Automatic sizing functions for unstructured surface mesh generation

Accurate sizing functions are crucial for efficient generation of high-quality meshes, but to define the sizing function is often the bottleneck in complicated mesh generation tasks because of the tedious user interaction involved. We present a novel algorithm to automatically create high-quality sizing functions for surface mesh generation. First, the tessellation of a Computer Aided Design (CAD) model is taken as the background mesh, in which an initial sizing function is defined by considering geometrical factors and user-specified parameters. Then, a convex nonlinear programming problem is formulated and solved efficiently to obtain a smoothed sizing function that corresponds to a mesh satisfying necessary gradient constraint conditions and containing a significantly reduced element number. Finally, this sizing function is applied in an advancing front mesher. With the aid of a walk-through algorithm, an efficient sizing-value query scheme is developed. Meshing experiments of some very complicated geometry models are presented to demonstrate that the proposed sizing-function approach enables accurate and fully automatic surface mesh generation

Grid generation for the solution of partial differential equations

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given

Tuned grid generation with ICEM CFD

ICEM CFD is a CAD based grid generation package that supports multiblock structured, unstructured tetrahedral and unstructured hexahedral grids. Major development efforts have been spent to extend ICEM CFD's multiblock structured and hexahedral unstructured grid generation capabilities. The modules added are: a parametric grid generation module and a semi-automatic hexahedral grid generation module. A fully automatic version of the hexahedral grid generation module for around a set of predefined objects in rectilinear enclosures has been developed. These modules will be presented and the procedures used will be described, and examples will be discussed

An advancing front technique for filling space with arbitrary separated objects

An advancing front technique for filling space with arbitrary, separated objects has been developed. The input required consists of the specification of the desired object type, the mean object size, the distance between objects in space, as well as an initial triangulation of the surface. The objects are assumed to be described by a coarse mesh of tetrahedra. One face at a time is removed from the active front, and, if possible, surrounded by admissible new objects. This operation is repeated until no active faces are left. Two techniques to obtain maximum packing are discussed: closest object placement (during generation) and move/enlarge (after generation). Several examples are included that demonstrate the capabilities of the technique. Copyright © 2009 John Wiley & Sons, Ltd

A general advancing front technique for filling space with arbitrary objects

An advancing front space‐filling technique for arbitrary objects has been developed. The input required consists of the specification of the desired mean point distance in space and an initial triangulation of the surface. One object at a time is removed from the active front, and, if possible, surrounded by admissible new objects. This operation is repeated until no active objects are left. Two techniques to obtain maximum packing are discussed: closest object placement (during generation) and move/enlarge (after generation). Different deposition or layering patterns can be achieved by selecting the order in which objects are eliminated from the active front. Timings show that for simple objects like spheres the scheme is considerably faster than volume mesh generators based on the advancing front technique, making it possible to generate large (> 106) yet optimal clouds of points in a matter of minutes on a PC. For more general objects, the performance may degrade depending on the complexity of the penetration checks. Several examples are included that demonstrate the capabilities of the technique.&nbsp

Geometry Modeling for Unstructured Mesh Adaptation

The quantification and control of discretization error is critical to obtaining reliable simulation results. Adaptive mesh techniques have the potential to automate discretization error control, but have made limited impact on production analysis workflow. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic mesh adaptation mechanics. However, the poor integration of initial mesh generation and adaptive mesh mechanics to typical sources of geometry has hindered adoption of adaptive mesh techniques, where these geometries are often created in Mechanical Computer- Aided Design (MCAD) systems. The difficulty of this coupling is compounded by two factors: the inherent complexity of the model (e.g., large range of scales, bodies in proximity, details not required for analysis) and unintended geometry construction artifacts (e.g., translation, uneven parameterization, degeneracy, self-intersection, sliver faces, gaps, large tolerances be- tween topological elements, local high curvature to enforce continuity). Manual preparation of geometry is commonly employed to enable fixed-grid and adaptive-grid workflows by reducing the severity and negative impacts of these construction artifacts, but manual process interaction inhibits workflow automation. Techniques to permit the use of complex geometry models and reduce the impact of geometry construction artifacts on unstructured grid workflows are models from the AIAA Sonic Boom and High Lift Prediction are shown to demonstrate the utility of the current approach

Developments and trends in three-dimensional mesh generation

An intense research effort over the last few years has produced several competing and apparently diverse methods for generating meshes. Recent progress is reviewed and the central themes are emphasized which form a solid foundation for future developments in mesh generation

Structured Mesh Generation : Open-source automatic nonuniform mesh generation for FDTD simulation

This article describes a cuboid structured mesh generator suitable for 3D numerical modelling using techniques such as finite-difference time-domain (FDTD) and transmission-line matrix (TLM). The mesh generator takes as its input an unstructured triangular surface mesh such as is available from many CAD systems, determines a suitable variable mesh discretisation and generates solid and surface meshes in a format suitable for import by the numerical solver. The mesher is implemented in the MATLAB language and is available as open source software