Advancing Front Techniques Research Articles

A Solution Verification Study for URANS Simulations of Flow Over a 5:1 Rectangular Cylinder Using Grid Convergence Index and Least Squares Procedures

Abstract A verification study was conducted for URANS (Unsteady Reynolds-Averaged Navier–Stokes) simulations of flow around a 5:1 rectangular cylinder at a Reynolds number of 56,700 (based on the cylinder depth) using the k–ω SST (shear stress transport) turbulence model and the γ−Reθ transition model for three types of grids (a fully structured grid and two hybrid grids generated using Delaunay and advancing front techniques). The grid convergence index (GCI) and least squares (LS) procedures were employed to estimate discretization error and associated uncertainties. The result indicates that the LS procedure provides the most reliable estimates of discretization error uncertainties for solution variables in the structured grid from the k–ω SST model. From the six solution variables of interest, the highest relative uncertainty was typically observed in the root-mean-square (rms) of lift coefficient, followed by time-averaged reattachment length and peak rms of pressure coefficient on the top and bottom surfaces of the cylinder. The solution variable with the lowest uncertainty was Strouhal number, followed by time-averaged drag coefficient. It is also noted that the GCI and LS procedures produce noticeably different uncertainty estimates, primarily due to inconsistences in their estimated observed orders of accuracy and safety factors. To successfully apply the procedures to practical problems, further research is required to reliably estimate uncertainties in solutions with “noisy” grid convergence behaviors and observed orders of accuracy.

Off-centre Steiner points for Delaunay-refinement on curved surfaces

An extension of the restricted Delaunay-refinement algorithm for surface mesh generation is described, where a new point-placement scheme is introduced to improve element quality in the presence of mesh size constraints. Specifically, it is shown that the use of off-centre Steiner points, positioned on the faces of the associated Voronoi diagram, typically leads to significant improvements in the shape- and size-quality of the resulting surface tessellations. The new algorithm can be viewed as a Frontal-Delaunay approach — a hybridisation of conventional Delaunay-refinement and advancing-front techniques in which new vertices are positioned to satisfy both element size and shape constraints. The performance of the new scheme is investigated experimentally via a series of comparative studies that contrast its performance with that of a typical Delaunay-refinement technique. It is shown that the new method inherits many of the best features of classical Delaunay-refinement and advancing-front type methods, leading to the construction of smooth, high quality surface triangulations with bounded radius-edge ratios and convergence guarantees. Experiments are conducted using a range of complex benchmarks, verifying the robustness and practical performance of the proposed scheme.

Finite element generation of arbitrary 3-D fracture networks for flow analysis in complicated discrete fracture networks

Finite element generation of complicated fracture networks is the core issue and source of technical difficulty in three-dimensional (3-D) discrete fracture network (DFN) flow models. Due to the randomness and uncertainty in the configuration of a DFN, the intersection lines (traces) are arbitrarily distributed in each face (fracture and other surfaces). Hence, subdivision of the fractures is an issue relating to subdivision of two-dimensional (2-D) domains with arbitrarily-distributed constraints. When the DFN configuration is very complicated, the well-known approaches (e.g. Voronoi Delaunay-based methods and advancing-front techniques) cannot operate properly. This paper proposes an algorithm to implement end-to-end connection between traces to subdivide 2-D domains into closed loops. The compositions of the vertices in the common edges between adjacent loops (which may belong to a single fracture or two connected fractures) are thus ensured to be topologically identical. The paper then proposes an approach for triangulating arbitrary loops which does not add any nodes to ensure consistency of the meshes at the common edges. In addition, several techniques relating to tolerance control and improving code robustness are discussed. Finally, the equivalent permeability of the rock mass is calculated for some very complicated DFNs (the DFN may contain 1272 fractures, 633 connected fractures, and 16,270 closed loops). The results are compared with other approaches to demonstrate the veracity and efficiency of the approach proposed in this paper.

Voronoi-based Point-placement for Three-dimensional Delaunay-refinement

An extension of the restricted Delaunay-refinement algorithm for three-dimensional tetrahedral mesh generation is described, in which an off-centre type point-placement scheme is utilised. It is shown that the use of generalised Steiner points, positioned along edges in the associated Voronoi complex, typically leads to improvements in the overall size, quality and grading of the resulting tetrahedral meshes. The new algorithm can be viewed as a Frontal-Delaunay approach – a hybridisation of conventional Delaunay-refinement and advancing-front techniques, in which new vertices are positioned to satisfy both element size- and shape- constraints. The new method is shown to inherit many of the best features of classical Delaunay-refinement and advancing-front type algorithms, combining good practical performance with theoretical robustness. Experimental comparisons show that the new method outperforms classical Delaunay-refinement techniques for a number of three-dimensional benchmark problems.

An insight into the science of unstructured meshes in computer numerical simulation

Computer numerical simulation is a beneficial tool for studying various domains of knowledge. Among the steps in the whole process of numerical simulation is the generation of unstructured meshes. Since the unstructured meshes are usually generated using automatic software, the fundamental knowledge of the unstructured meshes is often neglected. This paper highlighted some useful insights into the unstructured meshes in numerical simulation for several application domains, such as the radiative heat transfer problem, ocean modelling and biomedical engineering. It also reviewed some fundamental concepts and frameworks for element generation in producing unstructured meshes, particularly the Delaunay triangulation and advancing front techniques.

Face-centred Voronoi Refinement for Surface Mesh Generation

A Frontal-Delaunay surface meshing algorithm for closed 2-manifolds embedded in R3 is presented. This new algorithm is an extension of existing restricted Delaunay-refinement techniques, in which the point-placement scheme is modified to improve element quality in the presence of mesh size constraints. Specifically, it is shown that the use of off-centre Steiner vertices, positioned along facets in the associated Voronoi diagram, typically leads to an improvement in the shape- and size-quality of the resulting surface tessellation. The new method can be viewed as a hybridisation of conventional Delaunay-refinement and advancing-front techniques, in which new vertices are positioned to satisfy both element size and shape constraints. It is shown that by restricting point-placement to faces of the associated Voronoi diagram, the new Frontal-Delaunay algorithm maintains many of the theoretical guarantees commonly associated with conventional restricted Delaunay-refinement techniques. The performance of the new Frontal-Delaunay scheme is investigated experimentally, via a series of comparative studies designed to contrast the performance of the new algorithm with a typical Delaunay-refinement technique. It is shown that the new Frontal-Delaunay algorithm inherits many of the benefits of both Delaunay-refinement and advancing-front type methods, typically leading to the construction of very high quality triangulations in practice. Experiments are conducted using a range of complex benchmarks, verifying the robustness and practical performance of the proposed scheme.

Advancing front techniques for filling space with arbitrary separated objects

A review is given of advancing front techniques for filling space with arbitrary separated objects. Over the last decade, these techniques have reached a considerable degree of maturity and are being used to generate clouds of points for SPH and FPM simulations, as well as spheres, ellipsoids, objects defined by a collection of spheres or polyhedral objects for DEM simulations. Algorithmic as well as implementational aspects are discussed. Techniques to obtain maximum packing, such as closest object placement (during generation) and move/enlarge (after generation) are also considered. Several examples are included that demonstrate the capabilities developed.

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.

Fully unstructured Delaunay mesh generation using a modified advancing front approach for applications in technology cad

We introduce a combination of Delaunay methods with advancing front techniques especially suitable for local regridding and semiconductor simulation applications. element quality improvement can be handled by local mesh adaptation steps. the three-dimensional meshing algorithm is suitable for complicated structures, because of its fully unstructured nature. the resulting Delaunay mesh possesses the flexibility possible within the scope of a tetrahedral representation not like octree based or other cartesian meshes which are commonly employed in technology cad (TCAD).

A framework for advancing front techniques of finite element mesh generation

Advancing front techniques are a family of methods for finite element mesh generation that are particularly effective in dealing with complicated boundary geometries. In the first part of this paper, conditions are presented which ensure that any planar aft algorithm that meets these conditions terminates in a finite number of steps with a valid triangulation of the input domain. These conditions are described by specifying a framework of subtasks that can accommodate many aft methods and by prescribing the minimal requirements on each subtask that ensure correctness of an algorithm that conforms to the framework.