This work deals with discretizing viscous fluxes in the context of unstructured data based finite volume and meshless solvers, two competing methodologies for simulating viscous flows past complex industrial geometries. The two important requirements of a viscous discretization procedure are consistency and positivity. While consistency is a fundamental requirement, positivity is linked to the robustness of the solution methodology. The following advancements are made through this work within the finite volume and meshless frameworks. Finite Volume Method: Several viscous discretization procedures available in the literature are reviewed for: 1. ability to handle general grid elements 2. efficiency, particularly for 3D computations 3. consistency 4. positivity as applied to a model equation 5. global error behavior as applied to a model equation. While some of the popular procedures result in inconsistent formulation, the consistent procedures are observed to be computationally expensive and also have problems associated with robustness. From a systematic global error study, we have observed that even a formally inconsistent scheme exhibits consistency in terms of global error i.e., the global error decreases with grid refinement. This observation is important and also encouraging from the view point of devising a suitable discretization scheme for viscous fluxes. This study suggests that, one can relax the consistency requirement in order to gain in terms of robustness and computational cost, two key ingredients for any industrial flow solver. Some of the procedures are analysed for positivity as applied to a Laplacian and it is found that the two requirements of a viscous discretization procedure, consistency(accuracy) and positivity are essentially conflicting. Based on the review, four representative schemes are selected and used in HIFUN-2D(High resolution Flow Solver on UNstructured Meshes), an unstructured data based cell center finite volume flow solver, to simulate standard laminar and turbulent flow test cases. From the analysis, we can advocate the use of Green Gauss theorem based diamond path procedure which can render high level of robustness to the flow solver for industrial computations. Meshless Method: An Upwind-Least Squares Finite Difference(LSFD-U) meshless solver is developed for simulating viscous flows. Different viscous discretization procedures are proposed and analysed for positivity and the procedure which is found to be more positive is employed. Obtaining suitable point distribution, particularly for viscous flow computations happens to be one of the important components for the success of the meshless solvers. In principle, the meshless solvers can operate on any point distribution obtained using structured, unstructured and Cartesian meshes. But, the Cartesian meshing happens to be the most natural candidate for obtaining the point distribution. Therefore, the performance of LSFD-U for simulating viscous flows using point distribution obtained from Cartesian like grids is evaluated. While we have successfully computed laminar viscous flows, there are difficulties in terms of solving turbulent flows. In this context, we have evolved a strategy to generate suitable point distribution for simulating turbulent flows using meshless solver. The strategy involves a hybrid Cartesian point distribution wherein the region of boundary layer is filled with high aspect ratio body-fitted structured mesh and the potential flow region with unit aspect ratio Cartesian mesh. The main advantage of our solver is in terms of handling the structured and Cartesian grid interface. The interface algorithm is considerably simplified compared to the hybrid Cartesian mesh based finite volume methodology by exploiting the advantage accrue out of the use of meshless solver. Cheap, simple and robust discretization procedures are evolved for both inviscid and viscous fluxes, exploiting the basic features exhibited by the hybrid point distribution. These procedures are also subjected to positivity analysis and a systematic global error study. It should be remarked that the viscous discretization procedure employed in structured grid block is positive and in fact, this feature imparts the required robustness to the solver for computing turbulent flows. We have demonstrated the capability of the meshless solver LSFDU to solve turbulent flow past complex aerodynamic configurations by solving flow past a multi element airfoil configuration. In our view, the success shown by this work in computing turbulent flows can be considered as a landmark development in the area of meshless solvers and has great potential in industrial applications.

Large-eddy simulation (LES) and unsteady Reynolds-averaged Navier-Stokes (URANS) calculations have been performed to investigate the effects of different mathematical models for scalar variance and its dissipation rate as applied to both a non-reacting bluff-body turbulent flow and an extension to a reacting case. In the conserved scalar formalism, the mean value of a thermo-chemical variable is obtained through the PDF-weighted integration of the local description over the conserved scalar, the mixture fraction. The scalar variance, one of the key parameters for the determination of a presumed β-function PDF, is obtained by solving its own transport equation with the unclosed scalar dissipation rate modelled using either an algebraic expression or a transport equation. The proposed approach is first applied to URANS and then extended to LES. Velocity, length and time scales associated with the URANS modelling are determined using the standard two-equation k-ε transport model. In contrast, all three scales required by the LES modelling are based on the Smagorinsky subgrid scale (SGS) algebraic model. The present study proposes a new algebraic and a new transport LES model for the scalar dissipation rate required by the transport equation for scalar variance, with a time scale consistent with the Smagorinsky SGS model.

For turbulent flow calculations, some of the well-known turbulence models in the literature are applied on a previously developed Navier-Stokes solver designed to handle laminar flows. A finite volume formulation, which is cell-based for inviscid terms and cell-vertex for viscous terms, is used for numerical discretization of the Navier-Stokes equations in conservative form. This formulation is combined with one-step, explicit time marching Lax-Wendroff numerical scheme that is second order accurate in space. To minimize non-physical oscillations resulting from the numerical scheme, second and fourth order artificial smoothing terms are added. To increase the convergence rate of the solver, local time stepping technique is applied. Before applying turbulence models, Navier-Stokes solver is tested for a case of subsonic, laminar flow over a flat plate. The results are in close agreement with Blasius similarity solutions. To calculate turbulent flows, Boussinesq eddy-viscosity approach is utilized. The eddy viscosity (also called turbulent viscosity), which arises as a consequence of this approach, is calculated using Cebeci-Smith, Michel et. al., Baldwin-Lomax, Chien&rsquo / s k-epsilon and Wilcox&rsquo / s k-omega turbulence models. To evaluate the performances of these turbulence models and to compare them with each other, the solver has been tested for a case of subsonic, laminar - transition fixed - turbulent flow over a flat plate. The results are verified by analytical solutions and empirical correlations.

The aim of this study is to extend a parallel Fortran90 code to compute three&ndash / dimensional laminar and turbulent flowfields over rotary wing configurations. The code employs finite volume discretization and the compact, four step Runge-Kutta type time integration technique to solve unsteady, thin&ndash / layer Navier&ndash / Stokes equations. Zero&ndash / order Baldwin&ndash / Lomax turbulence model is utilized to model the turbulence for the computation of turbulent flowfields. A fine, viscous, H type structured grid is employed in the computations. To reduce the computational time and memory requirements parallel processing with distributed memory is used. The data communication among the processors is executed by using the MPI ( Message Passing Interface ) communication libraries. Laminar and turbulent solutions around a two bladed UH &ndash / 1 helicopter rotor and turbulent solution around a flat plate is obtained. For the rotary wing configurations, nonlifting and lifting rotor cases are handled seperately for subsonic and transonic blade tip speeds. The results are, generally, in good agreement with the experimental data.

Submitted by Dilene Paulo (dilene.fatima@ufcg.edu.br) on 2018-02-07T13:41:46Z No. of bitstreams: 1 VERA SOLANGE DE OLIVEIRA FARIAS – TESE PPGEP 2011.pdf: 7179434 bytes, checksum: 4a30c9a95f4a089e00fa550fbf1b42b8 (MD5) / Made available in DSpace on 2018-02-07T13:41:46Z (GMT). No. of bitstreams: 1 VERA SOLANGE DE OLIVEIRA FARIAS – TESE PPGEP 2011.pdf: 7179434 bytes, checksum: 4a30c9a95f4a089e00fa550fbf1b42b8 (MD5) Previous issue date: 2011-04-29 / CNPq / Este trabalho apresenta a solução numérica da equação de difusão tridimensional em regime transiente, para um domínio arbitrário. Para atingir os objetivos, a equação de difusão foi discretizada usando coordenadas generalizadas via método dos volumes finitos com uma formulação totalmente implícita, para condições de contorno de equilíbrio e convectiva. Para cada passo no tempo, o sistema de equações obtido para uma dada malha estruturada foi resolvido pelo método de Gauss-Seidel. O código computacional foi desenvolvido em FORTRAN, usando o estúdio CVF 6.6.0, na plataforma Windows Vista. A solução proposta foi validada usando soluções analíticas e numéricas da equação de difusão para várias geometrias, permitindo validar malhas ortogonais e não-ortogonais. A análise e comparação dos resultados mostraram que a solução proposta forneceu resultados coerentes para todos os casos investigados. O código computacional desenvolvido foi aplicado na simulação, a partir de dados experimentais da secagem de telhas cerâmicas para as seguintes condições experimentais: temperaturas de 55,6 °C, 69,7 °C, 82,7 °C e 98,6 °C e teor de umidade inicial variando de 0,2345 até 0,2405 (b.s.). A simulação tornou possível determinar o coeficiente de difusão efetivo em função da razão de umidade e da temperatura do ar de secagem e também o valor do coeficiente de transferência convectivo de massa correspondente para cada temperatura. / This work presents a three-dimensional numerical solution for the diffusion equation in transient state, in an arbitrary domain. The diffusion equation was discretized using the finite volume method with a fully implicit formulation and generalized coordinates, for the equilibrium and convective boundary condition. For each time step, the system of equations obtained for a given structured mesh was solved by the Gauss-Seidel method. A computational code in FORTRAN, using the CFV 6.6.0 Studio, in a Windows Vista platform was developed. The proposed solution was validated by analytical and numerical solutions of the diffusion equation for several geometries. The geometries tested enabled to validate both orthogonal and non-orthogonal meshes. The analysis and comparison of the results showed that the proposed solution provides correct results for all cases investigated. The developed computational code was applied in the simulation, using experimental data of the drying of ceramic roof tiles, for the following experimental conditions: temperature from 55.6; 69.7; 82.7; 72.8 and 98.7 °C, initial moisture content from 0.2345 up to 0.2405 (d.b.). The simulation makes it possible to determine an expression for the diffusion coefficient as a function of the moisture content and temperature of the drying air, and also the value of the convective mass transfer coefficient corresponding to each temperature.

Made available in DSpace on 2016-12-12T20:25:12Z (GMT). No. of bitstreams: 1 Maico Jeremias da Silva.pdf: 5502697 bytes, checksum: 292822b79334828b19d2d99087aae96b (MD5) Previous issue date: 2015-07-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work discusses the behaviour of the convection heat transfer coefficient in plane fins with variation of air flow velocity and fin spacing. The differential equation that governs heat transfer in fins is discretized by the finite volume method, which enables computation of the fin thermal characteristics, such as temperature distribution, heat transfer and fin efficiency. The determination of the convection coefficient, important parameter for thermal analysis, is performed by applying a heuristic optimization method, known as Particle Swarm Optimization, which combines data measured from experimental analysis conducted in wind tunnel with the aforementioned heat transfer numerical approximation of fins. / Este trabalho analisa os efeitos da velocidade do escoamento de ar e do espaçamento entre aletas no coeficiente de convecção forçada sobre as superfícies de aletas planas. As equações diferenciais que definem a transferência de calor em aletas são discretizadas pela técnica de volumes finitos possibilitando a determinação das características térmicas da aleta, tais como perfil de temperatura, calor transferido e eficiência térmica. A determinação do coeficiente de convecção, parâmetro fundamental para análises térmicas, é realizada mediante a aplicação de um método de otimização heurístico, conhecido como Método do Enxame de Partículas, que combina os dados obtidos da análise experimental realizada em túnel de vento com a aproximação numérica da troca de calor na aleta descrita acima

Ce travail est une contribution à la simulation numérique d'écoulements turbulents autour de corps non profilés. Après avoir précisé les ingrédients numériques et les modèles de turbulence utilisés dans nos simulations, nous présentons une étude sur l'évaluation des effets de la procédure dynamique des modèles de sous-maille dans un modèle VMS-LES et une approche hybride RANS/VMS-LES. Des problèmes d'écoulements autour d'un cylindre seul et en tandem sont considérés. Nous étudions ensuite le comportement de modèles de turbulence hybrides pour la simulation d'écoulements en régime sous-critique autour d'un cylindre circulaire. Le calcul de l'écoulement autour d'un cylindre de section rectangulaire par l'approche VMS-LES est aussi présenté. Enfin, dans une dernière partie, après avoir fait une revue des travaux importants sur les schémas d'avancement en temps multirate, nous proposons une nouvelle approche explicite multirate par agglomération de volumes finis que nous appliquons à des calculs d'écoulements turbulents complexes en utilisant un modèle de turbulence hybride. / This work is a contribution to the numerical simulation of turbulent flows around bluff bodies. After specifying the numerical ingredients and the turbulence models used in our simulations, we present a study on the impact of the dynamic sub-grid scale modeling in VMS-LES model and a RANS/VMS-LES hybrid turbulence approach. Simulations of flows around a cylinder and a tandem are performed. Next, we assess the behaviour of some hybrid turbulence models for the simulation of flows around a circular cylinder in the subcritical regime. The computation of the flow around a rectangular cylinder with the VMS-LES approach is also presented. At last, after a review of some important works on multirate time advancing schemes, we propose a new volume-agglomeration explicit multirate approach that is applied to the computation of complex turbulent flows by a hybrid turbulence model.

Title: Numerical Solution of the Three-dimensional Compressible Flow Author: Martin Kyncl Department: Department of Numerical Mathematics Supervisor: Doc. RNDr. Jiří Felcman, CSc. Abstract: This thesis deals with a fluid flow in 3D in general. The system of the equations, describing the compressible gas flow, is solved numerically, with the aid of the finite volume method. The main purpose is to describe particular boundary conditions, based on the analysis of the incomplete Riemann problem. The analysis of the original initial-value problem shows, that the right hand-side initial condition, forming the Riemann problem, can be partially replaced by the suitable complementary condition. Several modifications of the Riemann problem are introduced and analyzed, as an original result of this work. Algorithms to solve such problems were implemented and used in code for the solution of the compressible gas flow. Numerical experiments documenting the suggested methods are performed. Keywords: compressible fluid flow, the Navier-Stokes equations, the Euler equations, boundary conditions, finite volume method, the Riemann problem, numerical flux, tur- bulent flow

Les matériaux granulaires multiphasiques occupent une place très importante dans notre environnement qui suscitent un grand intérêt de nombreuses communautés scientifiques, notamment celles de la mécanique des sols ou de la géotechnique. Le caractère divisé permet les milieux granulaires multiphasiques d'avoir un comportement mécanique global qui trouve leur origine, leur distribution et interactions entre les phases de composition. Un modèle de couplage hydromécanique est présenté dans ce travail de thèse pour l'application à la modélisation microscopique des couplages hydromécaniques dans les matériaux granulaires saturés. Le modèle numérique est basé sur un couplage de la méthode des éléments discrets (DEM) avec une formulation en volumes finis, à l'échelle des pores (PFV), du problmème de l'écoulement d'un fluide visqueux incompressible. Le solide est modélisé comme un arrangement de particules sphériques avec des interactions de type élasto-plastique aux contacts solide-solide. On considère un écoulement de Stokes incompressible, en supposant que les forces inertielles sont négligeables par rapport aux forces visqueuses. La géométrie des pores et leur connectivité sont définies sur la base d'une triangulation régulière des sphères, qui aboutit à un maillage tétrahédrique. La définition des conductivités hydrauliques à l'échelle des pores est un point clef du modèle, qui se rapproche sur ce point à des modèles de type pore-network. Une importance particulière réside dans les lois d'interactions fluide-solide permettant de déterminer des forces de fluide appliquées sur chacune des particules, tout en assurant un coût de calcul acceptable pour la modélisation en trois dimensions avec plusieurs millieurs des particules. Des mesures de perméabilités sur des assemblages bidisperses de billes de verre sont présentées et comparées aux prédictions du modèle et aux formules empiriques/semi-empiriques dans la littérature, ce qui valide la définition de la conductivité locale et met en évidence le rôle de la distribution granulométrique et la porosité. Une approche numérique pour analyser l'interaction mécanique fluide-solide et les mécanismes d'érosion interne est finalement présentée. / Multiphase granular materials occupy a very important place in our environment that are of great interest to many scientific communities, including those of soil mechanics or geotechnical engineering. The divided nature allows multiphase granular media to have a global mechanical behaviour which originates from all component phases, their distribution and interactions. Acoupled hydromechanical model is presented in this work for the application to microscopic modeling of coupled hydromechanical in saturated granular materials. The numerical model uses a combination of the discrete element method (DEM) with a pore-scale finite volume (PFV) formulation of flow problem of an incompressible viscous fluid. The solid is modeled as an assembly of spherical particles, where contact interactions are governed by elasto-plasticrelations. Stokes flow is considered, assuming that inertial forces are small in comparison with viscous forces. Pore geometry and pore connections are defined locally through regular triangulation of spheres, from which a tetrahedral mesh arises. The definition of pore-scale hydraulic conductivities is a key aspect of this model. In this sense, the model is similar to a pore-network model. The emphasis of this model is, on one hand the microscopic description of the interaction between phases, with the determination of the forces applied on solid particles by the fluid, on the other hand, the model involves affordable computational costs, that allow the simulation of thousands of particles in three dimensional models. Permeability measurements on bidispersed glass beads are reported and compared with model predictions and empirical formulas/semi-empirical in the literature, validating the definition of local conductivities and bringing out the role of particle size distribution and porosity. A numerical approach to analyze the fluid-solid mechanical interaction and mechanisms of internal erosion is finally presented.

Made available in DSpace on 2016-08-31T13:24:10Z (GMT). No. of bitstreams: 1 AndreHFB_DISSERT.pdf: 2463155 bytes, checksum: 1554ed6a6d87b8a8535d92ad7432b8e5 (MD5) Previous issue date: 2012-01-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Drip irrigation is one of the most efficient methods for applying water to a crop, capable of delivering water at a rate close to the demand. Many efforts have been required to estimate the amount of water needed by plants. Therefore studying soil water extraction by plants linked to mathematical modeling for behavior prediction, and linked to computational resources to allow complex mathematical procedures to be realized in a short space of time, becomes a powerful and necessary alternative for the understanding and quantification of the involved processes. This work aims to simulate soil water movement under conditions of drip irrigation, including the quantification of soil evaporation and crop transpiration of soil water. The finite volumes method was used to numerically solve the Richards equation for the simulation of soil water movement. Equations from literature were used to estimate transpiration and evaporation, adjusting them for use in finite volumes and modifying them, when necessary, to adapt them to the used model. A software was developed to perform the simulations of soil water movement, formation of a wet bulb and quantification of transpiration and evaporation. Concerning mass conservation, the results of the lesser simulations presented a relative error smaller than 0.001%. The results of the simulations of water losses by evaporation and transpiration were very similar to observed data from a lysimeter experiment, making the model results satisfactory. However, more tests and comparisons with more robust models are suggested. / A irrigação por gotejamento superficial é um dos métodos mais eficientes na aplicação de água por poder fornecer água às plantas numa taxa mais próxima a da demanda hídrica da cultura quando comparado com outros métodos. Tem-se demandado muitos esforços na tentativa de se estimar a quantidade de água necessária às plantas. Dessa forma, o estudo da extração de água do solo pelas plantas aliado à modelagem matemática para a predição de comportamentos, e aos recursos computacionais para a realização de cálculo matemáticos complexos num curto espaço de tempo, se torna uma alternativa poderosa e necessária no entendimento e quantificação dos processos envolvidos. O presente trabalho tem por objetivo simular o movimento da água no solo sob condições de irrigação por gotejamento superficial, incluindo a quantificação da evaporação da água do solo e da transpiração da cultura. Foi utilizado o método dos volumes finitos na resolução numérica da equação de Richards para a simulação do movimento de água no solo. Utilizaram-se equações já desenvolvidas na literatura para abordar a transpiração e a evaporação, adequando-as para utilização em volumes finitos e modificando-as, quando necessário, para adaptá-las ao modelo proposto neste trabalho. Um software foi desenvolvido com a finalidade de se realizar as simulações de movimento de água, formação do bulbo molhado e quantificação da transpiração e da evaporação. Quanto à conservação de massa, os resultados das simulações apresentaram erro relativo menores que 0,001%. Os resultados das simulações das perdas de água por evaporação e transpiração foram bastante similares aos de um experimento realizado com lisímetro, tornando os resultados do modelo satisfatórios. Porém, sugere-se que sejam efetuados mais testes e comparações com modelos mais robustos.