Unstructured Mesh Generation Research Articles

Mesh Generation Using Unstructured Computational Meshes and Elliptic Partial Differential Equation Smoothing

A novel appro ach for generating unstructured meshes using elliptic smoothing is presented. Like structured mesh generation methods, the approach begins with the construction of a computational mesh. The computational mesh is used to solve elliptic partial differential equations that control grid point distributions and improve mesh quality. Two types of elliptic partial differential equations are employed; modified linear -elastic theory and Winslow equation s, with or without forcing functions . Results are included to il lustrate the use of these methods for unstructured mesh generation, mesh boundary shape modification, mesh untangling and mesh movement.

A Parallel Computing Framework and a Modular Collaborative CFD Workbench in JAVA

The aim of this study is to give the means for writing parallel programs and to transform sequential/shared memory programs into distributed programs, in an object-oriented environment and also to develop a parallel CFD workbench utilizing the framework. In this approach, the programmer controls the distribution of programs through control and data distribution. The authors have defined and implemented a parallel framework, including the expression of object distributions, and the transformations required to run a parallel program in a distributed environment. The authors provide programmers with a unified way to express parallelism and distribution by the use of collections storing active and passive objects. The distribution of classes/packages leads to the distribution of their elements and therefore to the generation of distributed programs. The authors have developed a full prototype to write parallel programs and to transform those programs into distributed programs with a host of about 12 functions. This prototype has been implemented with the Java language, and does not require any language extensions or modifications to the standard Java environment. The parallel program is utilized by developing a CFD workbench equipped with high end FEM unstructured mesh generation and flow solving tools with an easy-to-use GUI implemented entirely on the parallel framework.

A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell’s equations in time domain

In this paper, we present a non-dissipative spatial high-order discontinuous Galerkin method to solve the Maxwell equations in the time domain. The non-intuitive choice of the space of approximation and the basis functions induce an important gain for mass, stiffness and jump matrices in terms of memory. This spatial approximation, combined with a leapfrog scheme in time, leads also to a fast explicit and accurate method. A study of the dispersive error is carried out and a stability condition for the proposed scheme is established. Some comparisons with other schemes are presented to validate the new scheme and to point out its advantages. Finally, in order to improve the efficiency of the method in terms of CPU time on general unstructured meshes, a strategy of local time-stepping is proposed.

Domain Decomposition Approach for Automatic Parallel Generation of Tetrahedral Grids

AbstractThe desire to simulate even more geometrical and physical features of technical structures and the availability of parallel computers and parallel numerical solvers which can exploit the power of these machines have led to a steady increase in the number of the grid elements used. Memory requirements and computational time are too large for usual serial PCs. An a priori partitioning algorithm for the parallel generation of 3D non-overlapping compatible unstructured meshes based on a CAD surface description is presented in this paper. Emphasis is placed on practical issues and implementation rather than on theoretical complexity. In order to achieve robustness of the algorithm with respect to the geometrical shape of the structure, the authors propose that there should be several or many but relatively simple algorithmic steps. The geometrical domain decomposition approach has been applied. It allows us to use standard 2D and 3D high-quality Delaunay mesh generators for independent and simultaneous volume meshing. Different aspects of load balancing methods are also explored in the paper. The MPI library and SPMD model are used for parallel grid generator implementation. Several 3D examples are given.

Integrated high performance computational tools for simulations of transport and diffusion of contaminants in urban areas

Rapid analysis of transport and diffusion of chemical and biological aerosols and contaminants in an urban environment is a critical part of any homeland security response team. High performance computing (HPC) is a valuable technique for such analysis. The time constraint needed to create fully developed complex 3D city terrain models to support such dispersion simulations requires a task of converting agency data to the format necessary on the simulation platform. Numerous data sets have been employed in the development of complex 3D city models. Such data include the use of multi-layer building morphology data, the use of geographic information system (GIS) based shapefiles and digital elevation models (DEM), and the use of remote sensing data such as Light Detection and Ranging (LIDAR). The constructed geometry models are used to generate large-scale computational domains on a platform that supports our HPC tools. These tools include fully automated unstructured mesh generation, parallel and scalable flow solvers based on stabilized finite element formulations and a remote client-server environment for large-scale flow visualization. The stabilized finite element formulations, which are based on the SUPG and PSPG techniques, are parallelized and vectorized on the Cray X1. The 3D validation problem involves transient simulation of flow past a building with a source point releasing traces. A 3D application problem is presented to demonstrate the capability of the integrated HPC tools.

Robust generation of high‐quality unstructured meshes on realistic biomedical geometry

AbstractIn this paper, we propose efficient and robust unstructured mesh generation methods based on computed tomography (CT) and magnetic resonance imaging (MRI) data, in order to obtain a patient‐specific geometry for high‐fidelity numerical simulations. Surface extraction from medical images is carried out mainly using open source libraries, including the Insight Segmentation and Registration Toolkit and the Visualization Toolkit, into the form of facet surface representation. To create high‐quality surface meshes, we propose two approaches. One is a direct advancing front method, and the other is a modified decimation method. The former emphasizes the controllability of local mesh density, and the latter enables semi‐automated mesh generation from low‐quality discrete surfaces. An advancing‐front‐based volume meshing method is employed. Our approaches are demonstrated with high‐fidelity tetrahedral meshes around medical geometries extracted from CT/MRI data. Copyright © 2005 John Wiley & Sons, Ltd.

A stitching method for the generation of unstructured meshes for use with co-volume solution techniques

The successful implementation of co-volume time-domain solution techniques requires the use of high quality, smooth dual meshes. The generation of Delaunay–Voronoï diagrams with these properties, for two-dimensional domains of complicated geometrical shape, is considered. In the adopted approach, near-boundary regions are discretised according to prescribed criteria and the remainder of the computational domain is discretised using an ideal mesh. The two meshes are stitched together to provide a consistent mesh for the complete domain. After smoothing, the resulting mesh is found to be of a quality which exceeds that of meshes produced by standard, automatic, unstructured mesh generation methods. Examples, involving electromagnetic wave scattering, are included to demonstrate the computational performance that can be achieved with a co-volume time domain solution algorithm on these meshes.

OPTIMAL CONVERGENCE OF NON-OVERLAPPING SCHWARZ METHODS FOR THE HELMHOLTZ EQUATION

The non-overlapping Schwarz method with absorbing boundary conditions instead of the Dirichlet boundary conditions is an efficient variant of the overlapping Schwarz method for the Helmholtz equation. These absorbing boundary conditions defined on the interface between the subdomains are the key ingredients to obtain a fast convergence of the iterative Schwarz algorithm. In a one-way subdomains splitting, non-local optimal absorbing boundary conditions can be obtained and leads to the convergence of the Schwarz algorithm in a number of iterations equal to the number of subdomains minus one. This paper investigates different local approximations of these optimal absorbing boundary conditions for finite element computations in acoustics. Different approaches are presented both in the continuous and in the discrete analysis, including high-order optimized continuous absorbing boundary conditions, and discrete absorbing boundary conditions based on algebraic approximation. A wide range of new numerical experiments performed on unbounded acoustics problems demonstrate the comparative performance and the robustness of the proposed methods on general unstructured mesh partitioning.

An algorithm for tetrahedral mesh generation based on conforming constrained Delaunay tetrahedralization

An unstructured tetrahedral mesh generation algorithm for 3D model with constraints is presented. To automatically generate a tetrahedral mesh for model with constraints, an advancing front algorithm is presented based on conforming constrained Delaunay tetrahedralization (CCDT). To reduce the number of visibility tests between vertices with respect to model faces as well as the computation of constrained Delaunay tetrahedra, a sufficient condition for DT (constrained Delaunay tetrahedralization whose simplexes are all Delaunay) existence is presented and utilized coupled to uniform grid and advancing front techniques in our algorithm. The mesh generator is robust and exhibits a linear time complexity for mechanical models with uniform density distribution.

Node placement for triangular mesh generation by Monte Carlo simulation

AbstractA new approach of node placement for unstructured mesh generation is proposed. It is based on the Monte Carlo method to position nodes for triangular or tetrahedral meshes. Surface or volume geometries to be meshed are treated as atomic systems, and mesh nodes are considered as interacting particles. By minimizing system potential energy with Monte Carlo simulation, particles are placed into a near‐optimal configuration. Well‐shaped triangles or tetrahedra can then be created after connecting the nodes by constrained Delaunay triangulation or tetrahedrization. The algorithm is simple, easy to implement, and works in an almost identical way for 2D and 3D meshing. Copyright © 2005 John Wiley & Sons, Ltd.

3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric

In this paper we present a 3D tetrahedral, unstructured and anisotropic mesh generator that is not based on the Delaunay, frontal or octree method. Instead, it proceeds by local optimizations and uses an anisotropic shape criterion to fit a metric field. Then, we introduce a new 3D metric field that tightens the mesh around interfaces when the calculation domain is divided in several subdomains, and a 3D metric field that places enough elements through each subdomain thickness, without introducing too many nodes in the other directions. Finally, we show some applications for material forming geometries.

Modelling sediment transport using a lightweight bed material

Details are given of a combined physical and numerical model study of sediment transport processes in a square harbour caused by tidal motion. The effects on bed level changes due to tidal currents and the configuration of the harbour entrance were investigated. A lightweight material called Cation Resin was used in this study to represent bed sediments in the laboratory experiments. This material enabled the erosion and deposition processes to be exaggerated within the model harbour, in which the magnitude of the flow velocities was relatively small. An unstructured mesh generation technique, namely a quad-tree grid, was incorporated into an existing two-dimensional depth-integrated numerical model to predict the transport of water quality constituents and sediment particle fluxes. The numerical model was further refined to include the prediction of bed level changes. Detailed comparisons between the numerical model predictions and the laboratory data were undertaken. It was found that the numerical model predictions and the laboratory measurements were in good agreement. It was also concluded that Cation Resin was an appropriate material to use for physical modelling of sediment transport processes in laboratory model studies.

Parallel complete remeshing for adaptive schemes

In order to improve the convergence ratio and to automate Finite Element Methods, several strategies have been introduced. One of these is the adaptive scheme. This approximation presents limitations for parallelism since the generation of a conformal, valid and well conditioned finite element mesh is a time consuming task, and now it appears as a main task in each iteration of the adaptation procedure. This work is motivated by the use of the h-adaptive method in its most flexible form, where a complete reconstruction of the whole mesh has to be performed whenever a solution over the current mesh has been obtained and until error criteria are achieved. We focused on the problem of the fast generation of tetrahedral unstructured meshes in a parallel fashion over geometric models with some given refinement criteria. The chosen strategy implies the use of an octal tree, octree, as a key hierarchical data structure to guide the algorithm. The codes have been developed using the MPI library in a SGI Origin 200 multiprocessor.

Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids

We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.

Meshing Requirements for Tidal Modeling in the Western North Atlantic

This paper presents an a posteriori approach to unstructured mesh generation via a localized truncation error analysis and applies it to the Western North Atlantic Tidal (WNAT) model domain. The WNAT model domain encompasses the Gulf of Mexico, the Caribbean Sea, and the North Atlantic Ocean east to the 60°W Meridian. Herein, we pay particular attention to the area surrounding the Bahamas. A bathymetric data set with fine resolution is employed in seven separate linear, harmonic simulations of shallow water tidal flow for seven different tidal-forcing constituents. Each set of simulation results is used to perform a truncation error analysis of a linear, harmonic form of the depth-averaged momentum equations for each of the seven different tidal-forcing frequencies. Truncation error is then driven to a more uniform, domain-wide value by solving for local node spacing requirements. The process is built upon successful research aiming to produce unstructured grids for large-scale domains that can be used in the accurate and efficient modeling of shallow water flow. The methodology described herein can also be transferred to other modeling applications.

Efficient parallel implementations of near Delaunay triangulation with High Performance Fortran

Unstructured mesh generation exposes highly irregular computation patterns, which imposes a challenge in implementing triangulation algorithms on parallel machines. This paper reports on an efficie...

The Effects of Different Mesh Generation Methods on Computational Fluid Dynamic Analysis and Power Loss Assessment in Total Cavopulmonary Connection

The flow field and energetic efficiency of total cavopulmonary connection (TCPC) models have been studied by both in vitro experiment and computational fluid dynamics (CFD). All the previous CFD studies have employed the structured mesh generation method to create the TCPC simulation model. In this study, a realistic TCPC model with complete anatomical features was numerically simulated using both structured and unstructured mesh generation methods. The flow fields and energy losses were compared in these two meshes. Two different energy loss calculation methods, the control volume and viscous dissipation methods, were investigated. The energy losses were also compared to the in vitro experimental results. The results demonstrated that: (1) the flow fields in the structured model were qualitatively similar to the unstructured model; (2) more vortices were present in the structured model than in the unstructured model; (3) both models had the least energy loss when flow was equally distributed to the left and right pulmonary arteries, while high losses occurred for extreme pulmonary arterial flow splits; (4) the energy loss results calculated using the same method were significantly different for different meshes; and (5) the energy loss results calculated using different methods were significantly different for the same mesh.

A finite volume scheme for anisotropic diffusion problems

A new finite volume for the discretization of anisotropic diffusion problems on general unstructured meshes in any space dimension is presented. The convergence of the approximate solution and its discrete gradient is proven. The efficiency of the scheme is illustrated by numerical results. To cite this article: R. Eymard et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

Three-dimensional anisotropic geometric metrics based on local domain curvature and thickness

A three-dimensional anisotropic Riemannian metric is constructed from a triangulated CAD model to control its spatial discretization for numerical analysis. In addition to the usual curvature criterion, the present geometric metric is also based on the local thickness of the modeled domain. This local thickness is extracted from the domain skeleton while local curvature is deduced from the model triangulated boundaries. A Cartesian background octree is used as the support medium for this metric and skeletonization takes advantage of this structure through an octree extension of a digital medial axis transform. For this purpose, the octree has to be refined according to not only boundary curvature but also a local separation criterion from digital topology theory. The resulting metric can be used to geometrically adapt any mesh type as long as metric-based adaptation tools are available. To illustrate such an application, geometric adaptation of overlay meshes used in grid-based methods for unstructured hexahedral mesh generation is presented. However, beyond mesh generation, the present metric may also be useful as a shape analysis tool and such a possibility could be explored in future developments.

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.