Fully automatic and fast mesh size specification for unstructured mesh generation

A fully automatic surface mesh generation system is presented in this paper. The automation is achieved by an automatic determination of a consistent mesh size distribution, which is based on geometry rasterisation. The user specifies a minimal and maximal allowed mesh size, and a maximal allowed curvature angle for the complete geometry, or, rather, parts of it. Now, these local curvature and local characteristic lengths of the geometry are computed, which determine the local mesh size. These local mesh sizes are stored and smoothed in a Cartesian background mesh. Afterwards, the triangulation is generated by an advancing front triangulator: the local resolution of the surface triangulation is determined by the mesh sizes stored in the Cartesian background mesh. The object-oriented design and implementation is described. The complete system is very fast due to an efficient parallelisation based on MPI for computer systems with distributed memory.     

Hexahedral mesh smoothing via local element regularization and global mesh optimization

The quality of finite element meshes is one of the key factors that affect the accuracy and reliability of finite element analysis results. In order to improve the quality of hexahedral meshes, we present a novel hexahedral mesh smoothing algorithm which combines a local regularization for each hexahedral mesh, using dual element based geometric transformation, with a global optimization operator for all hexahedral meshes. The global optimization operator is composed of three main terms, including the volumetric Laplacian operator of hexahedral meshes and the geometric constraints of surface meshes which keep the volumetric details and the surface details, and another is the transformed node displacements condition which maintains the regularity of all elements. The global optimization operator is formulated as a quadratic optimization problem, which is easily solved by solving a sparse linear system. Several experimental results are presented to demonstrate that our method obtains higher quality results than other state-of-the-art approaches.     

Domain decomposition method for unstructured meshes in an OpenMP computing environment

In this paper, an efficient unstructured mesh calculation method in an OpenMP parallel computation using multi-core processor is proposed. This is a new domain decomposition method with two characteristics. The first characteristic is to define the size of the sub-block in the computation domain by the size of the cache memory in each core. The second one is to reduce idle time by distributing a defined sub-block for each core appropriately. Using the proposed method, a computation on compressible flow around a plane was able to achieve speed-up more than about 20% in comparison with a conventional method.     

Molecular dynamics-based unstructured grid generation method for aerodynamic applications

A new approach to triangular mesh generation based on the molecular dynamics method is proposed. Mesh nodes are considered as interacting particles. After the node placement by molecular dynamics simulation, well-shaped triangles or tetrahedra can be created after connecting the nodes by Delaunay triangulation or tetrahedrization. Some examples are considered in order to illustrate the method’s ability to generate a mesh for an aircraft with a complicated boundary. Mesh adaptation technology for molecular dynamics simulation is presented.     

解析二维非结构网格生成方法及其应用

提出弱区域指示函数描述流场形状并证明了其存在和不唯一性;利用该函数基于Delaunay方法依据流场尺度生成二维非结构网格。其中,边界引力有效解决了流场边界恢复和内嵌边界问题,弹簧振子和正三角形趋进技术有效改善网格质量。最后,弹簧振子随着弱区域指示函数的演变与监测函数的指导成功应用到自适应网格生成。     

An implicit gas-kinetic scheme for turbulent flow on unstructured hybrid mesh

In this study, an implicit scheme for the gas-kinetic scheme (GKS) on the unstructured hybrid mesh is proposed. The Spalart–Allmaras (SA) one equation turbulence model is incorporated into the implicit gas-kinetic scheme (IGKS) to predict the effects of turbulence. The implicit macroscopic governing equations are constructed and solved by the matrix-free lower-upper symmetric-Gauss–Seidel (LU-SGS) method. To reduce the number of cells and computational cost, the hybrid mesh is applied. A modified non-manifold hybrid mesh data(NHMD) is used for both unstructured hybrid mesh and uniform grid. Numerical investigations are performed on different 2D laminar and turbulent flows. The convergence property and the computational efficiency of the present IGKS method are investigated. Much better performance is obtained compared with the standard explicit gas-kinetic scheme. Also, our numerical results are found to be in good agreement with experiment data and other numerical solutions, demonstrating the good applicability and high efficiency of the present IGKS for the simulations of laminar and turbulent flows.     

The geometric element transformation method for mixed mesh smoothing

The geometric element transformation method (GETMe) is a geometry-based smoothing method for mixed and non-mixed meshes. It is based on a simple geometric transformation applicable to elements bounded by polygons with an arbitrary number of nodes. The transformation, if applied iteratively, leads to a regularization of the polygons. Global mesh smoothing is accomplished by averaging the new node positions obtained by local element transformations. Thereby, the choice of transformation parameters as well as averaging weights can be based on the element quality which leads to high quality results. In this paper, a concept of an enhanced transformation approach is presented and a proof for the regularizing effect of the transformation based on eigenpolygons is given. Numerical examples confirm that the GETMe approach leads to superior mesh quality if compared to other geometry-based methods. In terms of quality it can even compete with optimization-based techniques, despite being conceptually significantly simpler.     

A comparison of GPU strategies for unstructured mesh physics

There have been few efforts to date to write physics algorithms for general unstructured meshes (meshes composed of arbitrary polygons/polyhedra) on graphics processing units (GPUs). Typical strategies for GPU memory management, such as double‐buffering and coalescing memory accesses, are difficult to apply to the irregular memory storage patterns of unstructured meshes. This paper presents results from an initial GPU version of a typical unstructured mesh kernel. Three different memory management strategies are described and implemented. Timing results for all three strategies are presented, in some cases showing speedups of over 20 times compared with the original CPU code.Copyright © 2012 John Wiley & Sons, Ltd.     

基于GPU的加锁并行化非结构网格生成方法研究

非结构网格的生成在时间和内存上有一定的缺陷,这里提出了一种新的方法,命名为GPU-PDMG,是基于CUDA架构的GPU并行非结构网格生成技术。该技术结合了GPU的高速并行计算能力与Delaunay三角化的优点,在英伟达GPU模块下采用CUDA程序模型,开发出了加锁并行区划分技术,通过对NACA0012翼型、多段翼型等算例进行测试,分析此方法的加速比和效率,对其计算性能展开评估。实验结果表明,GPU-PDMG优于现存在的CPU算法的速度,在保证网格质量的同时,提高了效率。     

A two-layered mesh array for matrix multiplication

A two-layered mesh array for matrix multiplication is presented. It computers the matrix product faster than the standard array.     

Towards an efficient storage and retrieval mechanism for large unstructured grids

The size of spatial scientific datasets is steadily increasing due to improvements in instruments and availability of computational resources. However, much of the research on efficient storage and access to spatial datasets has focused on large multidimensional arrays. In contrast, unstructured grids consisting of collections of simplices (e.g. triangles or tetrahedra) present special challenges that have received less attention. Data values found at the vertices of the simplices may be dispersed throughout a datafile, producing especially poor disk locality.Our previous work has focused on addressing this locality problem. In this paper, we reorganize the unstructured grid to improve locality of disk access by maintaining the spatial neighborhood relationships inherent in the unstructured grid. This reorganization produces significant gains in performance by reducing the number of accesses made to the data file. We also examine the effects of different chunking configurations on data retrieval performance. A major motivation for reorganizing the unstructured grid is to allow the application of iteration aware prefetching. Applying this prefetching method to unstructured grids produces further performance gains over and above the gains seen from reorganization alone.The work presented in this journal contains at least 40% new material not included in our conference paper (Akande and Rhodes 2013).     

Design and initial performance of a high-level unstructured mesh framework on heterogeneous parallel systems

OP2 is a high-level domain specific library framework for the solution of unstructured mesh-based applications. It utilizes source-to-source translation and compilation so that a single application code written using the OP2 API can be transformed into multiple parallel implementations for execution on a range of back-end hardware platforms. In this paper we present the design and performance of OP2’s recent developments facilitating code generation and execution on distributed memory heterogeneous systems. OP2 targets the solution of numerical problems based on static unstructured meshes. We discuss the main design issues in parallelizing this class of applications. These include handling data dependencies in accessing indirectly referenced data and design considerations in generating code for execution on a cluster of multi-threaded CPUs and GPUs. Two representative CFD applications, written using the OP2 framework, are utilized to provide a contrasting benchmarking and performance analysis study on a number of heterogeneous systems including a large scale Cray XE6 system and a large GPU cluster. A range of performance metrics are benchmarked including runtime, scalability, achieved compute and bandwidth performance, runtime bottlenecks and systems energy consumption. We demonstrate that an application written once at a high-level using OP2 is easily portable across a wide range of contrasting platforms and is capable of achieving near-optimal performance without the intervention of the domain application programmer.     

Parallel three-dimensional DSMC method using mesh refinement and variable time-step scheme

Application of variable time-step and unstructured adaptive mesh refinement in parallel three-dimensional Direct Simulation Monte Carlo (DSMC) method is presented. A variable time-step method using the particle fluxes conservation (mass, momentum and energy) across the cell interface is implemented to reduce the number of simulated particles and the number of iterations of transient period towards steady state, without sacrificing the solution accuracy. In addition, a three-dimensional h-refined unstructured adaptive mesh with simple but effective mesh-quality control, obtained from a preliminary parallel DSMC simulation, is used to increase the accuracy of the DSMC solution. Completed code is then applied to compute several external and internal flows, and compared with previous results wherever available.     

Inverse adaptation of a Hex-dominant mesh for large deformation finite element analysis

In the finite element analysis of metal forming processes, many mesh elements are usually deformed severely in the later stage of the analysis because of the corresponding large deformation of the geometry. Such highly distorted elements are undesirable in finite element analysis because they introduce error into the analysis results, and, in the worst case, inverted elements can cause the analysis to terminate prematurely. This paper proposes a new inverse-adaptation method that reduces or eliminates the number of inverted mesh elements created in the later stage of finite element analysis, thereby lessening the chances of early termination and improving the accuracy of the analysis results. By this method, a simple uniform mesh is created initially, and a pre-analysis is run in order to observe the deformation behavior of the elements. Next, an input hex-dominant mesh is generated in which each element is “inversely adapted”, or pre-deformed in such a way that it has approximately the opposite shape of the final shape that normal analysis would deform it into. Thus, when finite element analysis is performed, the analysis starts with an input mesh of inversely adapted elements whose shapes are not ideal. As the analysis continues, the element shape quality improves to almost ideal, and then, toward the final stage of analysis, degrades again, but much less than would be the case without the inverse adaptation. This method permits the analysis to run to the end, or to a further stage, with no inverted elements. Besides its pre-skewing the element shape, the proposed method is also capable of controlling the element size according to the equivalent plastic strain information collected from the pre-analysis. The proposed inverse adaptation can be repeated iteratively until reaching the final stage of deformation.     

A practical procedure for mesh motion in arbitrary Lagrangian-Eulerian method

Conventional Lagrangian and Eulerian type formulation methods are applied to simulate some metal forming processes. These formulations possess certain difficulties when applied to finite strain deformation problems, especially when boundary conditions need to be updated during the course of deformation. An Arbitrary Lagrangian-Eulerian (ALE) formulation method is employed to overcome these difficulties. This paper presents an efficient mesh motion scheme for the ALE formulation method. A practical and more efficient scheme for handling supplementary constraint equations, arising from mesh motion algorithms, on the element level is presented. A procedure for handling boundary motion within the scheme and ensuring homogeneous mesh results is described. The presented scheme is employed to simulate punch forging and plane strain metal extrusion processes.     

骨架驱动的三维模型变形方法

为发展三维网格模型的变形技术,研究了多种三维模型变形算法,通过对骨架驱动变形算法的深入研究,针对现行算法多是以单一骨架驱动变形的不足,提出了一种新的基于多骨架点驱动的交互式局部变形方法.有效结合模型的骨架图结构,确定各骨架点对应的局部区域.并将骨架点拟合为二次Bézier曲线,通过交互式拖动任意骨架点计算与之相连的多骨架点的动态变化,实现模型局部区域的自然形变.实验结果表明了该算法的有效性和直观性.     

一种新的六面体有限元网格算法

在有限元网格产生过程中，吸取弦须编织法中的STC概念，将六面体以节点剖分为基础的思想转变为以单元点为基础，建立了以单元生长为核心的剖分算法，以期解决节点拓扑结构在三维情况下的控制问题，对进一步实现稳定、全自动的六面体剖分具有很大的帮助。     

A multigrain Delaunay mesh generation method for multicore SMT-based architectures

Given the proliferation of layered, multicore- and SMT-based architectures, it is imperative to deploy and evaluate important, multi-level, scientific computing codes, such as meshing algorithms, on these systems. We focus on Parallel Constrained Delaunay Mesh (PCDM) generation. We exploit coarse-grain parallelism at the subdomain level, medium-grain at the cavity level and fine-grain at the element level. This multi-grain data parallel approach targets clusters built from commercially available SMTs and multicore processors. The exploitation of the coarser degree of granularity facilitates scalability both in terms of execution time and problem size on loosely-coupled clusters. The exploitation of medium-grain parallelism allows performance improvement at the single node level. Our experimental evaluation shows that the first generation of SMT cores is not capable of taking advantage of fine-grain parallelism in PCDM. Many of our experimental findings with PCDM extend to other adaptive and irregular multigrain parallel algorithms as well.     

A new method of mesh simplification for 3-Dimension terrain using Laplace operator

This paper proposes a new method to simplify mesh in 3D terrain.The 3D terrain is presented by digital elevation model.First,Laplace operator is introduced to calculate sharp degree of mesh point,which indicates the variation trend of the terrain.Through setting a critical value of sharp degree,feature points are selected.Second,critical mesh points are extracted by an recursive process,and constitute the simplified mesh.Third,the algorithm of linear-square interpolation is employed to restore the characteristics of the terrain.Last,the terrain is rendered with color and texture.The experimental results demonstrate that this method can compress data by 16% and the error is lower than 10%.     

多参考坐标系法和滑移网格法在汽车前端进气数值模拟中的比较

为比较多参考坐标系(Multiple Reference Frame,MRF)法和滑移网格法在汽车工程应用中的差异,基于FLUENT软件,分别用这两种方法对汽车风扇旋转流动区域进行数值模拟,得到汽车前端发动机冷却系统流场的计算结果;比较两种计算结果中前端冷却气流的流量、压力分布以及风扇局部流场的分布.最后以滑移网格法的计算结果为基准,给出通常使用的MRF定常处理旋转区域方法在工程应用中的评价.