Constrained Delaunay Triangulation Algorithm Research Articles

An adaptive mesh refinement method for a medium with discrete fracture network: The enriched Persson’s method

Discrete fracture network has significant effects on the thermal–hydraulic–mechanical–chemical coupling analysis in a highly fractured medium. Due to the complex configuration of interior fracture network, generation of a high resolving mesh is crucial in achieving accurate numerical results. An adaptive mesh refinement method is developed for generating adaptive meshes in a domain with discrete fracture networks. An optimized size function is embedded into Persson’s mesh generator. The constrained Delaunay triangulation algorithm is integrated into the analogous force equilibrium method. An assessment method of mesh size quality is proposed. Fractures are pre-meshed with a user-specified length in advance. The whole domain is then adaptively meshed using a constrained Delaunay method in a locally relaxation manner. Varying meshes can be generated with fine meshes around fractures and coarse meshes in the domain. Two case studies are carried out and compared with those obtained from conventional methods. Results show that the present method is advantageous in generating a high resolving mesh. Finer meshes are adaptively generated around fractures and gradually changed to sparser meshes away from fractures. Smoothly and gradually varying meshes are generated with little sacrifice of the size and angle quality. The adaptive mesh refinement method can be used for a wide range of thermal, hydraulic, mechanical, chemical simulations and their numerical coupling system in a fractured medium.

A LINE-BASED 3D ROOF MODEL RECONSTRUCTION ALGORITHM: TIN-MERGING AND RESHAPING (TMR)

Abstract. Three-dimensional building model is one of the major components of a cyber-city and is vital for the realization of 3D GIS applications. In the last decade, the airborne laser scanning (ALS) data is widely used for 3D building model reconstruction and object extraction. Instead, based on 3D roof structural lines, this paper presents a novel algorithm for automatic roof models reconstruction. A line-based roof model reconstruction algorithm, called TIN-Merging and Reshaping (TMR), is proposed. The roof structural line, such as edges, eaves and ridges, can be measured manually from aerial stereo-pair, derived by feature line matching or inferred from ALS data. The originality of the TMR algorithm for 3D roof modelling is to perform geometric analysis and topology reconstruction among those unstructured lines and then reshapes the roof-type using elevation information from the 3D structural lines. For topology reconstruction, a line constrained Delaunay Triangulation algorithm is adopted where the input structural lines act as constraint and their vertex act as input points. Thus, the constructed TINs will not across the structural lines. Later at the stage of Merging, the shared edge between two TINs will be check if the original structural line exists. If not, those two TINs will be merged into a polygon. Iterative checking and merging of any two neighboured TINs/Polygons will result in roof polygons on the horizontal plane. Finally, at the Reshaping stage any two structural lines with fixed height will be used to adjust a planar function for the whole roof polygon. In case ALS data exist, the Reshaping stage can be simplified by adjusting the point cloud within the roof polygon. The proposed scheme reduces the complexity of 3D roof modelling and makes the modelling process easier. Five test datasets provided by ISPRS WG III/4 located at downtown Toronto, Canada and Vaihingen, Germany are used for experiment. The test sites cover high rise buildings and residential area with diverse roof type. For performance evaluation, the adopted roof structural lines are manually measured from the provided stereo-pair. Experimental results indicate a nearly 100% success rate for topology reconstruction was achieved provided that the 3D structural lines can be enclosed as polygons. On the other hand, the success rate at the Reshaping stage is dependent on the complexity of the rooftop structure. Thus, a visual inspection and semi-automatic adjustment of roof-type is suggested and implemented to complete the roof modelling. The results demonstrate that the proposed scheme is robust and reliable with a high degree of completeness, correctness, and quality, even when a group of connected buildings with multiple layers and mixed roof types is processed.

A Constrained Delaunay Triangulation Algorithm Based on Incremental Points

The foundation ofdelaunay triangulationandconstrained delaunay triangulationis the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generatingconstrained delaunay triangulationin two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures related to constrained edges and polygons. In order to maintain the delaunay criterion largely，some new incremental points are added onto the constrained ones. After the data set is preprocessed, the foundation ofconstrained delaunay triangulationis showed as follows: firstly, the constrained edges and polygons generate initial triangulations，then the remained points completes the triangulation . Some pseudo-codes involved in the algorithm are provided. Finally, some conclusions and further studies are given.

Challenges and Technologies in Reservoir Modeling

Reservoir modeling is playing an increasingly important role in developing and producing hydrocarbon reserves. In this paper, we provide a brief overview of some main challenges in reservoir modeling, i.e., accurate and efficient modeling of complex reservoir geometry and heterogeneous reservoir properties. We then present modeling techniques we recently developed in addressing these challenges, including a method for generating constrained Voronoi grids and a generic global scale-up method. We focus on the Voronoi gridding method, which is based on a new constrained Delaunay triangulation algorithm and a rigorous method of adapting Voronoi grids to piecewise linear constraints. The global scale-up method based on generic flows is briefly described. Numerical examples are provided to demonstrate the techniques and the advantage of combining them in constructing accurate and efficient reservoir models. AMS subject classifications: 37M05, 76S05, 86A60, 65M50, 65N50

Finite element-based model for crack propagation in polycrystalline materials

In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element method (X-FEM) and microstructures are simulated using a kinetic Monte Carlo Potts algorithm. In the X-FEM, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the two-dimensional asymptotic crack-tip fields. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack growth simulations can be carried out without the need for remeshing. First, the convergence of the method for crack problems is studied and its rate of convergence is established. Microstructural calculations are carried out on a regular lattice and a constrained Delaunay triangulation algorithm is used to mesh the microstructure. Fracture properties of the grain boundaries are assumed to be distinct from that of the grain interior, and the maximum energy release rate criterion is invoked to study the competition between intergranular and transgranular modes of crack growth.

Finite element-based model for crack propagation in polycrystalline materials

In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element method (X-FEM) and microstructures are simulated using a kinetic Monte Carlo Potts algorithm. In the X-FEM, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the two-dimensional asymptotic crack-tip fields. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack growth simulations can be carried out without the need for remeshing. First, the convergence of the method for crack problems is studied and its rate of convergence is established. Microstructural calculations are carried out on a regular lattice and a constrained Delaunay triangulation algorithm is used to mesh the microstructure. Fracture properties of the grain boundaries are assumed to be distinct from that of the grain interior, and the maximum energy release rate criterion is invoked to study the competition between intergranular and transgranular modes of crack growth.

Brittle fracture in polycrystalline microstructures with the extended finite element method

AbstractA two‐dimensional numerical model of microstructural effects in brittle fracture is presented, with an aim towards the understanding of toughening mechanisms in polycrystalline materials such as ceramics. Quasi‐static crack propagation is modelled using the extended finite element method (X‐FEM) and microstructures are simulated within the framework of the Potts model for grain growth. In the X‐FEM, a discontinuous function and the two‐dimensional asymptotic crack‐tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Hence, crack propagation can be simulated without any user‐intervention or the need to remesh as the crack advances. The microstructural calculations are carried out on a regular lattice using a kinetic Monte Carlo algorithm for grain growth. We present a novel constrained Delaunay triangulation algorithm with grain boundary smoothing to create a finite element mesh of the microstructure. The fracture properties of the microstructure are characterized by assuming that the critical fracture energy of the grain boundary (Gcgb) is different from that of the grain interior (Gci). Numerical crack propagation simulations for varying toughness ratios Gcgb/Gci are presented, to study the transition from the intergranular to the transgranular mode of crack growth. This study has demonstrated the capability of modelling crack propagation through a material microstructure within a finite element framework, which opens‐up exciting possibilities for the fracture analysis of functionally graded material systems. Copyright © 2003 John Wiley & Sons, Ltd.

Automatic generation of 3D meshes for complicated solids

To approach full automatic mesh generation, three problems have to be solved: (1) full automatic generation of geometry specifying the mesh from the solid model; (2) a constrained triangulation algorithm for adding a new point to an existing mesh; and (3) a description and realization of the user's mesh distribution desires which may be implied by the problem itself, as in the case of self-adaptive finite element analysis. The authors merge a novel mesh control idea (see J.M. Zhou, 1989) with the constrained Delaunay triangulation algorithm and an initial triangulation algorithm to achieve efficient, flexible, and reliable triangulation of complicated solids. A new strategy for adaptive mesh refinement is also included. >