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Dapogny, Charles. "Shape optimization, level set methods on unstructured meshes and mesh evolution." Paris 6, 2013. http://www.theses.fr/2013PA066498.
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L’objectif principal de cette thèse est de concevoir une méthode d’optimisation de structures qui jouitd’une description exacte (i. E. Au moyen d’un maillage) de la forme à chaque itération du processus, touten bénéficiant des avantages de la méthode des lignes de niveaux lorsqu’il s’agit de suivre leur évolution. Indépendamment, on étudie également deux problèmes de modélisation en optimisation structurale. Dans une première partie bibliographique, on présente quelques notions classiques, ainsi qu’un état del’art sommaire autour des trois thématiques principales de la thèse - méthode des lignes de niveaux (Chapitre1), optimisation de formes (Chapitre 2) et maillage (Chapitre 3). La seconde partie de ce manuscrit traite de deux questions en optimisation de formes, celle de la répartitionoptimale de plusieurs matériaux au sein d’une structure donnée (Chapitre 4), et celle de l’optimisation robustede fonctions dépendant du domaine lorsque des perturbations s’exercent sur le modèle (Chapitre 5). Dans une troisième partie, on étudie laconception de schémas numériques en lien avec la méthode deslignes de niveaux lorsque le maillage de calcul est simplicial (et potentiellement adapté). Le calcul de ladistance signée à un domaine est étudié dans le chapitre 6, et la résolution de l’équation de transport d’unefonction ‘level set’ est détaillée dans le chapitre 7. La quatrième partie (Chapitre 8) traite des aspects de la thèse liés à la modification locale de maillagessurfaciques et volumiques. Enfin, la dernière partie (Chapitre 9) détaille la stratégie conçue pour l’évolution de maillage en optimisation de formes, à partir des ingrédients des chapitres 6, 7 et 8The main purpose of this thesis is to propose a method for structural optimization which combines theaccuracy of featuring an exact description of shapes (i. E. With a mesh) at each iteration of the process withthe versatility of the level set method for tracking their evolution. Independently, we also study two problemsrelated to modeling in structural optimization. In the first, bibliographical part, we present several classical notions, together with some recent developmentsabout the three main issues of this thesis - namely level set methods (Chapter 1), shape optimization(Chapter 2), and meshing (Chapter 3). The second part of this manuscript deals with two issues in shape optimization, that of the optimalrepartition of several materials within a fixed structure (Chapter 4), and that of the robust optimization offunctions depending on the domain when perturbations are expected over the considered mechanical model. In the third part, we study the design of numerical schemes for performing the level set method onsimplicial (and possibly adapted) computational meshes. The computation of the signed distance functionto a domain is investigated in Chapter 6, and the resolution of the level set advection equation is presentedin Chapter 7. The fourth part (Chapter 8) is devoted to the meshing techniques introduced in this thesis. Eventually, the last part (Chapter 9) describes the proposed strategy for mesh evolution in the contextof shape optimization, relying on the numerical ingredients introduced in Chapters 7, 8, 9
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Hindenlang, Florian [Verfasser]. "Mesh Curving Techniques for High Order Parallel Simulations on Unstructured Meshes / Florian Hindenlang." München : Verlag Dr. Hut, 2014. http://d-nb.info/1060587653/34.
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Harbrecht, Helmut, Ulf Kähler, and Reinhold Schneider. "Wavelet Galerkin BEM on unstructured meshes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601459.
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The present paper is devoted to the fast solution of boundary integral equations on unstructured meshes by the Galerkin scheme. On the given mesh we construct a wavelet basis providing vanishing moments with respect to the traces of polynomials in the space. With this basis at hand, the system matrix in wavelet coordinates can be compressed to $\mathcal{O}(N\log N)$ relevant matrix coefficients, where $N$ denotes the number of unknowns. The compressed system matrix can be computed within suboptimal complexity by using techniques from the fast multipole method or panel clustering. Numerical results prove that we succeeded in developing a fast wavelet Galerkin scheme for solving the considered class of problems.
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ROCHA, ALLAN CARLOS AVELINO. "ILLUSTRATIVE VOLUME VISUALIZATION FOR UNSTRUCTURED MESHES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2011. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=18748@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORTécnicas de visualização científica criam imagens na tentativa de revelar estruturas e fenômenos complexos. Técnicas ilustrativas têm sido incorporadas aos sistemas de visualizacão científica para melhorar a expressividade de tais imagens. A visualização de linhas caracteríticas é uma técnica importante para transmitir uma melhor informacão sobre a forma das superfícies. Neste trabalho, propomos combinar visualização volumétrica de malhas não estruturadas com isosuperfícies ilustradas. Isto é feito estendendo um algoritmo de traçado de raio em GPU para incorporar ilustração com linhas de variação extrema da iluminação(photic extremum lines), um tipo de linha característica que captura mudanças bruscas de luminância, revelando formas de um jeito perceptualmente correto.
Scientic visualization techniques create images attempting to reveal complex structures and phenomena. Illustrative techniques have been incorporated to scientic visualization systems in order to improve the expressiveness of such images. The rendering of feature lines is an important technique for better depicting surface shapes and features. In this thesis, we propose to combine volume visualization of unstructured meshes with illustrative isosurfaces. This is accomplished by extending a GPU-based ray-casting algorithm to incorporate illustration with photic extremum lines, a type of feature lines able to capture sudden changes of luminance, conveying shapes in a perceptually correct way.
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MIRANDA, FABIO MARKUS NUNES. "VOLUME RENDERING OF UNSTRUCTURED HEXAHEDRAL MESHES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2011. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=28921@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
Importantes aplicações de engenharia usam malhas não estruturadas de hexaedros para simulações numéricas. Células hexaédricas, comparadas com tetraedros, tendem a ser mais numericamente estáveis e requerem um menor refinamento da malha. Entretando, visualização volumétrica de malhas não estruturadas é um desafio devido a variação trilinear do campo escalar dentro da célula. A solução convencional consiste em subdividir cada hexaedro em cinco ou seis tetraedros, aproximando uma variação trilinear por uma inadequada série de funções lineares. Isso resulta em imagens inadequadas e aumenta o consumo de memória. Nesta tese, apresentamos um algoritmo preciso de visualização volumétrica utilizando ray-casting para malhas não estruturadas de hexaedros. Para capturar a variação trilinear ao longo do raio, nós propomos usar uma integração de quadratura. Nós também propomos uma alternativa rápida que melhor aproxima a variação trilinear, considerando os pontos de mínimo e máximo da função escalar ao longo do raio. Uma série de experimentos computacionais demonstram que nossa proposta produz resultados exatos, com um menor gasto de memória. Todo algoritmo é implementado em placas gráficas, garantindo uma performance competitiva.
Important engineering applications use unstructured hexahedral meshes for numerical simulations. Hexahedral cells, when compared to tetrahedral ones, tend to be more numerically stable and to require less mesh refinement. However, volume visualization of unstructured hexahedral meshes is challenging due to the trilinear variation of scalar fields inside the cells. The conventional solution consists in subdividing each hexahedral cell into five or six tetrahedra, approximating a trilinear variation by an inadequate piecewise linear function. This results in inaccurate images and increases the memory consumption. In this thesis, we present an accurate ray-casting volume rendering algorithm for unstructured hexahedral meshes. In order to capture the trilinear variation along the ray, we propose the use of quadrature integration. We also propose a fast approach that better approximates the trilinear variation to a series of linear ones, considering the points of minimum and maximum of the scalar function along the ray. A set of computational experiments demonstrates that our proposal produces accurate results, with reduced memory footprint. The entire algorithm is implemented on graphics cards, ensuring competitive performance.
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Burgess, David A. "Parallel computing for unstructured mesh algorithms." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318758.
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Perez, Sansalvador Julio. "Parallel unstructured mesh adaptation and applications." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/parallel-unstructured-mesh-adaptation-and-applications(26248d4d-48a6-4101-a687-004218e39cb4).html.
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In this thesis we develop 2D parallel unstructured mesh adaptation methods for the solution of partial differential equations (PDEs) by the finite element method (FEM). Additionally, we develop a novel block preconditioner for the iterative solution of the linear systems arising from the finite element discretisation of the Föppl-von Kàrmàn equations. Two of the problems arising in the numerical solution of PDEs by FEM are the memory constraints that limit the solution of large problems, and the inefficiency of solving the associated linear systems by direct or iterative solvers. We initially focus on mesh adaptation, which is a memory demanding task of the FEM. The size of the problem increases by adding more elements and nodes to the mesh during mesh refinement. In problems involving a large number of elements, the problem size is limited by the memory available on a single processor. In order to be able to work with large problems, we use a domain decomposition approach to distribute the problem over multiple processors. One of the main objectives of this thesis is the development of 2D parallel unstructured mesh adaptation methods for the solution of PDEs by the FEM in a variety of problems; including domains with curved boundaries, holes and internal boundaries. Our newly developed methods are implemented in the software library oomph-lib, an open-source object oriented multi-physics software library implementing the FEM. We validate and demonstrate their utility in a set of increasingly complex problems ranging from scalar PDEs to fully coupled multi-physics problems. Having implemented and validated the infrastructure which facilitates the finite-element-based discretisation of PDEs in a distributed environment, we shift our focus to the second problem concerning this thesis and one of the major challenges in the computational solution of PDEs: the solution of the large linear systems arising from their discretisation. For sufficiently large problems, the solution of their associated linear system by direct solvers becomes impossible or inefficient, typically because of memory and time constraints. We therefore focus on preconditioned Krylov subspace methods whose efficiency depends crucially on the provision of a good preconditioner. These preconditioners are invariably problem dependent. We illustrate their application and development in the solution of two elasticity problems which give rise to relatively large problems. First we consider the solution of a linear elasticity problem and compute the stress distribution near a crack tip where strong local mesh refinement is required. We then consider the deformation of thin plates which are described by the nonlinear Föppl-von Kàrmàn equations. A key contribution of this work is the development of a novel block preconditioner for the iterative solution of these equations, we present the development of the preconditioner and demonstrate its practical performance.
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Hindenlang, Florian [Verfasser], and Claus-Dieter [Akademischer Betreuer] Munz. "Mesh curving techniques for high order parallel simulations on unstructured meshes / Florian Hindenlang. Betreuer: Claus-Dieter Munz." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2014. http://d-nb.info/1063938082/34.
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Bushrod, Rebecca. "Unstructured mesh generation for mesh improvement techniques and contour meshing." Thesis, Swansea University, 2005. https://cronfa.swan.ac.uk/Record/cronfa42434.
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This thesis will investigate surface mesh generation and develop ideas to improve the quality of surface meshes that are currently produced. Surface geometries are represented by a CAD definition, but the CAD definition does not necessarily guarantee that the surface geometry is acceptable for mesh generation. CAD geometries will often contain a number of detailed features which will need to be improved by processes such as CAD repair before mesh generation can take place. Even then the geometries can still contain problems in the features such as, small sliver surface patches and sliver edges. These features cause major difficulties when meshed, as they generate small distorted elements. Here we will look to improve the meshes by merging together neighboring surface patches to create a super patch and then generate the mesh on this one surface. The merging of surfaces is controlled by the angle between surface patches. Another method that will be investigated involves the re-meshing of the geometry based on a prescribed metric. In addition to looking at this problem of CAD representation we will also look at the growing area of medical imaging. Here we will look to produce a 3D mesh from a set of contours. From this the mesh produced will be remeshed using the previous ideas to produce a mesh that can be used for analysis.
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Kumar, Amitesh. "Hole patching in 3D unstructured surface mesh." Birmingham, Ala. : University of Alabama at Birmingham, 2007. http://www.mhsl.uab.edu/dt/2007m/kumar.pdf.
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Bunt, Richard A. "Performance engineering unstructured mesh, geometric multigrid codes." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/89503/.
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High Performance Computing (HPC) is a vital tool for scientific simulations; it allows the recreation of conditions which are too expensive to produce in situ or over too vast a time scale. However, in order to achieve the increasing levels of performance demanded by these applications, the architecture of computers has shifted several times since the 1970s. The challenge of engineering applications to leverage the performance which comes with past and future shifts is an on-going challenge. This work focuses on solving this challenge for unstructured mesh, geometric multigrid applications through three existing performance engineering methodologies: instrumentation, performance modelling and mini-applications. First, an auto instrumentation tool is developed which enables the collection of performance data over several versions of a code base, with only a single definition of the data to collect. This information allows the comparison of prospective optimisations (e.g. reduced synchronisation), and an assessment of competing hardware (e.g. Intel Haswell/Ivybridge). Second, this work details the development and use of a runtime performance model of unstructured mesh, geometric multigrid behaviour. The power of the model is demonstrated by i) exposing a synchronisation issue which degrades total application runtime by 1.41x on machines which have poor support for overlapping communication with computation; and, ii) accurately predicting the negative impact of the geometric partitioning algorithm on executions using 512 partitions. Third, a mini-application is developed to provide a vehicle for optimising and porting activities, where it would be prohibitively time consuming to use a large, legacy application. The use of the mini-application is demonstrated by examining the impact of Intel Haswell's fused multiply and advanced vector extension instructions on performance. It is found that significant code modifications would be required to benefit from these instructions, but the architecture shows promise from an energy perspective.
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Zhang, Zhao. "Unstructured mesh methods for stratified turbulent flows." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/16617.
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Developments are reported of unstructured-mesh methods for simulating stratified, turbulent and shear flows. The numerical model employs nonoscillatory forward in-time integrators for anelastic and incompressible flow PDEs, built on Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and a preconditioned conjugate residual elliptic solver. Finite-volume spatial discretisation adopts an edge-based data structure. Tetrahedral-based and hybrid-based median-dual options for unstructured meshes are developed, enabling flexible spatial resolution. Viscous laminar and detached eddy simulation (DES) flow solvers are developed based on the edge-based NFT MPDATA scheme. The built-in implicit large eddy simulation (ILES) capability of the NFT scheme is also employed and extended to fully unstructured tetrahedral and hybrid meshes. Challenging atmospheric and engineering problems are solved numerically to validate the model and to demonstrate its applications. The numerical problems include simulations of stratified, turbulent and shear flows past obstacles involving complex gravity-wave phenomena in the lee, critical-level laminar-turbulence transitioning and various vortex structures in the wake. Qualitative flow patterns and quantitative data analysis are both presented in the current study.
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Hong, Sung Min. "Shape Modeling of Plant Leaves with Unstructured Meshes." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1182.
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The plant leaf is one of the most challenging natural objects to be realistically depicted by computer graphics due to its complex morphological and optical characteristics. Although many studies have been done on plant modeling, previous research on leaf modeling required for close-up realistic plant images is very rare. In this thesis, a novel method for modeling of the leaf shape based on the leaf venation is presented. As the first step of the method, the leaf domain is defined by the enclosure of the leaf boundary. Second, the leaf venation is interactively modeled as a hierarchical skeleton based on the actual leaf image. Third, the leaf domain is triangulated with the skeleton as constraints. The skeleton is articulated with nodes on the skeleton. Fourth, the skeleton is interactively transformed to a specific shape. A user can manipulate the skeleton using two methods which are complementary to each other: one controls individual joints on the skeleton while the other controls the skeleton through an intermediate spline curve. Finally, the leaf blade shape is deformed to conform to the skeleton by interpolation. An interactive modeler was developed to help a user to model a leaf shape interactively and several leaves were modeled by the interactive modeler. The ray-traced rendering images demonstrate that the proposed method is effective in the leaf shape modeling.
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FRANCESCHIN, BERNARDO BIANCHI. "VISUALIZATION OF ARBITRARY CROSS SECTION OF UNSTRUCTURED MESHES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=23874@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
PROGRAMA DE EXCELENCIA ACADEMICA
Na visualização de campos escalares de dados volumétricos, o uso de seções de corte é uma técnica eficaz para se inspecionar a variação do campo no interior do domínio. A técnica de visualização consiste em mapear sobre a superfície da seção de corte um mapa de cores, o qual representa a variação do campo escalar na interseção da superfície com o volume. Este trabalho propõe um método eficiente para o mapeamento de campos escalares de malhas não estruturadas em seções de corte arbitrárias. Trata-se de um método de renderização direta (a interseção da superfície com o modelo não é extraída) que usa a GPU para garantir bom desempenho. A idéia básica do método proposto é utilizar o rasterizador da placa gráfica para gerar os fragmentos da superfície de corte e calcular a interseção de cada fragmento com o modelo em GPU. Para isso, é necessário testar a localização de cada fragmento na malha não estruturada de maneira eficiente. Como estrutura de aceleração, foram testadas três variações de grades regulares para armazenar os elementos (células) da malha, e cada elemento é representado pela lista de planos de suas faces, facilitando o teste de pertinência fragmento-elemento. Uma vez determinado o elemento que contém o fragmento, são aplicados procedimentos para interpolar o campo escalar e para identificar se o fragmento está próximo à fronteira do elemento, a fim de representar o aramado (wireframe) da malha na superfície de corte. Resultados obtidos demonstram a eficácia e a eficiência do método proposto.
For the visualization of scalar fields in volume data, the use of cross sections is an effective technique to inspect the field variation inside the domain. The technique consists in mapping, on the cross section surfaces, a colormap that represents the scalar field on the surfasse-volume intersection. In this work, we propose an efficient method for mapping scalar fields of unstructured meshes on arbitrary cross sections. It is a direct-rendering method (the intersection of the surface and the model is not extracted) that uses GPU to ensure efficiency. The basic idea is to use the graphics rasterizer to generate the fragments of the cross-section surface and to compute the intersection of each fragment with the model. For this, it is necessary to test the location of each fragment with respect to the unstructured mesh in an efficient way. As acceleration data structure, we tested three variations of regular grids to store the elements (cells) of the mesh, and each elemento is represented by the list of face planes, easing the in-out test between fragments and elements. Once the element that contains the fragment is determined, it is applied procedures to interpolate the scalar field and to check if the fragment is close to the element boundary, to reveal the mesh wireframe on the surface. Achieved results demonstrate the effectiveness and the efficiency of the proposed method.
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Davey, Robert A. "Decomposition of unstructured meshes for efficient parallel computation." Thesis, University of Edinburgh, 1997. http://hdl.handle.net/1842/13572.
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This thesis addresses issues relating to the use of parallel high performance computer architectures for unstructured mesh calculations. The finite element and finite volume methods are typical examples of such calculations which arise in a wide range of scientific and engineering applications. The work in this thesis is focused on the development at Edinburgh Parallel Computing Centre of a software library to support static mesh decomposition, known as PUL-md. The library provides a variety of mesh decomposition and graph partitioning algorithms, including both global methods and local refinement techniques. The library implements simple random, cyclic and lexico-graphic partitioning, Farhat's greedy algorithm, recursive layered, coordinate, inertial and spectral bisections, together with subsequent refinement by either the Kernighan and Lin algorithm or by one of two variants of the Mob algorithm. The decomposition library is closely associated with another library, PUL-sm, which provides run-time support for unstructured mesh calculations. The decomposition of unstructured meshes is related to the partitioning of undirected graphs. We present an exhaustive survey of algorithms for these related tasks. Implementation of the decomposition algorithms provided by PUL-md is discussed, and the tunable parameters that optimise the algorithm's behaviour are detailed. On the basis of various metrics of decomposition quality, we evaluate the relative merits of the algorithms and explore the tunable parameter space. To validate these metrics, and further demonstrate the utility of the library, we examine how the runtime of a demonstration application (a finite element code) depends on decomposition quality. Additional related work is presented, including research into the development of a novel 'seed-based' optimisation approach to graph partitioning. In this context gradient descent, simulated annealing and parallel genetic algorithms are explored.
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Wilson, Cian. "Modelling multiple-material flows on adaptive unstructured meshes." Thesis, Imperial College London, 2009. http://hdl.handle.net/10044/1/5526.
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The ability to distinguish between regions with different material properties is essential when numerically modelling many physical systems. Using a dual control volume mesh that avoids the problem of corner coupling, the HyperC face value scheme is extended to multiple dimensions and applied as a device for material advection on unstructured simplex meshes. The new scheme performs well at maintaining sharp interfaces between materials and is shown to produce small advection errors, comparable to those of standard material advection methods on structured meshes. To further minimise numerical diffusion of material interfaces a total variation bounded flux limiter, UltraC, is defined using a normalised variable diagram. Combining the material tracking scheme with dynamically adapting meshes, the use of a minimally dissipative bounded projection algorithm for interpolating fields from the old mesh to the new, optimised mesh is demonstrated that conserves the mass of each material. More generally, material conservation during the advection process is ensured through the coupling of the material tracking scheme to the momentum and mass equations. A new element pair for the discretisation of velocity and pressure is proposed that maintains the stability of the system while conserving the mass of materials. When modelling multiple materials the use of independent advection algorithms for each material can lead to the problem of non-physical material overlap. A novel coupled flux limiter is developed to overcome this problem. This automatically generalises to arbitrary numbers of materials. Using the fully coupled (and rigorously verified) multi-material model, several geophysically relevant simulations are presented examining the generation of waves by landslides. The model is validated by demonstrating close agreement between model predictions and experimental results of wave generation, propagation and run-up. The simulations also showcase the powerful capabilities of an unstructured, adaptive multi-material model in real world scenarios.
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Gorman, Gerard John. "Parallel anisotropic unstructured mesh optimisation and its applications." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.430146.
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Manickam, Pradeep. "Unstructured mesh based models for incompressible turbulent flows." Thesis, Loughborough University, 2013. https://dspace.lboro.ac.uk/2134/14126.
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A development of high resolution NFT model for simulation of incompressible flows is presented. The model uses finite volume spatial discretisation with edge based data structure and operates on unstructured meshes with arbitrary shaped cells. The key features of the model include non-oscillatory advection scheme Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and non-symmetric Krylov-subspace elliptic solver. The NFT MPDATA model integrates the Reynolds Average Navier Stokes (RANS) equations. The implementation of the Spalart-Allmaras one equations turbulence model extends the development further to turbulent flows. An efficient non-staggered mesh arrangement for pressure and velocity is employed and provides smooth solutions without a need of artificial dissipation. In contrast to commonly used schemes, a collocated arrangement for flow variables is possible as the stabilisation of the NFT MPDATA scheme arises naturally from the design of MPDATA. Other benefits of MPDATA include: second order accuracy, strict sign-preserving and full multidimensionality. The flexibility and robustness of the new approach is studied and validated for laminar and turbulent flows. Theoretical developments are supported by numerical testing. Successful quantitative and qualitative comparisons with the numerical and experimental results available from literature confirm the validity and accuracy of the NFT MPDATA scheme and open the avenue for its exploitation for engineering problems with complex geometries requiring flexible representation using unstructured meshes.
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Bouvattier, Marc-Antoine. "Unstructured mesh adaptation for turbo-machinery RANS computation." Thesis, KTH, Flygdynamik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-211161.
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This paper gives an overview of the mathematical and practical tools that can be used in turbo-machinery RANS simulation to realize unstructured mesh adaptation. It first presents the concept of metric and recalls that the hessian of the physical flow properties can become, thanks to small modifications, both a metric and a upper bound of the P1 projection error. The resulting metric is then studied on a simple 2D case. In a second part, the industrial application of this concept is addressed and the tools used to overcome the turbo-machinery specificities are explained. Finally, some 2D and 3D results are presented.
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Sharbatdar, Mahkame. "Error estimation and mesh adaptation paradigm for unstructured mesh finite volume methods." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/60359.
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Error quantification for industrial CFD requires a new paradigm in which a robust flow solver with error quantification capabilities reliably produces solutions with known error bounds. Error quantification hinges on the ability to accurately estimate and efficiently exploit the local truncation error. The goal of this thesis is to develop a reliable truncation error estimator for finite-volume schemes and to use this truncation error estimate to improve flow solutions through defect correction, to correct the output functional, and to adapt the mesh. We use a higher-order flux integral based on lower order solution as an estimation of the truncation error which includes the leading term in the truncation error. Our results show that using this original truncation error estimate is dominated by rough modes and fails to provide the desired convergence for the applications of defect correction, output error estimation and mesh adaptation. So, we tried to obtain an estimate of the truncation error based on the continuous interpolated solution to improve their performance. Two different methods for interpolating were proposed: CGM's 3D surfaces and C¹ interpolation of the solution. We compared the effectiveness of these two interpolating schemes for defect correction and using C¹ interpolation of the solution for interpolating is more helpful compared to CGM, so we continued using C¹ interpolation for other purposes. For defect correction, although using the modified truncation error does not improve the order of accuracy, significant quantitative improvements are obtained. Output functional correction is based on the truncation error and the adjoint solution. Both discrete and continuous adjoint solutions can be used for functional correction. Our results for a variety of governing equations suggest that the interpolating scheme can improve the correction process significantly and improve accuracy asymptotically. Different adaptation indicators were considered for mesh adaptation and our results show that the estimate of the truncation error based on the interpolated solution is a more accurate indicator compared to the original truncation error. Adjoint-based mesh adaptation combined with modified truncation error provides even faster convergence of the output functional.Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
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Jofre, Cruanyes Lluís. "Numerical simulation of multiphase immiscible flow on unstructured meshes." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/277545.
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The present thesis aims at developing a basis for the numerical simulation of multiphase flows of immiscible fluids. This approach, although limited by the computational power of the present computers, is potentially very important, since most of the physical phenomena of these flows often happen on space and time scales where experimental techniques are impossible to be utilized in practice. In particular, this research is focused on developing numerical discretizations suitable for three-dimensional (3-D) unstructured meshes.
In detail, the first chapter delimits the considered multiphase flows to the case in which the components are immiscible fluids. In particular, the focus is placed on those cases where two or more continuous streams of different fluids are separated by interfaces, and hence, correspondingly named separated flows. Additionally, once the type of flow is determined, the chapter introduces the physical characteristics and the models available to predict its behavior, as well as the mathematical formulation that sustains the numerical techniques developed within this thesis.
The second chapter introduces and analyzes a new geometrical Volume-of-Fluid (VOF) method for capturing interfaces on 3-D Cartesian and unstructured meshes. The method reconstructs interfaces as first- and second-order piecewise planar approximations (PLIC), and advects volumes in a single unsplit Lagrangian-Eulerian (LE) geometrical algorithm based on constructing flux polyhedrons by tracing back the Lagrangian trajectories of the cell-vertex velocities. In this way, the situations of overlapping between flux polyhedrons are minimized.
Complementing the previous chapter, the third one proposes a parallelization strategy for the VOF method. The main obstacle is that the computing costs are concentrated in the interface between fluids. Consequently, if the interface is not homogeneously distributed, standard domain decomposition (DD) strategies lead to imbalanced workload distributions. Hence, the new strategy is based on a load balancing process complementary to the underlying domain decomposition. Its parallel efficiency has been analyzed using up to 1024 CPU-cores, and the results obtained show a gain with respect to the standard DD strategy up to 12x, depending on the size of the interface and the initial distribution.
The fourth chapter describes the discretization of the single-phase Navier-Stokes equations to later extend it to the case of multiphase immiscible flow. One of the most important characteristics of the discretization schemes, aside from accuracy, is their capacity to discretely conserve kinetic energy, specially when solving turbulent flow. Hence, this chapter analyzes the accuracy and conservation properties of two particular collocated and staggered mesh schemes.
The extension of the numerical schemes suitable for the single-phase Navier-Stokes equations to the case of multiphase immiscible flow is developed in the fifth chapter. Particularly, while the numerical techniques for the simulation of turbulent flow have evolved to discretely preserve mass, momentum and, specially, kinetic energy, the mesh schemes for the discretization of multiphase immiscible flow have evolved to improve their stability and robustness. Therefore, this chapter presents and analyzes two particular collocated and staggered mesh discretizations, able to simulate multiphase immiscible flow, which favor the discrete conservation of mass, momentum and kinetic energy.
Finally, the sixth chapter numerically simulates the Richtmyer-Meshkov (RM) instability of two incompressible immiscible liquids.
This chapter is a general assessment of the numerical methods developed along this thesis. In particular, the instability has been simulated by means of a VOF method and a staggered mesh scheme. The corresponding numerical results have shown the capacity of the discrete system to obtain accurate results for the RM instability.Aquesta tesi té com a objectiu desenvolupar una base per a la simulació numèrica de fluids multi-fase immiscibles. Aquesta estratègia, encara que limitada per la potència computacional dels computadors actuals, és potencialment molt important, ja que la majoria de la fenomenologia d'aquests fluids sovint passa en escales temporals i especials on les tècniques experimentals no poden ser utilitzades. En particular, aquest treball es centra en desenvolupar discretitzacions numèriques aptes per a malles no-estructurades en tres dimensions (3-D). En detall, el primer capítol delimita els casos multifásics considerats al cas en que els components són fluids immiscibles. En particular, la tesi es centra en aquells casos en que dos o més fluids diferents són separats per interfases, i per tant, corresponentment anomenats fluxos separats. A més a més, un cop el tipus de flux es determinat, el capítol introdueix les característiques físiques i els models disponibles per predir el seu comportament, així com també la formulació matemàtica i les tècniques numèriques desenvolupades en aquesta tesi. El segon capítol introdueix i analitza un nou mètode "Volume-of-Fluid" (VOF) apte per a capturar interfases en malles Cartesianes i no-estructurades 3-D. El mètode reconstrueix les interfases com aproximacions "piecewise planar approximations" (PLIC) de primer i segon ordre, i advecciona els volums amb un algoritme geomètric "unsplit Lagrangian-Eulerian" (LE) basat en construïr els poliedres a partir de les velocitats dels vèrtexs de les celdes. D'aquesta manera, les situacions de sobre-solapament entre poliedres són minimitzades. Complementant el capítol anterior, el tercer proposa una estratègia de paral·lelització pel mètode VOF. L'obstacle principal és que els costos computacionals estan concentrats en les celdes de l'interfase entre fluids. En conseqüència, si la interfase no està ben distribuïda, les estratègies de "domain decomposition" (DD) resulten en distribucions de càrrega desequilibrades. Per tant, la nova estratègia està basada en un procés de balanceig de càrrega complementària a la DD. La seva eficiència en paral·lel ha sigut analitzada utilitzant fins a 1024 CPU-cores, i els resultats obtinguts mostren uns guanys respecte l'estratègia DD de fins a 12x, depenent del tamany de la interfase i de la distribució inicial. El quart capítol descriu la discretització de les equacions de Navier-Stokes per a una sola fase, per després estendre-ho al cas multi-fase. Una de les característiques més importants dels esquemes de discretització, a part de la precisió, és la seva capacitat per conservar discretament l'energia cinètica, específicament en el cas de fluxos turbulents. Per tant, aquest capítol analitza la precisió i propietats de conservació de dos esquemes de malla diferents: "collocated" i "staggered". L'extensió dels esquemes de malla aptes per els casos de una sola fase als casos multi-fase es desenvolupa en el cinquè capítol. En particular, així com en el cas de la simulació de la turbulència les tècniques numèriques han evolucionat per a preservar discretament massa, moment i energia cinètica, els esquemes de malla per a la discretització de fluxos multi-fase han evolucionat per millorar la seva estabilitat i robustesa. Per lo tant, aquest capítol presenta i analitza dos discretitzacions de malla "collocated" i "staggered" particulars, aptes per simular fluxos multi-fase, que afavoreixen la conservació discreta de massa, moment i energia cinètica. Finalment, el capítol sis simula numèricament la inestabilitat de Richtmyer-Meshkov (RM) de dos fluids immiscibles i incompressibles. Aquest capítol es una prova general dels mètodes numèrics desenvolupats al llarg de la tesi. En particular, la inestabilitat ha sigut simulada mitjançant un mètode VOF i un esquema de malla "staggered". Els resultats numèrics corresponents han demostrat la capacitat del sistema discret en obtenir bons resultats per la inestabilitat RM.
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Vilmin, Stéphane. "Turbulence modeling on unstructured meshes for 3D turbomachinery CFD /." Lausanne : EPFL, 1998. http://library.epfl.ch/theses/?nr=1864.
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Borrell, Pol Ricard. "Parallel algorithms for computational fluid dynamics on unstructured meshes." Doctoral thesis, Universitat Politècnica de Catalunya, 2012. http://hdl.handle.net/10803/124702.
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La simulació numèrica directa (DNS) de fluxos complexes és actualment una utopia per la majoria d'aplicacions industrials ja que els requeriments computacionals son massa elevats. Donat un flux, la diferència entre els recursos computacionals necessaris i els disponibles és cobreix mitjançant la modelització/simplificació d'alguns termes de les equacions originals que regeixen el seu comportament. El creixement continuat dels recursos computacionals disponibles, principalment en forma de super-ordinadors, contribueix a reduir la part del flux que és necessari aproximar. De totes maneres, obtenir la eficiència esperada dels nous super-ordinadors no és una tasca senzilla i, per aquest motiu, part de la recerca en el camp de la Mecànica de Fluids Computacional es centra en aquest objectiu. En aquest sentit, algunes contribucions s'han presentat en el marc d'aquesta tesis.
El primer objectiu va ser el desenvolupament d'un codi de CFD de propòsit general i paral·lel, basat en la metodologia de volums finits en malles no estructurades, per resoldre problemes de multi-física. Aquest codi, anomenat TermoFluids (TF), té un disseny orientat a objectes i pensat per ser usat de forma altament eficient en els super-ordinadors actuals. Amb el temps, ha esdevingut pel grup una eina fonamental en projectes tant de recerca bàsica com d'interès industrial.
En el context d'aquesta tesis, el treball s'ha focalitzat en el desenvolupament de dos de les llibreries més bàsiques de TermoFluids: i) La Basics Objects Library (BOL), que es una plataforma de software sobre la qual estan programades la resta de llibreries del codi, i que conté els mètodes algebraics i geomètrics fonamentals per la implementació paral·lela dels algoritmes de discretització, ii) la Linear Solvers Library (LSL), que conté un gran nombre de mètodes per resoldre els sistemes d'equacions lineals derivats de les discretitzacions.
El primer capítol d'aquesta tesi conté les principals idees subjacents al disseny i la implementació de la BOL i la LSL, juntament amb alguns exemples i algunes aplicacions industrials. En els capítols posteriors hi ha una explicació detallada de solvers específics per algunes aplicacions concretes.
En el segon capítol, es presenta un solver paral·lel i directe per la resolució de l'equació de Poisson per casos en els quals una de les direccions del domini té condicions d'homogeneïtat. En la simulació de fluxos incompressibles, l'equació de Poisson es resol almenys una vegada en cada pas de temps, convertint-se en una de les parts més costoses i difícils de paral·lelitzar del codi. El mètode que proposem és una combinació d'una descomposició directa de Schur (DDS) i una diagonalització de Fourier. La darrera descompon el sistema original en un conjunt de sub-sistemes 2D independents que es resolen mitjançant l'algorisme DDS. Atès que no s'imposen restriccions a les direccions no periòdiques del domini, aquest mètode és aplicable a la resolució de problemes discretitzats mitjançat l'extrusió de malles 2D no estructurades. L'escalabilitat d'aquest mètode ha estat provada amb èxit amb un màxim de 8192 CPU per malles de fins a ~10⁹ volums de control.
En el darrer capitol capítol, es presenta un mètode de resolució per l'equació de Transport de Boltzmann (BTE). La estratègia emprada es basa en el mètode d'Ordenades Discretes i pot ser aplicat en discretitzacions no estructurades. El flux per a cada ordenada angular es resol amb un mètode de substitució equivalent a la resolució d'un sistema lineal triangular. La naturalesa seqüencial d'aquest procés fa de la paral·lelització de l'algoritme el principal repte. Diversos algorismes de substitució han estat analitzats, esdevenint una de les heurístiques proposades la millor opció en totes les situacions analitzades, amb excel·lents resultats. Els testos d'eficiència paral·lela s'han realitzat usant fins a 2560 CPU.Direct Numerical Simulation (DNS) of complex flows is currently an utopia for most of industrial applications because computational requirements are too high. For a given flow, the gap between the required and the available computing resources is covered by modeling/simplifying of some terms of the original equations. On the other hand, the continuous growth of the computing power of modern supercomputers contributes to reduce this gap, reducing hence the unresolved physics that need to be attempted with approximated models. This growth, widely relies on parallel computing technologies. However, getting the expected performance from new complex computing systems is becoming more and more difficult, and therefore part of the CFD research is focused on this goal. Regarding to it, some contributions are presented in this thesis. The first objective was to contribute to the development of a general purpose multi-physics CFD code. referred to as TermoFluids (TF). TF is programmed following the object oriented paradigm and designed to run in modern parallel computing systems. It is also intensively involved in many different projects ranging from basic research to industry applications. Besides, one of the strengths of TF is its good parallel performance demonstrated in several supercomputers. In the context of this thesis, the work was focused on the development of two of the most basic libraries that compose TF: I) the Basic Objects Library (BOL), which is a parallel unstructured CFD application programming interface, on the top of which the rest of libraries that compose TF are written, ii) the Linear Solvers Library (LSL) containing many different algorithms to solve the linear systems arising from the discretization of the equations. The first chapter of this thesis contains the main ideas underlying the design and the implementation of the BOL and LSL libraries, together with some examples and some industrial applications. A detailed description of some application-specific linear solvers included in the LSL is carried out in the following chapters. In the second chapter, a parallel direct Poisson solver restricted to problems with one uniform periodic direction is presented. The Poisson equation is solved, at least, once per time-step when modeling incompressible flows, becoming one of the most time consuming and difficult to parallelize parts of the code. The solver here proposed is a combination of a direct Schur-complement based decomposition (DSD) and a Fourier diagonalization. The latter decomposes the original system into a set of mutually independent 2D sub-systems which are solved by means of the DSD algorithm. Since no restrictions are imposed in the non-periodic directions, the overall algorithm is well-suited for solving problems discretized on extruded 2D unstructured meshes. The scalability of the solver has been successfully tested using up to 8192 CPU cores for meshes with up to 10 9 grid points. In the last chapter, a solver for the Boltzmann Transport Equation (BTE) is presented. It can be used to solve radiation phenomena interacting with flows. The solver is based on the Discrete Ordinates Method and can be applied to unstructured discretizations. The flux for each angular ordinate is swept across the computational grid, within a source iteration loop that accounts for the coupling between the different ordinates. The sequential nature of the sweep process makes the parallelization of the overall algorithm the most challenging aspect. Several parallel sweep algorithms, which represent different options of interleaving communications and calculations, are analyzed. One of the heuristics proposed consistently stands out as the best option in all the situations analyzed. With this algorithm, good scalability results have been achieved regarding both weak and strong speedup tests with up to 2560 CPUs.
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De, la Puente Josep. "Seismic Wave Simulation for Complex Rheologies on Unstructured Meshes." Diss., lmu, 2008. http://nbn-resolving.de/urn:nbn:de:bvb:19-80745.
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Theodoropoulos, Theodoros. "Prediction of three-dimensional engine flow on unstructured meshes." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/46575.
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Dawkins, Ian. "Development of practical evolution Galerkin algorithms on unstructured meshes." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390460.
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Willcox, Karen E. (Karen Elizabeth). "Aeroelastic computations in the time domain using unstructured meshes." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/11185.
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Shala, Mehmet. "Unstructured staggered mesh discretisation methods for computational fluid dynamics." Thesis, University of Greenwich, 2007. http://gala.gre.ac.uk/6297/.
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There are many branches of engineering science that require solution of fluid flow problems. Some of these examples are aerodynamics of aircraft and vehicles, hydrodynamics of ships, electrical and electronic engineering and many others. Some of these flows may involve complex geometrical shapes which are usually modelled using the unstructured mesh discretisation techniques. There are well established methods that are used in such simulations. The aim of this project is to investigate the staggered positioning of variables on an unstructured based context and hence compare it to well known methods such as the cell-centred approach. A two dimensional unstructured staggered mesh discretisation method for the solution of fluid flow and heat transfer problems has been developed. This method stores and solves the vector variables at the cell faces and other scalar variables are stored at the cell centres. The very well known pressure based scheme SIMPLE is employed for pressure and velocity coupling. Three different approaches on unstructured staggered meshes are proposed. The first method solves for normal velocity component and interpolates the tangential velocity component, the second method solves for normal and tangential velocity components whereas the third method also solves for normal and tangential velocity components but uses a different upwind scheme for convection. The discretisation on unstructured staggered mesh methods is validated for a variety of fluid flow and heat transfer problems and comparisons are made between unstructured staggered mesh methods, the cell-centred approach and benchmark solutions. The first and third unstructured staggered mesh methods are shown to perform well and give comparable results to benchmark solutions. The third unstructured staggered mesh method does not always work.
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Jones, Beryl Wyn. "Mapping unstructured mesh codes onto local memory parallel architectures." Thesis, University of Greenwich, 1994. http://gala.gre.ac.uk/6201/.
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Initial work on mapping CFD codes onto parallel systems focused upon software which employed structured meshes. Increasingly, many large scale CFD codes are being based upon unstructured meshes. One of the key problems when implementing such large scale unstructured problems on a distributed memory machine is the question of how to partition the underlying computational domain efficiently. It is important that all processors are kept busy for as large a proportion of the time as possible and that the amount, level and frequency of communication should be kept to a minimum. Proposed techniques for solving the mapping problem have separated out the solution into two distinct phases. The first phase is to partition the computational domain into cohesive sub-regions. The second phase consists of embedding these sub-regions onto the processors. However, it has been shown that performing these two operations in isolation can lead to poor mappings and much less optimal communication time. In this thesis we develop a technique which simultaneously takes account of the processor topology whilst identifying the cohesive sub-regions. Our approach is based on an unstructured mesh decomposition method that was originally developed by Sadayappan et al [SER90] for a hypercube. This technique forms a basis for a method which enables a decomposition to an arbitrary number of processors on a specified processor network topology. Whilst partitioning the mesh, the optimisation method takes into account the processor topology by minimising the total interprocessor communication. The problem with this technique is that it is not suitable for dealing with very large meshes since the calculations often require prodigious amounts of computing processing power.
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Smith, Cameron Walter. "Improving Scalability of Parallel Unstructured Mesh-Based Adaptive Workflows." Thesis, Rensselaer Polytechnic Institute, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10269567.
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High performance parallel adaptive simulations operating on leadership class systems are constructed from multiple pieces of software developed over many years. As increasingly complex systems are deployed new methods must be created to extract performance and scalability. This thesis addresses two key scalability limitations for unstructured mesh based simulations.
Attaining simulation performance at ever higher concurrency levels requires increased performance of transformations within each procedure, as well as the transfer of data between procedures.
Controlling the transformations requires distributing the work evenly across the processors while executing efficient data transfers requires local operations that avoid shared or contended resources. This thesis addresses these requirements through multi-criteria load balancing procedures and in-memory data transfer techniques.
Partition improvement methods defined in this work enable improved application strong scaling on over one million processors through careful control of the balancing requirements. Applied to a computational fluid dynamics simulation running on 524,288 processes with 1.2 billion elements these methods reduce the time of the dominant computational step by up to 28% versus the best existing methods.
The scalable data transfer requirement is addressed through an in-memory functional coupling that avoids the high cost of fileystem access. The methods developed are applied to two adaptive simulations in which the time required for information exchange is reduced by over an order of magnitude versus file based couplings. Three additional simulations for industrial applications are then provided that highlight an in-memory coupling and the automation of key simulation processes.
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Oyarzún, Altamirano Guillermo Andrés. "Heterogeneous parallel algorithms for computational fluid dynamics on unstructured meshes." Doctoral thesis, Universitat Politècnica de Catalunya, 2015. http://hdl.handle.net/10803/323892.
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Frontiers of computational fluid dynamics (CFD) are constantly expanding and eagerly demanding more computational resources. Currently, we are experiencing an rapid evolution in the high performance computing systems driven by power consumption constraints. New HPC nodes incorporate accelerators that are used as math co-processors for increasing the throughput and the FLOP per watt ratio. On the other hand, multi-core CPUs have turned into energy efficient system-on-chip architectures. By doing so, the main components of the node are fused and integrated into a single chip reducing the energy costs. Nowadays, several institutions and governments are investing in the research and development of different aspects of HPC that could lead to the next generations of supercomputers. This initiatives have entitled the problem as the exascale challenge. This goal can only be achieved by incorporating major changes in computer architecture, memory design and network interfaces. The CFD community faces an important challenge: keep the pace at the rapid changes in the HPC resources. The codes and formulations need to be re-design in other to exploit the different levels of parallelism and complex memory hierarchies of the new heterogeneous systems. The main characteristics demanded to the new CFD software are: memory awareness, extreme concurrency, modularity and portability.
This thesis is devoted to the study of a CFD algorithm re-factoring for the adoption of new technologies. Our application context is the solution of incompressible flows (DNS or LES) on unstructured meshes. The first approach was using GPUs for accelerating the Poisson solver, that is the most computational intensive part of our application. The positive results obtained in this first step motivated us to port the complete time integration phase of our application. This requires a major redesign of the code. We propose a portable implementation model for CFD applications. The main idea was substituting stencil data structures and kernels by algebraic storage formats and operators. By doing so, the algorithm was restructured into a minimal set of algebraic operations. The implementation strategy consisted in the creation of a low-level algebraic layer for computations on CPUs and GPUs, and a high-level user-friendly discretization layer for CPUs that is fully localized at the preprocessing stage where performance does not play an important role. As a result, at the time-integration phase the code relies only on three algebraic kernels: sparse-matrix-vector product (SpMV), linear combination of two vectors (AXPY) and dot product (DOT). Such a simple set of basic linear algebra operations naturally provides the desired portability to any computing architecture. Special attention was paid at the development of data structures compatibles with the stream processing model. A detailed performance analysis was studied in both sequential and parallel execution engaging up to 128 GPUs in a hybrid CPU/GPU supercomputer.
Moreover, we tested the portable implementation model of TermoFluids code in the Mont-Blanc mobile-based supercomputer.
The re-design of the kernels exploits a heterogeneous execution model using both computing devices CPU and GPU of the ARM-based nodes. The load balancing between the two computing devices exploits a tabu search strategy that tunes the workload distribution during the preprocessing stage. A comparison of the Mont-Blanc prototypes with high-end supercomputers in terms of the achieved net performance and energy consumption provided some guidelines of the behavior of CFD applications in ARM-based architectures. Finally, we present a memory aware auto-tuned Poisson solver for problems with one Fourier diagonalizable direction. This work was developed and tested in the BlueGene/Q Vesta supercomputer, and aims at demonstrating the relevance of vectorization and memory awareness for fully exploiting the modern energy efficient CPUs.Las fronteras de la dinámica de fluidos computacional (CFD) están en constante expansión y demandan más y más recursos computacionales. Actualmente, estamos experimentando una evolución en los sistemas de computación de alto rendimiento (HPC) impulsado por restricciones de consumo de energía. Los nuevos nodos HPC incorporan aceleradores que se utilizan como co-procesadores para incrementar el rendimiento y la relación FLOP por vatio. Por otro lado, CPUs multi-core se han convertido en arquitecturas system-on-chip. Hoy en día, varias instituciones y gobiernos están invirtiendo en la investigación y desarrollo de los diferentes aspectos de HPC que podrían llevar a las próximas generaciones de superordenadores. Estas iniciativas han titulado el problema como el "exascale challenge". Este objetivo sólo puede lograrse mediante la incorporación de cambios importantes en: la arquitectura de ordenador, diseño de la memoria y las interfaces de red. La comunidad de CFD se enfrenta a un reto importante: mantener el ritmo a los rápidos cambios en las infraestructuras de HPC. Los códigos y formulaciones necesitan ser rediseñados para explotar los diferentes niveles de paralelismo y complejas jerarquías de memoria de los nuevos sistemas heterogéneos. Las principales características exigidas al nuevo software CFD son: estructuras de datos, la concurrencia extrema, modularidad y portabilidad. Esta tesis está dedicada al estudio de un modelo de implementation CFD para la adopción de nuevas tecnologías. Nuestro contexto de aplicación es la solución de los flujos incompresibles (DNS o LES) en mallas no estructuradas. El primer enfoque se basó en utilizar GPUs para acelerar el solver de Poisson. Los resultados positivos obtenidos en este primer paso nos motivaron a la portabilidad completa de la fase de integración temporal de nuestra aplicación. Esto requiere un importante rediseño del código. Proponemos un modelo de implementacion portable para aplicaciones de CFD. La idea principal es sustituir las estructuras de datos de los stencils y kernels por formatos de almacenamiento algebraicos y operadores. La estrategia de implementación consistió en la creación de una capa algebraica de bajo nivel para los cálculos de CPU y GPU, y una capa de discretización fácil de usar de alto nivel para las CPU. Como resultado, la fase de integración temporal del código se basa sólo en tres funciones algebraicas: producto de una matriz dispersa con un vector (SPMV), combinación lineal de dos vectores (AXPY) y producto escalar (DOT). Además, se prestó especial atención en el desarrollo de estructuras de datos compatibles con el modelo stream processing. Un análisis detallado de rendimiento se ha estudiado tanto en ejecución secuencial y paralela utilizando hasta 128 GPUs en un superordenador híbrido CPU / GPU. Por otra parte, hemos probado el nuevo modelo de TermoFluids en el superordenador Mont-Blanc basado en tecnología móvil. El rediseño de las funciones explota un modelo de ejecución heterogénea utilizando tanto la CPU y la GPU de los nodos basados en arquitectura ARM. El equilibrio de carga entre las dos unidades de cálculo aprovecha una estrategia de búsqueda tabú que sintoniza la distribución de carga de trabajo durante la etapa de preprocesamiento. Una comparación de los prototipos Mont-Blanc con superordenadores de alta gama en términos de rendimiento y consumo de energía nos proporcionó algunas pautas del comportamiento de las aplicaciones CFD en arquitecturas basadas en ARM. Por último, se presenta una estructura de datos auto-sintonizada para el solver de Poisson en problemas con una dirección diagonalizable mediante una descomposicion de Fourier. Este trabajo fue desarrollado y probado en la superordenador BlueGene / Q Vesta, y tiene por objeto demostrar la relevancia de vectorización y las estructuras de datos para aprovechar plenamente las CPUs de los superodenadores modernos.
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Simmons, Daniel. "Hybrid methods for modelling advanced electromagnetic systems using unstructured meshes." Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/33230/.
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The aim of this project is the conception, implementation, and application of a simulation tool for the accurate modeling of electromagnetic fields within inhomogeneous materials with complex shapes and the propagation of the resulting fields in the surrounding environment. There are many methods that can be used to model the scattering of an electromagnetic field, however one of the most promising for hybridisation is the Boundary Element Method (BEM), which is a surface technique, and the Unstructured Transmission Line Modeling (UTLM) method, which is a volume technique. The former allows accurate description of the scatterer's boundary and the field's radiation characteristics, but cannot model scattering by materials characterized by a non-uniform refraction index. The latter, on the contrary, can model a very broad range of materials, but is less accurate, since it has to rely on approximate absorbing boundary conditions. A method resulting in the hybridisation of BEM and UTLM can be used to construct a tool that takes into account both the interaction with non-uniform tissue and propagation in its environment. The project aims to describe in detail the implementation of the novel method, and deploy it in a heterogeneous distributed computing environment.
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Asproulis, Panagiotis. "High resolution numerical predictions of hypersonic flows on unstructured meshes." Thesis, Imperial College London, 1994. http://hdl.handle.net/10044/1/8357.
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Rahmati, M. T. "Incompressible Navier-Stokes inverse design method based on unstructured meshes." Thesis, University College London (University of London), 2006. http://discovery.ucl.ac.uk/1445805/.
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Two inverse methods for turbomachinery blade design are developed. In these inverse design approaches blade shapes are computed for a specified design parameter such as mass-averaged tangential velocity or pressure loading distribution. These inverse methods directly define a geometry needed to obtain these prescribed target design parameters which are related to the performance of turbomachinery blades. The first method is based on the prescription of pressure loading on the blade while the second method is based on the prescription of mass-averaged tangential velocity on the blade. In both methods the blade thickness is also prescribed. These choices of target design prescription allow the designer to control the blade work distribution and the overall flow field effectively. It also prevents the generation of unrealistic blades as the designer directly control the blade thickness. Mesh movement algorithm is an integral part of the current inverse design method as once the blade surface is modified during the design iterations the corresponding unstructured mesh also has to be altered. The mesh movement algorithm is based on a linear tension spring analogy which is a very fast and robust mesh movement method. The capabilities of these design methodologies have been verified for inverse design of two dimensional turbomachinery blades. The flow analysis algorithm is an integral part of the current methodologies. It is based on the incompressible Navier-Stokes flow equations on unstructured meshes. The capability of the flow analysis algorithm is verified for three-dimensional external and internal incompressible flow solutions. Indeed the current method is applied for simulation of flow over marine propeller blades in open water. Also it is applied for the flow analysis of the stator and rotor blades of a low-speed axial turbine.
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Issman, Emmanuel. "Implicit solution strategies for compressible flow equations on unstructured meshes." Doctoral thesis, Universite Libre de Bruxelles, 1997. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212181.
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ESPINHA, RODRIGO DE SOUZA LIMA. "INTERACTIVE VOLUME VISUALIZATION OF UNSTRUCTURED MESHES USING PROGRAMMABLE GRAPHICS CARDS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2005. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=6586@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORA visualização volumétrica é uma importante técnica para a exploração de dados tridimensionais complexos, como, por exemplo, o resultado de análises numéricas usando o método dos elementos finitos. A aplicação eficiente dessa técnica a malhas não-estruturadas tem sido uma importante área de pesquisa nos últimos anos. Há dois métodos básicos para a visualização dos dados volumétricos: extração de superfícies e renderização direta de volumes. Na primeira, iso-superfícies de um campo escalar são extraídas explicitamente. Na segunda, que é a utilizada neste trabalho, dados escalares são classificados a partir de uma função de transferência, que mapeia valores do campo escalar em cor e opacidade, para serem visualizados. Com a evolução das placas gráficas (GPU) dos computadores pessoais, foram desenvolvidas novas técnicas para visualização volumétrica interativa de malhas não-estruturadas. Os novos algoritmos tiram proveito da aceleração e da possibilidade de programação dessas placas, cujo poder de processamento cresce a um ritmo superior ao dos processadores convencionais (CPU). Este trabalho avalia e compara dois algoritmos para visualização volumétrica de malhas não-estruturadas, baseados em GPU: projeção de células independente do observador e traçado de raios. Adicionalmente, são propostas duas adaptações dos algoritmos estudados. Para o algoritmo de projeção de células, propõe-se uma estruturação dos dados na GPU para eliminar o alto custo de transferência de dados para a placa gráfica. Para o algoritmo de traçado de raios, propõe-se fazer a integração da função de transferência na GPU, melhorando a qualidade da imagem final obtida e permitindo a alteração da função de transferência de maneira interativa.
Volume visualization is an important technique for the exploration of threedimensional complex data sets, such as the results of numerical analysis using the finite elements method. The efficient application of this technique to unstructured meshes has been an important area of research in the past few years. There are two basic methods to visualize volumetric data: surface extraction and direct volume rendering. In the first, the iso-surfaces of the scalar field are explicitly extracted. In the second, which is the one used in this work, scalar data are classified by a transfer function, which maps the scalar values to color and opacity, to be visualized. With the evolution of personal computer graphics cards (GPU), new techniques for volume visualization have been developed. The new algorithms take advantage of modern programmable graphics cards, whose processing power increases at a faster rate than the one observed in conventional processors (CPU). This work evaluates and compares two GPU- based algorithms for volume visualization of unstructured meshes: view- independent cell projection (VICP) and ray-tracing. In addition, two adaptations of the studied algorithms are proposed. For the cell projection algorithm, we propose a GPU data structure in order to eliminate the high costs of the CPU to GPU data transfer. For the raytracing algorithm, we propose to integrate the transfer function in the GPU, which increases the quality of the generated image and allows to interactively change the transfer function.
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Kaus, Cynthia Christine 1965. "Topological and geometrical considerations for Maxwell's equations on unstructured meshes." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/282472.
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A discrete differential form approach to solving Maxwell's equations numerically on unstructured meshes is presented. A differential form representation of Maxwell's equations provides a natural and coordinate-free means of studying these equations and their solutions in the presence of curved objects. We begin by reviewing basic properties of differential forms and the operators associated with them for their use in describing electromagnetic fields and sources. Because we are interested in numerically solving Maxwell's equations on unstructured meshes, we introduce discrete representations of these differential forms and the underlying manifolds. This allows a discrete representation of Maxwell's equations in terms of chains and cochains on an arbitrary polyhedral cell complex. The discrete boundary operator, coboundary operator and star operator on cochains are constructed and shown to maintain divergence-free regions. The constructions of the dual of a polyhedral cell complex and the star operator, which give a one-to-one correspondence between the primary and the dual cell complexes, are introduced. This star operation gives the relationship between the magnetic field 1-cochain on the dual cell complex and the magnetic flux 2-cochain on the primary cell complex, and the relationship between the electric field 1-cochain on the primary cell and the electric flux 2-cochain on the dual cell complex. With the construction of these operators, the dual cell complex, and the associated cochains, we have determined the corresponding numerical update equations for the electromagnetic fields on unstructured meshes. The numerical update equations provided by the discrete differential form approach are determined explicitly for cubical, parallelepiped, tetrahedral, and trapezoid cell complexes. For the special cases of an orthogonal complex and a parallelepiped complex, these discrete differential form update equations recover those provided by both Yee's algorithm and the discrete surface integral (DSI) algorithm. It is demonstrated that the discrete differential form update equations differ from those obtained with the DSI approach on the more irregular trapezoid cell complex and, hence, may overcome the known late-time instabilities associated with the DSI approach applied to such highly unstructured meshes.
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Charlesworth, David John. "Solution of the incompressible Navier-Stokes equations on unstructured meshes." Thesis, University College London (University of London), 2004. http://discovery.ucl.ac.uk/1446891/.
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Since Patankar first developed the SIMPLE (Semi Implicit Method for Pressure Linked Equations) algorithm, the incompressible Navier-Stokes equations have been solved using a variety of pressure-based methods. Over the last twenty years these methods have been refined and developed however the majority of this work has been based around the use of structured grids to mesh the fluid domain of interest. Unstructured grids offer considerable advantages over structured meshes when a fluid in a complex domain is being modelled. By using triangles in two dimensions and tetrahedrons in three dimensions it is possible to mesh many problems for which it would be impossible to use structured grids. In addition to this, unstructured grids allow meshes to be generated with relatively little effort, in comparison to structured grids, and therefore shorten the time taken to model a particular problem. Also, through the use adaptive refinement, the mesh generation process can be coupled to the solution algorithm to allow the mesh to be refined in areas where complex flow patterns exist. Whilst the advantages to unstructured meshes are obvious they have inherent difficulties associated with them. The computational overheads of using an unstructured grid are increased and the discretisation process becomes more complex. Also, it is inevitable that some of the discretisation methods used as standard on structured grids, do not perform as accurately when used on an unstructured mesh. Therefore, the use of unstructured meshes in computational fluid dynamics (CFD) is still an area of active research. This thesis aims to investigate the use of unstructured meshes to solve the incompressible Navier-Stokes equations using the SIMPLE algorithm. A discretisation strategy drawing on the work of others is developed, that attempts to maintain the accuracy of the solution despite the discretisation problems that unstructured grids present. Particular attention is paid to the convective term in the momentum equations, which is often the cause of inaccuracy in pressure-based solvers. High order convective models, first developed for structured meshes, are adapted for use within an unstructured discretisation to ensure stable and bounded solutions are calculated. To reduce computational costs, the discretisation is based on a pointer system that aims to minimise the amount of connectivity data stored for a particular grid. In addition an efficient multigrid algorithm accelerates the solution of the equations to achieve more realistic calculation times. As an initial test of the solver's accuracy and efficiency, calculated results are compared with standard laminar flow problems in both two and three dimensions. However, for any solution strategy to be of practical use it must be able to model turbulent flow. To that end the algorithm is extended to find solutions to the incompressible Reynolds averaged Navier-Stokes equations, using the k-? turbulence model to close the equations. Again, two and three-dimensional problems are used to test the solver's accuracy and efficiency at calculating turbulent flow. Finally the findings of the research work are summarised and conclusions drawn.
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Parrish, Michael H. "A selective approach to conformal refinement of unstructured hexahedral meshes /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1985.pdf.
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Parrish, Michael Hubbard. "A Selective Approach to Hexahedral Refinement of Unstructured Conformal Meshes." BYU ScholarsArchive, 2007. https://scholarsarchive.byu.edu/etd/979.
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Hexahedral refinement increases the density of an all-hexahedral mesh in a specified region, improving numerical accuracy. Previous research using solely sheet refinement theory made the implementation computationally expensive and unable to effectively handle multiply-connected transition elements and self-intersecting hexahedral sheets. The Selective Approach method is a new procedure that combines two diverse methodologies to create an efficient and robust algorithm able to handle the above stated problems. These two refinement methods are: 1) element by element refinement and 2) directional refinement. In element by element refinement, the three inherent directions of a hexahedron are refined in one step using one of seven templates. Because of its computational superiority over directional refinement, but its inability to handle multiply-connected transition elements, element by element refinement is used in all areas of the specified region except regions local to multiply-connected transition elements. The directional refinement scheme refines the three inherent directions of a hexahedron separately on a hexahedron by hexahedron basis. This differs from sheet refinement which refines hexahedra using hexahedral sheets. Directional refinement is able to correctly handle multiply-connected transition elements. A ranking system and propagation scheme allow directional refinement to work within the confines of the Selective Approach Algorithm.
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Croft, Thomas Nicholas. "Unstructured mesh : finite volume algorithms for swirling, turbulent, reacting flows." Thesis, University of Greenwich, 1998. http://gala.gre.ac.uk/6371/.
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The work presented in this thesis develops techniques, employing the Finite Volume discretisation method, which allow the numerical simulation of three dimensional heat transfer and fluid flow problems using unstructured meshes. The method solves and stores all variables at the element centres which lowers storage requirements and generally shortens run times compared with the Control Volume-Finite Element approach. Correction terms are formulated which address two of the main forms of errors caused by mesh skewness. To allow a generic handling of any unstructured mesh the Cartesian components of velocity are solved under all circumstances. This leads to the requirement to adjust the discretisation of the momentum equations when there is significant flow curvature. The changes are presented in this study both when the position of the flow axis is known prior to the simulation and when its position is known only as a result of the simulation, this being the case when there is more than one source of swirling flow. These original features contribute to a Computational Fluid Dynamics code which is capable of solving swirling, turbulent fluid flow and reactive, radiative heat transfer on highly complex geometries. Specifically the techniques are applied to the simulation of processes occurring in the direct smelting of iron. The use of the Finite Volume method makes it relatively easy to employ many techniques and physical models developed for structured codes. The evaluation of the face convective fluxes is effected through the Rhie - Chow interpolation method. The SIMPLE algorithm is used in the pressure - velocity coupling. In the simulation of swirling flows it is shown that both the standard and ReNormalisation Group k-e models fail to accurately predict turbulent effects. An anisotropic hybrid (k-e and mixing length) model is developed which produces excellent numerical results for the flows of interest. The Simple Chemical Reaction Scheme is used to evaluate the transport of the various chemical species. Radiation effects are simulated through the use of the radiosity model. A series of simulation results are presented which show the capabilities of the methods in test cases ranging from simple heat transfer problems through to the simulation of two swirling jets in a three dimensional unstructured mesh.
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Birger, Christopher. "Optimal Coherent Reconstruction of Unstructured Mesh Sequences with Evolving Topology." Thesis, Linköpings universitet, Medie- och Informationsteknik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-112095.
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This thesis work will investigate and implement a method for reconstructing an unstructured mesh sequence with evolving topology. The goal of the method is to increase frame-to-frame coherency of the triangulation. The motivation of the method is that many of current state-of-the-art mesh compression and decimation algorithms for mesh sequences are based on static connectivity.
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Okusanya, Tolulope Olawale 1972. "An algorithm for parallel unstructured mesh generation and flow analysis." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/46452.
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McDonald, Cameron L. "Automatic, Unstructured Mesh Generation for 2D Shelf Based Tidal Models." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1550.pdf.
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Chow, Peter M. Y. "Control volume unstructured mesh procedure for convection-diffusion solidification processes." Thesis, University of Greenwich, 1993. http://gala.gre.ac.uk/6133/.
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The research work presented herein addresses the unstructured mesh problem in finite volume (FV) or control volume (CV) method used in numerical simulations. The modelling work conducted is in context of solidification for casting processes. The control volume-unstructured mesh (CV-UM) method can be categorised into two approaches, a vertex-centred and a cell-centred approach. The classification of the approach is based on the relationship between the control volume and the unstructured mesh. The vertex-centred is naturally unstructured and has been used successfully in fluid flow and heat transfer calculations. The cell-centred on the other hand has always been associated with structured (quadrilateral) meshes, this has been extended to handle unstructured mesh in the current work and is called the irregular control volume (ICV) method. Both approaches have been studied for solidification by conduction only, using several standard phase change test cases and one with experimental data from the casting industry. The result of this work is reported and their suitability for solidification addressed. For the ICV method, the extension to solve the full convective-diffusive solidification was undertaken, these are primarily the fluid flow and energy equations solved using the well known SIMPLE algorithm. One spin-off from the ICV is the appearance of "highorder cell" control volumes, control volumes with more than the standard four cell faces in two-dimensions. The high-order cell technique is exhibiting the same characteristics as high-order schemes used in standard CV method, when applied to standard CFD test cases. The one current drawback for the technique is the generation of these high-ordercells, currently no fully- or semi-automatic mesh generation is available. This prevented further study of the technique and used in the solidification test cases, where in one, experimental data is available for the phase change fronts. This was carried Out using quadrilateral meshes, but solved using the unstructured approach of the ICV. The predicted solution is in qualitative agreement with experiment. The second convective-diffusive solidification problem is the first to demonstrate the CV-UM integrated framework by solving two major casting components simultaneously, the solidification (the work undertaken in this research) and the residual stress for deformation. This is still an on going research work, where refinement and validation are required and further integration of casting processes, such as mould filling, are necessary to complete the various stages of the shape casting process. This kind of integrated simulation requires huge amount of computations, it will take days for traditional scalar computers to do one prediction. Vector and parallel machines offer ways in which to bring down the computing times to a level that is in hours instead of days. To utilise machines with vector and parallel capability efficiently, the algorithm of the model process need to be mapped onto such architectures for it to take full advantage of the computing powers. The solidification algorithm in threedimensions has been vectorised and a speed-up of five is possible. This was part of a collective study into mapping algorithms Onto vector and parallel computers, where it emerged that the ideal computing architecture is a network of processors each with its own vector capabilities.
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Gargallo, Peiró Abel. "Validation and generation of curved meshes for high-order unstructured methods." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/275977.
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In this thesis, a new framework to validate and generate curved high-order meshes for complex models is proposed. The main application of the proposed framework is to generate curved meshes that are suitable for finite element analysis with unstructured high-order methods. Note that the lack of a robust and automatic curved mesh generator is one of the main issues that has hampered the adoption of high-order methods in industry. Specifically, without curved high-order meshes composed by valid elements and that match the domain boundary, the convergence rates and accuracy of high-order methods cannot be realized. The main motivation of this work is to propose a framework to address this issue.
First, we propose a definition of distortion (quality) measure for curved meshes of any polynomial degree. The presented measures allow validating if a high-order mesh is suitable to perform finite element analysis with an unstructured high-order method. In particular, given a high-order element, the measures assign zero quality if the element is invalid, and one if the element corresponds to the selected ideal configuration (desired shape and nodal distribution). Moreover, we prove that if the quality of an element is not zero, the region where the determinant of the Jacobian is not positive has measure zero. We present several examples to illustrate that the proposed measures can be used to validate high-order isotropic and boundary layer meshes.
Second, we develop a smoothing and untangling procedure to improve the quality for curved high-order meshes. Specifically, we propose a global non-linear least squares minimization of the defined distortion measures. The distortion is regularized to allow untangling invalid meshes, and it ensures that if the initial configuration is valid, it never becomes invalid. Moreover, the optimization procedure preserves, whenever is possible, some geometrical features of the linear mesh such as the shape, stretching, straight-sided edges, and element size. We demonstrate through examples that the implementation of the optimization problem is robust and capable of handling situations in which the mesh before optimization contains a large number of invalid elements. We consider cases with polynomial approximations up to degree ten, large deformations of the curved boundaries, concave boundaries, and highly stretched boundary layer elements.
Third, we extend the definition of distortion and quality measures to curved high-order meshes with the nodes on parameterized surfaces. Using this definition, we also propose a smoothing and untangling procedure for meshes on CAD surfaces. This procedure is posed in terms of the parametric coordinates of the mesh nodes to enforce that the nodes are on the CAD geometry. In addition, we prove that the procedure is independent of the surface parameterization. Thus, it can optimize meshes on CAD surfaces defined by low-quality parameterizations.
Finally, we propose a new mesh generation procedure by means of an a posteriori approach. The approach consists of modifying an initial linear mesh by first, introducing high-order nodes, second, displacing the boundary nodes to ensure that they are on the CAD surface, and third, smoothing and untangling the resulting mesh to produce a valid curved high-order mesh. To conclude, we include several examples to demonstrate that the generated meshes are suitable to perform finite element analysis with unstructured high-order methods.
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Antoniadis, Antonios Foivos. "High-order methods on mixed-element unstructured meshes for aeronautical applications." Thesis, Cranfield University, 2012. http://dspace.lib.cranfield.ac.uk/handle/1826/7891.
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Higher resolution and reliability are the desiderata for Computational Fluid Dynamics
and main drivers for the development, implementation and validation of highorder
accurate methods. Complex fluid dynamic phenomena such as shock-wave
boundary-layer interactions, turbulent separated flows and fluid problems involving
multiple scales are adequately resolved with high-order schemes. The spatial representation
of the flow field by an unstructured mesh provides flexibility, automation,
fast and effortless grid generation and exceptional load balance on multiple processor
computers. This plethora of advantages is mirrored by the unprecedented popularity
of unstructured-based schemes.
The objective of this PhD project is the implementation of two high-order schemes
for the compressible Navier-Stokes equations in the context of the finite volume “kexact”
framework: the MUSCL-TVD and WENO. The schemes are formulated in
two and three space dimensions for mixed-element unstructured meshes; in addition,
the Spalart-Allmaras turbulence model is implemented into the developed numerical
framework. A wide range of applications are considered spanning from low-speed
flows (M = 0.08) to supersonic conditions (M = 5.0); inviscid and viscous simulations
in a broad spectrum of Reynolds numbers ranging from Re = 500 up to Re = 37×106.
The applications include: the Taylor-Green vortex, the ONERA-M6 wing, flat plate,
the NACA-0012 and the MD 30P-30N aerofoils, and a shock-wave boundary-layer
interaction.
For the examined cases, WENO schemes demonstrate superior accuracy, numerical
dissipation and non-oscillatory behaviour over the MUSCL-TVD. High-order schemes
inherit low numerical dissipation properties while turbulence models induce dissipation,
this disequilibrium has adverse effects on the stability, convergence and accuracy
of the simulation; therefore, turbulence model re-calibration would be required in order
to accommodate high-order discretisation methods.
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Kieri, Emil. "Accuracy aspects of the reaction-diffusion master equation on unstructured meshes." Thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-145978.
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The reaction-diffusion master equation (RDME) is a stochastic model for spatially heterogeneous chemical systems. Stochastic models have proved to be useful for problems from molecular biology since copy numbers of participating chemical species often are small, which gives a stochastic behaviour. The RDME is a discrete space model, in contrast to spatially continuous models based on Brownian motion. In this thesis two accuracy issues of the RDME on unstructured meshes are studied. The first concerns the rates of diffusion events. Errors due to previously used rates are evaluated, and a second order accurate finite volume method, not previously used in this context, is implemented. The new discretisation improves the accuracy considerably, but unfortunately it puts constraints on the mesh, limiting its current usability. The second issue concerns the rates of bimolecular reactions. Using the macroscopic reaction coefficients these rates become too low when the spatial resolution is high. Recently, two methods to overcome this problem by calculating mesoscopic reaction rates for Cartesian meshes have been proposed. The methods are compared and evaluated, and are found to work remarkably well. Their possible extension to unstructured meshes is discussed.
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Li, Yenjung. "Compressible Navier-Stokes computations for two-dimensional geometries using unstructured meshes." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339144.
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Denner, Fabian. "Balanced-force two-phase flow modelling on unstructured and adaptive meshes." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/28101.
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Two-phase flows occur regularly in nature and industrial processes and their understanding is of significant interest in engineering research and development. Various numerical methods to predict two-phase phase flows have been developed as a result of extensive research efforts in past decades, however, most methods are limited to Cartesian meshes. A fully-coupled implicit numerical framework for two-phase flows on unstructured meshes is presented, solving the momentum equations and a specifically constructed continuity constraint in a single equation system. The continuity constraint, derived using a momentum interpolation method, satisfies continuity, provides a strong pressure-velocity coupling and ensures a discrete balance between pressure gradient and body forces. The numerical framework is not limited to specific density ratios or a particular interface topology and includes several novelties. A further step towards a more accurate prediction of two-phase flows on unstructured meshes is taken by proposing a new method to evaluate the interface curvature. The curvature estimates obtained with this new method are shown to be as good as or better than methods reported in literature, which are mostly limited to Cartesian meshes, and the accuracy on structured and unstructured meshes is shown to be comparable. Furthermore, lasting contributions are made towards the understanding of convolution methods for two-phase flow modelling and the underlying mechanisms of parasitic currents are studied in detailed. The mesh resolution is of particular importance for two-phase flows due to the inherent first-order accuracy of the interface position using interface capturing methods. A mesh adaption algorithm for tetrahedral meshes with application to two-phase flows and its implementation are presented. The algorithm is applied to study mesh resolution requirements at interfaces and force-balancing for surface-tension-dominated two-phase flows on adaptive meshes.