.     

基于机器学习的非结构网格阵面推进生成技术初探

网格生成和自适应是制约计算流体力学未来发展的瓶颈问题之一,网格生成自动化和智能化仍是一个需要持续研究的领域.随着高性能计算算力的提升和大数据时代的到来,以机器学习为代表的人工智能方法已经成功应用于包括流体力学在内的多个领域,革命性地推动了这些领域的发展.本文首先简要综述机器学习方法在非结构网格生成领域的研究进展,分析基...     

任意平面区域的变尺寸有限元网格划分

利用任意平面域边界表述中的拓年要素定义网格的控制信息,通过引入节点间距函数来控制区域内网格尺寸变化,并将结合前沿生成法和Ｄｅｌａｕｎａｙ三角化方法的优点,优先处理前沿的最长边,尽可能在局部生成边长逐渐减小的Ｄｅｌａｕｎａｙ三角形,最终实验区域内网格的疏密过渡。     

A two‐phase adaptive finite element method for solid–fluid coupling in complex geometries

In this paper we present a method to solve the Navier–Stokes equations in complex geometries, such as porous sands, using a finite‐element solver but without the complexity of meshing the porous space. The method is based on treating the solid boundaries as a second fluid and solving a set of equations similar to those used for multi‐fluid flow. When combined with anisotropic mesh adaptivity, it is possible to resolve complex geometries starting with an arbitrary coarse mesh. The approach is validated by comparing simulation results with available data in three test cases. In the first we simulate the flow past a cylinder. The second test case compares the pressure drop in flow through random packs of spheres with the Ergun equation. In the last case simulation results are compared with experimental data on the flow past a simplified vehicle model (Ahmed body) at high Reynolds number using large‐eddy simulation (LES). Results are in good agreement with all three reference models. Copyright © 2010 John Wiley & Sons, Ltd.     

适应复杂外形的三维粘性混合网格生成算法

提出一类适应复杂外形的粘性混合网格生成算法。表面网格由前沿推进三角形曲面网格程序获得,边界层布置各向异性的三棱柱体网格,远物面区域采用Delaunay方法生成四面体网格。针对模型的复杂几何特征,综合采用了各种网格处理技术,以保证边界层网格的质量,并避免算法失效问题。网格实例及计算结果表明了本文算法的实用性及和效性。     

Surface triangulation for polygonal models based on CAD data

This paper presents an approach to the generation of unstructured surface meshes for Computer‐Aided Design (CAD) surface models represented as lists of polygons with minimum user interventions. Stereolithography (STL) data are adopted as an interface between a CAD system and the surface grid generator. STL files often include problems such as overlapping surfaces, gaps, and intersections. They have to be revised quickly and automatically before the surface models are used for the background grid of the surface grid generation. In this paper, we describe an automatic revision method for use with STL‐defined surface models. The advancing front method using geometric features is adopted directly on the modified STL surfaces. The capability of the method is demonstrated for several 3D surface models. Copyright © 2002 John Wiley & Sons, Ltd.     

Local mesh adaptation technique for front tracking problems

A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented in this paper: the broken dam problem and the Rayleigh–Taylor instability. Good agreement has been obtained in the comparison of the numerical results with theory or available experimental data. © 1998 John Wiley & Sons, Ltd.     

An assessment of a parallel,finite element method for three‐dimensional,moving‐boundary flows driven by capillarity for simulation of viscous sintering

A parallel, finite element method is presented for the computation of three‐dimensional, free‐surface flows where surface tension effects are significant. The method employs an unstructured tetrahedral mesh, a front‐tracking arbitrary Lagrangian–Eulerian formulation, and fully implicit time integration. Interior mesh motion is accomplished via pseudo‐solid mesh deformation. Surface tension effects are incorporated directly into the momentum equation boundary conditions using surface identities that circumvent the need to compute second derivatives of the surface shape, resulting in a robust representation of capillary phenomena. Sample results are shown for the viscous sintering of glassy ceramic particles. The most serious performance issue is error arising from mesh distortion when boundary motion is significant. This effect can be severe enough to stop the calculations; some simple strategies for improving performance are tested. Copyright © 2001 John Wiley & Sons, Ltd.     

Hybrid mesh generation using advancing reduction technique

This paper presents an application of the advancing reduction technique for 2D hybrid mesh generation (triangles + quadrilaterals). Based on an initial rectangle mesh (RM) covering the whole domain, the advancing reduction technique coarsens the base RM in a marching way from the boundary to the interior of the domain so that different zones of sub‐RMs with different edge lengths are recognized. These sub‐RMs are connected to each other with the so‐called transition layers which consist of the transition triangles and quadrilaterals. As demonstrated by examples, the proposed method is simple, efficient, and easy to implement. Copyright © 2015 John Wiley & Sons, Ltd.     

Combined swept region and intersection‐based single‐material remapping method

A typical arbitrary Lagrangian–Eulerian algorithm consists of a Lagrangian step, where the computational mesh moves with the fluid flow; a rezoning step, where the computational mesh is smoothed and repaired in case it gets too distorted; and a remapping step, where all fluid quantities are conservatively interpolated on this new mesh. In single‐material simulations, the remapping process can be represented in a flux form, with fluxes approximated by integrating a reconstructed function over intersections of neighboring computational cells on the original and rezoned computational mesh. This algorithm is complex and computationally demanding – Therefore, a simpler approach that utilizes regions swept by the cell edges during rezoning is often used in practice. However, it has been observed that such simplification can lead to distortion of the solution symmetry, especially when the mesh movement is not bound by such symmetry. For this reason, we propose an algorithm combining both approaches in a similar way that was proposed for multi‐material remapping (two‐step hybrid remap). Intersections and exact integration are employed only in certain parts of the computational mesh, marked by a switching function – Various different criteria are presented in this paper. The swept‐based method is used elsewhere in areas that are not marked. This way, our algorithm can retain the beneficial symmetry‐preserving capabilities of intersection‐based remapping while keeping the overall computational cost moderate.