Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

Analysis and Generation of Quality Polytopal Meshes with Applications to the Virtual Element Method

This thesis explores the concept of the quality of a mesh, the latter being intended as the discretization of a two- or three- dimensional domain. The topic is interdisciplinary in nature, as meshes are massively used in several fields from both the geometry processing and the numerical analysis communities. The goal is to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. In other words, a good quality mesh that is also cheap to handle, overcoming the typical trade-off between quality and computational cost. To reach this goal, we first need to answer the question: ''How, and how much, does the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depend on the particular mesh adopted to model the problem? And which geometrical features of the mesh most influence the result?'' We present a comparative study of the different mesh types, mesh generation techniques, and mesh quality measures currently available in the literature related to both engineering and computer graphics applications. This analysis leads to the precise definition of the notion of quality for a mesh, in the particular context of numerical simulations of partial differential equations with the virtual element method, and the consequent construction of criteria to determine and optimize the quality of a given mesh. Our main contribution consists in a new mesh quality indicator for polytopal meshes, able to predict the performance of the virtual element method over a particular mesh before running the simulation. Strictly related to this, we also define a quality agglomeration algorithm that optimizes the quality of a mesh by wisely agglomerating groups of neighboring elements. The accuracy and the reliability of both tools are thoroughly verified in a series of tests in different scenarios

7th International Meshing Roundtable '98

The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries

Lattice cleaving: a multimaterial tetrahedral meshing algorithm with guarantees

pre-printWe introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach

ICASE/LaRC Workshop on Adaptive Grid Methods

Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field

Liquid simulation with mesh-based surface tracking

Animating detailed liquid surfaces has always been a challenge for computer graphics researchers and visual effects artists. Over the past few years, researchers in this field have focused on mesh-based surface tracking to synthesize extremely detailed liquid surfaces as efficiently as possible. This course provides a solid understanding of the steps required to create a fluid simulator with a mesh-based liquid surface. The course begins with an overview of several existing liquid-surface-tracking techniques and the pros and cons of each method. Then it explains how to embed a triangle mesh into a finite-difference-based fluid simulator and describes several methods for allowing the liquid surface to merge together or break apart. The final section showcases the benefits and further applications of a mesh-based liquid surface, highlighting state-of-the-art methods for tracking colors and textures, maintaining liquid volume, preserving small surface features, and simulating realistic surface-tension waves

The aerodynamic flow over a bluff body in ground proximity: CFD prediction of road vehicle aerodynamics using unstructured grids

The prediction of external automobile aerodynamics using Computational Fluid Dynamics (CFD) is still in its infancy. The restrictions on grid size for practical use limit the ability of most organisations to predict the full flow over an automobile. Some insight into the flow over a passenger car can be made by examining the flow over a bluff body in close proximity to the ground. One such body is the Ahmed body composed of a rounded front, straight mid-section and variable slant-rear section. This body exhibits many of the 3D flow structures exhibited by passenger cars. The main feature of the flow around this body is the change in flow structure as the angle of the slant surface at the rear of the body is increased. The flow starts fully attached and ends fully separated. In between these two regimes is a third high drag regime. The flow structure is characterised by strong counter-rotating longitudinal vortices originating from the interaction between the flow from the sides and top of the body, and a small separation from the top/slant edge on the centre-plane of the body. The flow reattaches to the slant surface and the low-pressure fluid within the separation bubble increases the drag considerably. The use of CFD incorporating tine averaged statistical turbulence models to reproduce these flow patterns is assessed in this study. Initial work concentrated on evaluating structured grid methods for this flow type. Some success was achieved with the flow fields for the attached and fully separated cases but the third high drag regime was not predicted. The flow field also exhibited a grid dependent flow structure and drag result. To examine these effects further without high grid overheads an unstructured mesh generator was developed and used to provide meshes with more grid cells clustered around the body and it's wake. Analysis and refinement of the unstructured grids proved successful at removing the grid dependent flow field but still showed no evidence of the third high drag flow regime. Further, the bulk levels of drag in all cases was too high and the fully separated flow regime occurred too late in the slant surface angle sweep, coming at 40° instead of the 30° seen in the wind tunnel results. Further analysis of the flow field using highly refined mixed meshes showed no improvement in the drag or flow field prediction with the high drag flow field still not present. The use of higher order differencing schemes and anisotropic turbulence models reduced the drag levels considerably but not to the levels seen in the wind tunnel results. Comparison of the results from this work with the work of other authors is difficult for two reasons. Firstly, work on the specific body used in this thesis is sparse and, secondly, much of the work done by other authors was in conjunction with automotive manufacturers and details of the specific numerical methods employed are not available. The most important parallel conclusion from the work presented here and that of other authors is the inability of the CFD prediction to capture the change in flow mode as the angle of slant surface is increased. This failure can, in all probability, be attributed to the use of a steady-state CFD solution algorithm to capture the flow field around the body. A small possibility perhaps still exists that further grid refinement, very localised around the body, would help, but the detailed and careful predictions presented in this study make this highly unlikely. The most important piece of further work that could follow this work would therefore be the application of a time-accurate (unsteady) CFD solution algorithm to the bluff body in ground proximity problem. Whether these predictions should be of an unsteady RANS nature, or full LES predictions would be best answered by applying these methods to the present flow problem which is fundamental to the study of automobile aerodynamics

Numerical simulation of fracture pattern development and implications for fuid flow

Simulations are instrumental to understanding flow through discrete fracture geometric representations that capture the large-scale permeability structure of fractured porous media. The contribution of this thesis is threefold: an efficient finite-element finite-volume discretisation of the advection/diffusion flow equations, a geomechanical fracture propagation algorithm to create fractured rock analogues, and a study of the effect of growth on hydraulic conductivity. We describe an iterative geomechanics-based finite-element model to simulate quasi-static crack propagation in a linear elastic matrix from an initial set of random flaws. The cornerstones are a failure and propagation criterion as well as a geometric kernel for dynamic shape housekeeping and automatic remeshing. Two-dimensional patterns exhibit connectivity, spacing, and density distributions reproducing en echelon crack linkage, tip hooking, and polygonal shrinkage forms. Differential stresses at the boundaries yield fracture curving. A stress field study shows that curvature can be suppressed by layer interaction effects. Our method is appropriate to model layered media where interaction with neighbouring layers does not dominate deformation. Geomechanically generated fracture patterns are the input to single-phase flow simulations through fractures and matrix. Thus, results are applicable to fractured porous media in addition to crystalline rocks. Stress state and deformation history control emergent local fracture apertures. Results depend on the number of initial flaws, their initial random distribution, and the permeability of the matrix. Straightpath fracture pattern simplifications yield a lower effective permeability in comparison to their curved counterparts. Fixed apertures overestimate the conductivity of the rock by up to six orders of magnitude. Local sample percolation effects are representative of the entire model flow behaviour for geomechanical apertures. Effective permeability in fracture dataset subregions are higher than the overall conductivity of the system. The presented methodology captures emerging patterns due to evolving geometric and flow properties essential to the realistic simulation of subsurface processes