This research extends the capabilities of Non-oscillatory Forward-in-Time (NFT) solvers operating on unstructured meshes to allow for accurate simulation of incompressible turbulent flows. This is achieved by the development of Large Eddy Simulation (LES) and Detached Eddy Simulation (DES) turbulent flow methodologies and the development of parallel option of the flow solver. The effective use of LES and DES requires a development of a subgrid-scale model. Several subgrid-scale models are implemented and studied, and their efficacy is assessed. The NFT solvers employed in this work are based on the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) that facilitates novel implicit Large Eddy Simulation (ILES) approach to treating turbulence. The flexibility and robustness of the new NFT MPDATA solver are studied and successfully validated using well established benchmarks and concentrate on a flow past a sphere. The flow statistics from the solutions are compared against the existing experimental and numerical data and fully confirm the validity of the approach. The parallel implementation of the flow solver is also documented and verified showing a substantial speedup of computations. The proposed method lays foundations for further studies and developments, especially for exploring the potential of MPDATA in the context of ILES and associated treatments of boundary conditions at solid boundaries.

In this thesis, the method of Proper Orthogonal Decomposition (POD) is implemented to construct approximate, reduced order models (ROM) of mesh movement methods. Three mesh movement algorithms are implemented and comparatively evaluated, namely radial basis function interpolation, mesh optimization and elastic deformation. POD models of the mesh movement algorithms are constructed using a series of system observations, or snapshots of a given mesh for a set of boundary deformations. The scalar expansion coefficients for the POD basis modes are computed in three different ways, through coefficient optimization, Galerkin projection of the governing set of equations and coefficient interpolation. It is found that using only coefficient interpolation yields mesh movement models that accurately approximates the full order mesh movement, with CPU cost savings in excess of 99%. We further introduce a novel training procedure whereby the POD models are generated in a fully automated fashion. The technology is applicable to any mesh movement method and enables potential reductions of up to four orders of magnitude in mesh movement related costs. The proposed model can be implemented without having to pre-train the POD model, to any fluid-structure interaction code with an existing mesh movement scheme. Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Mechanical and Aeronautical Engineering / unrestricted

Ce travail est consacré au développement de schémas numériques pour approcher les solutions de modèles d'écoulement type “depth averaged”. Dans un premier temps, nous détaillons la construction d'approches Volumes Finis pour le système Shallow Water avec termes sources sur maillages non structurés. En se basant sur une reformulation appropriée des équations, nous mettons en place un schéma équilibré et préservant la positivité de la hauteur d'eau, et suggérons des extensions MUSCL adaptées. La méthode est capable de gérer des topographies irrégulières et exhibe de fortes propriétés de stabilité. L'inclusion des termes de friction fait l'objet d'une analyse poussée, aboutissant à l'établissement d'une propriété type “Asymptotic Preserving” à travers l'amélioration d'un autre récent schéma Volumes Finis. La seconde composante de cette étude concerne les méthodes Elements Finis type Galerkin discontinu. Certaines des idées avancées dans le contexte Volumes Finis sont employées pour aborder le système Shallow Water surmaillages triangulaires. Des résultats numériques sont exposés et la méthode se révèle bien adaptée à la description d'une large variété d'écoulements. Partant de ces observations nous proposons finalement d'exploiter ces caractéristiques pour étendre l'approche à une nouvelle famille d'équations type Green-Nadghi. Des validations numériques sont également proposées pour valider le modèle numérique. / This work is devoted to the development of numerical schemes to approximatesolutions of depth averaged flow models. We first detail the construction of Finite Volume approaches for the Shallow Water system with source terms on unstructured meshes. Based on a suitable reformulation of the equations, we implement a well-balanced and positive preserving approach, and suggest adapted MUSCL extensions. The method is shown to handle irregular topography variations and demonstrates strong stabilities properties. The inclusion of friction terms is subject to a thorough analysis, leading to the establishment of some Asymptotic Preserving property through the enhancement of another recent Finite Volume scheme.The second aspect of this study concerns discontinuous Galerkin Finite Elementmethods. Some of the ideas advanced in the Finite Volume context areemployed to broach the Shallow Water system on triangular meshes. Numericalresults are exposed and the method turns out to be well suited to describe a large variety of flows. On these observations we finally propose to exploit its features to extend the approach to a new family of Green-Nadghi equations. Numerical experiments are also proposed to validate this numerical model.

Le besoin croissant en simulation a conduit à l’élaboration de supercalculateurs complexes et d’un nombre croissant de logiciels hautement parallèles. Ces supercalculateurs requièrent un rendement énergétique et une puissance de calcul de plus en plus importants. Les récentes évolutions matérielles consistent à augmenter le nombre de noeuds de calcul et de coeurs par noeud. Certaines ressources n’évoluent cependant pas à la même vitesse. La multiplication des coeurs de calcul implique une diminution de la mémoire par coeur, plus de trafic de données, un protocole de cohérence plus coûteux et requiert d’avantage de parallélisme. De nombreuses applications et modèles actuels peinent ainsi à s’adapter à ces nouvelles tendances. En particulier, générer du parallélisme massif dans des méthodes d’éléments finis utilisant des maillages non structurés, et ce avec un nombre minimal de synchronisations et des charges de travail équilibrées, s’avèrent particulièrement difficile. Afin d’exploiter efficacement les multiples niveaux de parallélisme des architectures actuelles, différentes approches parallèles doivent être combinées. Cette thèse propose plusieurs contributions destinées à paralléliser les codes et les structures irrégulières de manière efficace. Nous avons développé une approche parallèle hybride par tâches à grain fin combinant les formes de parallélisme distribuée, partagée et vectorielle sur des structures irrégulières. Notre approche a été portée sur plusieurs applications industrielles développées par Dassault Aviation et a permis d’importants gains de performance à la fois sur les multicoeurs classiques ainsi que sur le récent Intel Xeon Phi. / The growing need for numerical simulations results in larger and more complex computing centers and more HPC softwares. Actual HPC system architectures have an increasing requirement for energy efficiency and performance. Recent advances in hardware design result in an increasing number of nodes and an increasing number of cores per node. However, some resources do not scale at the same rate. The increasing number of cores and parallel units implies a lower memory per core, higher requirement for concurrency, higher coherency traffic, and higher cost for coherency protocol. Most of the applications and runtimes currently in use struggle to scale with the present trend. In the context of finite element methods, exposing massive parallelism on unstructured mesh computations with efficient load balancing and minimal synchronizations is challenging. To make efficient use of these architectures, several parallelization strategies have to be combined together to exploit the multiple levels of parallelism. This P.h.D. thesis proposes several contributions aimed at overpassing this limitation by addressing irregular codes and data structures in an efficient way. We developed a hybrid parallelization approach combining the distributed, shared, and vectorial forms of parallelism in a fine grain taskbased approach applied to irregular structures. Our approach has been ported to several industrial applications developed by Dassault Aviation and has led to important speedups using standard multicores and the Intel Xeon Phi manycore.

The objective of this PhD research programme is to investigate the effectiveness of a finite volume method incorporating radial basis functions for simulating nonlinear transport processes. The finite volume method is the favoured numerical technique for solving the advection-diffusion equations that arise in transport simulation. The method transforms the original problem into a system of nonlinear, algebraic equations through the process of discretisation. The accuracy of this discretisation determines to a large extent the accuracy of the final solution. A new method of discretisation is presented that employs radial basis functions (rbfs) as a means of local interpolation. When combined with Gaussian quadrature integration methods, the resulting finite volume discretisation leads to accurate numerical solutions without the need for very fine meshes, and the additional overheads they entail. The resulting nonlinear, algebraic system is solved efficiently using a Jacobian-free Newton-Krylov method. By employing the new method as an extension of existing shape function-based approaches, the number of nonlinear iterations required to obtain convergence can be reduced. Furthermore, information obtained from these iterations can be used to increase the efficiency of subsequent rbf-based iterations, as well as to construct an effective parallel reconditioner to further reduce the number of nonlinear iterations required. Results are presented that demonstrate the improved accuracy offered by the new method when applied to several test problems. By successively refining the meshes, it is also possible to demonstrate the increased order of the new method, when compared to a traditional shape function basedmethod. Comparing the resources required for both methods reveals that the new approach can be many times more efficient at producing a solution of a given accuracy.

Orientador: Maria Aparecida Silva / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-07T05:34:31Z (GMT). No. of bitstreams: 1 Katekawa_MarcelEiki_D.pdf: 5613864 bytes, checksum: f3c6dcb950a61ff8698eef8f2ed21fd8 (MD5) Previous issue date: 2006 / Resumo: O processo de secagem de sólidos induz efeitos colaterais no material seco, sendo que a redução de volume é um destes efeitos. O objetivo deste estudo é investigar as características do processo de encolhimento e propor uma estratégia para inclusão destes efeitos na simulação da secagem. Escolheu-se a banana como objeto de estudo devido a sua importância para o Brasil e à existência de alguns estudos sobre o encolhimento desta fruta. Estudou-se inicialmente o processo de encolhimento durante a secagem e os efeitos das condições de processo sobre o comportamento dimensional do material. Fatias de banana encolhem linearmente no início da secagem, mas esse comportamento não é observado para baixos teores de umidade. Como a banana possui uma estrutura potencialmente anisotrópica, o efeito do comportamento dos diferentes tecidos da fruta teve que ser levado em consideração através do estudo da transição vítrea de cada fase durante a secagem. Um dos tecidos, o mesocarpo, possui temperatura de transição vítrea de 46ºC quando seco e pode sofrer transição durante a secagem convectiva e afetar o volume final da amostra seca. Além disso, estudou-se como a umidade é compartimentalizada no interior de cada tecido pela técnica de RMN e a influência sobre o encolhimento da amostra. O mesocarpo é seco mais rapidamente, mesmo possuindo uma quantidade de umidade livre menor que o endocarpo. Finalmente, desenvolveu-se uma resolução de equações de balanço de massa e energia utilizando-se malhas não estruturadas para poder melhor adaptar o encolhimento na modelagem / Abstract: The drying process may induce collateral effects in the dry material, such as the volume reduction. The objectives of this study are to investigate the characteristics of the shrinking process and to consider a strategy for inclusion of these effects in a drying simulation. Banana was chosen as a case study due to its importance in Brazil and to the existence of some studies on the shrinking process of this fruit during drying. Initially the effects of the drying conditions on the dimensional behavior of the material were analyzed. Banana slices shrink linearly in the beginning of the drying process, though some deviation of this behavior is observed for low moisture content. As banana possesses a potentially anisotropic structure, the behavior of the different tissues from the edible fruit had to be taken into consideration through the study of the glass transition of each phase. One of the tissues, the mesocarp, has a glass transition temperature of 46ºC when totally dry and may undergo glass transition during convective drying, which affects the final volume of the dried sample. Moreover, moisture compartmentalization in the interior of each tissue was analyzed and related to the differential behavior during drying. The mesocarp is more easily dried even though it possesses a higher concentration of unbound moisture. Finally, a resolution of mass and energy balance equations using unstructured meshes in order to allow a better inclusion of the shrinkage effects in drying was developed. / Doutorado / Engenharia de Processos / Doutor em Engenharia Química

In this dissertation, we develop Adaptive Mesh Refinement (AMR) techniques for the steady-state multigroup SN neutron transport equation using a higher-order Discontinuous Galerkin Finite Element Method (DGFEM). We propose two error estimations, a projection-based estimator and a jump-based indicator, both of which are shown to reliably drive the spatial discretization error down using h-type AMR. Algorithms to treat the mesh irregularity resulting from the local refinement are implemented in a matrix-free fashion. The DGFEM spatial discretization scheme employed in this research allows the easy use of adapted meshes and can, therefore, follow the physics tightly by generating group-dependent adapted meshes. Indeed, the spatial discretization error is controlled with AMR for the entire multigroup SNtransport simulation, resulting in group-dependent AMR meshes. The computing efforts, both in memory and CPU-time, are significantly reduced. While the convergence rates obtained using uniform mesh refinement are limited by the singularity index of transport solution (3/2 when the solution is continuous, 1/2 when it is discontinuous), the convergence rates achieved with mesh adaptivity are superior. The accuracy in the AMR solution reaches a level where the solution angular error (or ray effects) are highlighted by the mesh adaptivity process. The superiority of higherorder calculations based on a matrix-free scheme is verified on modern computing architectures. A stable symmetric positive definite Diffusion Synthetic Acceleration (DSA) scheme is devised for the DGFEM-discretized transport equation using a variational argument. The Modified Interior Penalty (MIP) diffusion form used to accelerate the SN transport solves has been obtained directly from the DGFEM variational form of the SN equations. This MIP form is stable and compatible with AMR meshes. Because this MIP form is based on a DGFEM formulation as well, it avoids the costly continuity requirements of continuous finite elements. It has been used as a preconditioner for both the standard source iteration and the GMRes solution technique employed when solving the transport equation. The variational argument used in devising transport acceleration schemes is a powerful tool for obtaining transportconforming diffusion schemes. xuthus, a 2-D AMR transport code implementing these findings, has been developed for unstructured triangular meshes.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Uma simulação numérica que leva em conta os efeitos de estratificação e mistura escalar (como a temperatura, salinidade ou substância solúvel em água) é necessária para estudar e prever os impactos ambientais que um reservatório de usina hidrelétrica pode produzir. Este trabalho sugere uma metodologia para o estudo de escoamentos ambientais, principalmente aqueles em que o conhecimento da interação entre a estratificação e mistura pode dar noções importantes dos fenômenos que ocorrem. Por esta razão, ferramentas de simulação numérica 3D de escoamento ambiental são desenvolvidas. Um gerador de malha de tetraedros do reservatório e o modelo de turbulência algébrico baseado no número de Richardson são as principais ferramentas desenvolvidas. A principal dificuldade na geração de uma malha de tetraedros de um reservatório é a distribuição não uniforme dos pontos relacionada com a relação desproporcional entre as escalas horizontais e verticais do reservatório. Neste tipo de distribuição de pontos, o algoritmo convencional de geração de malha de tetraedros pode tornar-se instável. Por esta razão, um gerador de malha não estruturada de tetraedros é desenvolvido e a metodologia utilizada para obter elementos conformes é descrita. A geração de malha superficial de triângulos utilizando a triangulação Delaunay e a construção do tetraedros a partir da malha triangular são os principais passos para o gerador de malha. A simulação hidrodinâmica com o modelo de turbulência fornece uma ferramenta útil e computacionalmente viável para fins de engenharia. Além disso, o modelo de turbulência baseado no número de Richardson leva em conta os efeitos da interação entre turbulência e estratificação. O modelo algébrico é o mais simples entre os diversos modelos de turbulência. Mas, fornece resultados realistas com o ajuste de uma pequena quantidade de parâmetros. São incorporados os modelos de viscosidade/difusividade turbulenta para escoamento estratificado. Na aproximação das equações médias de Reynolds e transporte de escalar é utilizando o Método dos Elementos Finitos. Os termos convectivos são aproximados utilizando o método semi-Lagrangeano, e a aproximação espacial é baseada no método de Galerkin. Os resultados computacionais são comparados com os resultados disponíveis na literatura. E, finalmente, a simulação de escoamento em um braço de reservatório é apresentada. / To study and forecast the environmental impacts that a hydroelectric power plant reservoir may produce, a numerical simulation that takes into account the effects of stratification and scalar mixing (such as temperature, salinity or water-soluble substance) is required. This work proposes a methodology for the study of the environmental fluid flow phenomena, mainly for flows in which the knowledge of the interaction between stratification and mixing can give important notions of the phenomena that occur. For this, a numerical simulation tool for 3D environmental flow is developed. A tetrahedral mesh generator of the reservoir based on the terrain topology and an algebraic turbulence model based on the Richardson number are the main tools developed. The main difficulty in tetrahedral mesh generation of a reservoir is nonuniform distribution of the points related to the huge ratio between the horizontal and vertical scales of the reservoir. In this type of point distributions, conventional tetrahedron mesh generation algorithm may become unstable. For this reason, a unstructured tetrahedral mesh generator is developed and the methodology used to obtain conforming elements is described. Triangular surface mesh generation using the Delaunay triangulation and the construction of the tetrahedra from the triangular surface mesh are the main steps to the mesh generator. The hydrodynamic simulation of reservoirs with a turbulence model provides a useful tool that is computationally viable for engineering purposes. Furthermore, the turbulence model based on the Richardson number takes into account the effects of interaction between turbulence and stratification. The algebraic model is the simplest among the various models of turbulence, but provides realistic results with the fitting of a small amount of parameters. Eddy-Viscosity/Diffusivity models for stratified turbulent flows models are incorporated. Using the Finite Element Method (FEM) approximation the Reynolds-averaged Navier-Stokes (RANS) and mean scalar transport equations are approximated. The convective terms are discretized employing the Semi-Lagrangian method, and the spatial discretization is based on the Galerkin method. The computational results are compared with the results available in the literature. Finally, the simulation of the flow in a branch of a reservoir is presented.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Uma simulação numérica que leva em conta os efeitos de estratificação e mistura escalar (como a temperatura, salinidade ou substância solúvel em água) é necessária para estudar e prever os impactos ambientais que um reservatório de usina hidrelétrica pode produzir. Este trabalho sugere uma metodologia para o estudo de escoamentos ambientais, principalmente aqueles em que o conhecimento da interação entre a estratificação e mistura pode dar noções importantes dos fenômenos que ocorrem. Por esta razão, ferramentas de simulação numérica 3D de escoamento ambiental são desenvolvidas. Um gerador de malha de tetraedros do reservatório e o modelo de turbulência algébrico baseado no número de Richardson são as principais ferramentas desenvolvidas. A principal dificuldade na geração de uma malha de tetraedros de um reservatório é a distribuição não uniforme dos pontos relacionada com a relação desproporcional entre as escalas horizontais e verticais do reservatório. Neste tipo de distribuição de pontos, o algoritmo convencional de geração de malha de tetraedros pode tornar-se instável. Por esta razão, um gerador de malha não estruturada de tetraedros é desenvolvido e a metodologia utilizada para obter elementos conformes é descrita. A geração de malha superficial de triângulos utilizando a triangulação Delaunay e a construção do tetraedros a partir da malha triangular são os principais passos para o gerador de malha. A simulação hidrodinâmica com o modelo de turbulência fornece uma ferramenta útil e computacionalmente viável para fins de engenharia. Além disso, o modelo de turbulência baseado no número de Richardson leva em conta os efeitos da interação entre turbulência e estratificação. O modelo algébrico é o mais simples entre os diversos modelos de turbulência. Mas, fornece resultados realistas com o ajuste de uma pequena quantidade de parâmetros. São incorporados os modelos de viscosidade/difusividade turbulenta para escoamento estratificado. Na aproximação das equações médias de Reynolds e transporte de escalar é utilizando o Método dos Elementos Finitos. Os termos convectivos são aproximados utilizando o método semi-Lagrangeano, e a aproximação espacial é baseada no método de Galerkin. Os resultados computacionais são comparados com os resultados disponíveis na literatura. E, finalmente, a simulação de escoamento em um braço de reservatório é apresentada. / To study and forecast the environmental impacts that a hydroelectric power plant reservoir may produce, a numerical simulation that takes into account the effects of stratification and scalar mixing (such as temperature, salinity or water-soluble substance) is required. This work proposes a methodology for the study of the environmental fluid flow phenomena, mainly for flows in which the knowledge of the interaction between stratification and mixing can give important notions of the phenomena that occur. For this, a numerical simulation tool for 3D environmental flow is developed. A tetrahedral mesh generator of the reservoir based on the terrain topology and an algebraic turbulence model based on the Richardson number are the main tools developed. The main difficulty in tetrahedral mesh generation of a reservoir is nonuniform distribution of the points related to the huge ratio between the horizontal and vertical scales of the reservoir. In this type of point distributions, conventional tetrahedron mesh generation algorithm may become unstable. For this reason, a unstructured tetrahedral mesh generator is developed and the methodology used to obtain conforming elements is described. Triangular surface mesh generation using the Delaunay triangulation and the construction of the tetrahedra from the triangular surface mesh are the main steps to the mesh generator. The hydrodynamic simulation of reservoirs with a turbulence model provides a useful tool that is computationally viable for engineering purposes. Furthermore, the turbulence model based on the Richardson number takes into account the effects of interaction between turbulence and stratification. The algebraic model is the simplest among the various models of turbulence, but provides realistic results with the fitting of a small amount of parameters. Eddy-Viscosity/Diffusivity models for stratified turbulent flows models are incorporated. Using the Finite Element Method (FEM) approximation the Reynolds-averaged Navier-Stokes (RANS) and mean scalar transport equations are approximated. The convective terms are discretized employing the Semi-Lagrangian method, and the spatial discretization is based on the Galerkin method. The computational results are compared with the results available in the literature. Finally, the simulation of the flow in a branch of a reservoir is presented.

The simulation of physical systems in the early stages of conceptual designs has shown to be a key factor for adequate decision making and avoiding big and expensive issues downstream in engineering projects. In the case of aircraft cabin design, taking into account the thermal comfort of the passengers as well as the proper air circulation and renovation can make this difference. However, current numerical fluid simulations (CFD) are too computationally expensive for integrating them in early design stages where extensive comparative studies have to be performed. Instead, Zonal Models (ZM) appear to be a fast-computation approach that can provide coarse simulations for aircraft cabin flows. In this thesis, a Zonal Model solver is developed as well as a geometry-definition and meshing framework, both in Matlab®, for performing coarse, flexible and computationally cheap flow simulations of user-defined cabin designs. On one hand, this solver consists of a Fractional Step approach for coarse unstructured bi-dimensional meshes. On the other, the cabin geometry can be introduced by hand for simple shapes, but also with Computational Aided Design tools (CAD) for more complex designs. Additionally, it can be chosen to generate the meshes from scratch or morph them from previously generated ones. / <p>The presentation was online</p>