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Numeric models use a collection of triangular facets called elements connected over a domain in what is referred to as a mesh or unstructured grid as the computational basis for calculations. The density of elements in a mesh affects the numeric stability of a model when performing computations. Furthermore, these meshes can be difficult and time consuming to create. This thesis describes an automated process of creating meshes which utilizes local truncation analysis to generate a spatially varied size function. An advancing frontal mesh generation algorithm uses this function to optimize node placement and density. Further analysis to better understand appropriate applications of this technique is also presented. The toolbox was able to create efficient meshes with relatively little user input. The final mesh spacing honored the guidelines from the truncation error analysis and resulted in appropriate mesh density. It was also shown that the process could be applied to several shelf based meshes.

No description available.

It is widely accepted that the accuracy and efficiency of computational fluid dynamics (CFD) simulations is heavily influenced by the quality of the mesh upon which the solution is computed. Unfortunately, the computational tools available for assessing mesh quality remain rather limited. This report describes a methodology for rigorously investigating the interaction between a flow solver and a variety of mesh configurations for the purposes of deducing which mesh properties produce the best results from the solver. The techniques described herein permit a more detailed exploration of what constitutes a quality mesh in the context of a given solver and a desired flow regime. In the present work, these newly developed tools are used to investigate mesh quality as it pertains to a high-order accurate discontinuous Galerkin solver when it is used to compute inviscid and high-Reynolds number flows in domains possessing smoothly curving boundaries. For this purpose, two flow models have been generated and used to conduct parametric studies of mesh configurations involving curved elements. The results of these studies allow us to make some observations regarding mesh quality when the discontinuous Galerkin method is used to solve these types of problems. Briefly, we have found that for inviscid problems, the mesh elements used to resolve curved boundaries should be at least third order accurate. For viscous problems, the domain boundaries must be approximated by mesh elements that are of the same order as the polynomial approximation of the solution if the theoretical order of accuracy of the scheme is to be maintained. Increasing the accuracy of the boundary elements to at least one order higher than the solution approximation typically results in a noticeable improvement in the computed error norms. It is also noted that C1-continuity of the mesh is not required at element interfaces along the boundary.

Técnicas para geração de malhas volumétricas não estruturadas podem ser divididas em três categorias principais: técnicas baseadas em Octree, técnica de avanço de fronteira e técnicas Delaunay. Este trabalho faz uso de uma proposta para geração de malhas volumétricas não estruturadas baseada em uma técnica que utiliza uma triangulação adaptativa que contém similaridades com os métodos de geração de malhas baseados em Octree. Esta triangulação, além de decompor o domínio, oferece suporte para a construção de funções implícitas que aproximam a superfície do objeto de interesse. As funções implícitas são obtidas a partir de nuvens de pontos pelo método de Partição da Unidade Implícita - PUI. Um processo de poligonalização discretiza a isosuperfície fornecida pela função implícita gerando uma malha de triângulos superficial. Uma malha volumétrica é gerada a partir da malha superficial utilizando os tetraedros que decompõem o domínio criados pela triangulação. Apresentamos nesta tese um método original para a poligonalização de isosuperfícies obtidas através de nuvens de pontos. Apresentamos também uma abordagem para o melhoramento de malhas volumétricas baseadas na aplicação do conceito de molas virtuais. O foco principal é gerar malhas de qualidade para serem usadas em simulações de fluidos em artérias do corpo humano / Techniques for generation of three-dimensional unstructured meshes can be divided into three main categories: Octree-based techniques, advancing front techniques and Delaunay techniques. In the present study it is used a three-dimensional unstructured mesh generation approach based on a technique which uses an adaptive triangulation which contains similarities with Octree-based mesh generation techniques. This triangulation decomposes the domain and supports the construction of implicit functions that approximates the surface of an object of interest. The implicit functions are derived from point clouds by the Partition of Unity Implicits - PUI method. A polygonization process discretizes the isosurface provided by the implicit function generating a triangular mesh surface. A three-dimensional mesh is generated from the surface mesh using the tetrahedra that decomposes the domain created by the triangulation. In this tesis, we present an original polygonization method of isosurfaces obtained from point clouds. We also present an approach to improve tetrahedral meshes based on the application of the concept of virtual springs. The main focus is to generate quality meshes for fluid flow simulations in human arteries

Subject of this paper is triangulation of given domain also called as mesh generation. Overview of main mesh types (structured, unstructured and hybrid) is given. Groups of triangulation methods are defined and include collective triangulation, incremental triangulation, pliant mesh generation with post-triangulation and plaint mesh generation with retriangulation. Delaunay triangulation is described in greater detail and variuos Delaunay triangulation algorithms are presented including use of Delaunay triangulation for anisotropic mesh generation and method to generate Constrained Delaunay triangulation. Greedy insertion Delaunay and data dependent allgorithms are developed for hight fields surface aproximation. Significant improvements are made to these algorithms including faster recalculation, node selection and use of supplementary data sets in order to maximise efficiency of calculations. Main criteria to evaluate developed algorithms is overall error of approximation and speed of calculation. Data dependent algorithm generates better quality mesh (less approximation error), however Delaunay triangulation algorithm is significantly faster. Results and conclusions are presented at the end of paper.

The problem of selecting the connectivity of a triangulation in order to minimize a given cost function is studied. This problem is of great importance for applications, such as generating triangle mesh models of images and other bivariate functions. In early work, a well-known method named the local optimization procedure (LOP) was proposed by Lawson for solving the triangulation optimization problem. More recently, Yu et al. proposed a variant of the LOP called the LOP with lookahead (LLOP), which has proven to be more effective than the LOP. Unfortunately, each of the LOP and LLOP can only guarantee to yield triangulations that satisfy a weak optimality condition for most cost functions. That is, the triangulation optimized by the LOP or LLOP is only guaranteed to be such that no single edge flip can reduce the triangulation cost. In this thesis, a new optimality criterion named n-flip optimality is proposed, which has proven to be a useful tool for analyzing the optimality property. We propose a more general framework called the modified LOP (MLOP), with several free parameters, that can be used to solve the triangulation-cost optimization problem. By carefully selecting the free parameters, two MLOP-based methods called the MLOPB(L,M) and MLOPC(L) are derived from this framework. According to the optimality property introduced in the thesis, we have proven our proposed methods can satisfy a stronger optimality condition than the LOP and LLOP. That is, the triangulation produced by our MLOP-based methods cannot have their cost reduced by any single edge flip or any two edge flips. Due to satisfying this stronger optimality condition, our proposed methods tend to yield triangulations of significantly lower cost than the LOP and LLOP methods. In order to evaluate the performance of our MLOP-based methods, they are compared with two other competing approaches, namely the LOP and LLOP. Experimental results show that the MLOPB and MLOPC methods consistently yield triangulations of much lower cost than the LOP and LLOP. More specifically, our MLOPB and MLOPC methods yield triangulations with an overall median cost reduction of 16.36% and 16.62%, respectively, relative to the LOP, while the LLOP can only yield triangulations with an overall median cost reduction of 11.49% relative to the LOP. Moreover, our proposed methods MLOPB(2,i) and MLOPA(i) are shown to produce even better results if the parameter i is increased at the expense of increased computation time. / Graduate

In this thesis a methodology is presented to optimise non–linear mathematical models in numerical engineering applications. The method is based on biological evolution and uses known concepts of genetic algorithms and evolutionary compu- tation. The working principle is explained in detail, the implementation is outlined and alternative approaches are mentioned. The optimisation is then tested on a series of benchmark cases to prove its validity. It is then applied to two different types of problems in computational engineering. The first application is the mathematical modeling of turbulence. An overview of existing turbulence models is followed by a series of tests of different models applied to various types of flows. In this thesis the optimisation method is used to find improved coefficient values for the k–ε, the k–ω-SST and the Spalart–Allmaras models. In a second application optimisation is used to improve the quality of a computational mesh automatically generated by a third party software tool. This generation can be controlled by a set of parameters, which are subject to the optimisation. The results obtained in this work show an improvement when compared to non–optimised results. While computationally expensive, the genetic optimisation method can still be used in engineering applications to tune predefined settings with the aim to produce results of higher quality. The implementation is modular and allows for further extensions and modifications for future applications.

Técnicas para geração de malhas volumétricas não estruturadas podem ser divididas em três categorias principais: técnicas baseadas em Octree, técnica de avanço de fronteira e técnicas Delaunay. Este trabalho faz uso de uma proposta para geração de malhas volumétricas não estruturadas baseada em uma técnica que utiliza uma triangulação adaptativa que contém similaridades com os métodos de geração de malhas baseados em Octree. Esta triangulação, além de decompor o domínio, oferece suporte para a construção de funções implícitas que aproximam a superfície do objeto de interesse. As funções implícitas são obtidas a partir de nuvens de pontos pelo método de Partição da Unidade Implícita - PUI. Um processo de poligonalização discretiza a isosuperfície fornecida pela função implícita gerando uma malha de triângulos superficial. Uma malha volumétrica é gerada a partir da malha superficial utilizando os tetraedros que decompõem o domínio criados pela triangulação. Apresentamos nesta tese um método original para a poligonalização de isosuperfícies obtidas através de nuvens de pontos. Apresentamos também uma abordagem para o melhoramento de malhas volumétricas baseadas na aplicação do conceito de molas virtuais. O foco principal é gerar malhas de qualidade para serem usadas em simulações de fluidos em artérias do corpo humano / Techniques for generation of three-dimensional unstructured meshes can be divided into three main categories: Octree-based techniques, advancing front techniques and Delaunay techniques. In the present study it is used a three-dimensional unstructured mesh generation approach based on a technique which uses an adaptive triangulation which contains similarities with Octree-based mesh generation techniques. This triangulation decomposes the domain and supports the construction of implicit functions that approximates the surface of an object of interest. The implicit functions are derived from point clouds by the Partition of Unity Implicits - PUI method. A polygonization process discretizes the isosurface provided by the implicit function generating a triangular mesh surface. A three-dimensional mesh is generated from the surface mesh using the tetrahedra that decomposes the domain created by the triangulation. In this tesis, we present an original polygonization method of isosurfaces obtained from point clouds. We also present an approach to improve tetrahedral meshes based on the application of the concept of virtual springs. The main focus is to generate quality meshes for fluid flow simulations in human arteries