Beaucoup de méthodes numériques ont été développées pour résoudre l'équation de Vlasov, car obtenir des simulations numériques précises en un temps raisonnable pour cette équation est un véritable défi. Cette équation décrit en effet l'évolution de la fonction de distribution de particules (électrons/ions) qui dépend de 3 variables d'espace, 3 variables de vitesse et du temps. L'idée principale de cette thèse est de réécrire l'équation de Vlasov sous forme d'un système hyperbolique par semi-discrétisation en vitesse. Cette semi-discrétisation est effectuée par méthode d'éléments finis. Le modèle ainsi obtenu est appelé équation de Vlasov réduite. Nous proposons différentes méthodes numériques pour résoudre efficacement ce modèle: méthodes des volumes finis, méthodes semi-Lagrangiennes et méthodes Galerkin discontinus. / Many numerical methods have been developed in order to selve the Vlasov equation, because computing precise simulations in a reasonable time is a real challenge. This equation describes the time evolution of the distribution function of charged particles (electrons/ions), which depends on 3 variables in space, 3 in velocity and time. The main idea of this thesis is to rewrite the Vlasov equation in the form of a hyperbolic system using a semi-discretization of the velocity. This semi-discretization is achieved using the finite element method. The resulting model is called the reduced Vlasov equation. We propose different numerical methods to salve this new model efficiently: finite volume methods, semi-Lagrangian methods and discontinuous Galerkin methods.

Orientadores: Rubens Maciel Filho, Liliane Maria Ferrareso Lona / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-04T02:31:19Z (GMT). No. of bitstreams: 1 MendozaMarin_FlorentinoLazaro_D.pdf: 8929110 bytes, checksum: 9041b9e7f02f9a324fa10cde9a962f54 (MD5) Previous issue date: 2004 / Resumo: O modelo determinístico e processo homopolimerização na emulsão do estireno são aplicados em reator tubular contínuo sem e com deflectores angulares internos sob condição isotérmica e não isotérmica. Os resultados de modelagem e simulação foram realizados a estado estacionário, modelo unidimensional, coordenada cilíndrica, fluxo pistão laminar completamente desenvolvido, modelo Smith-Ewart para estimar a conversão do monômero, cinética química de Arrhenius corno modelo de velocidade finita laminar para computar a geração química. O objetivo é modelar, simular e analisar o comportamento do reator de homopolimerização na emulsão do estireno com deflectores angulares inclinados internos, e comparar com reator tubular. Os métodos experimental e matemático-dedutivo foram aplicados para obter resultados, por meio de programação computacional, usando Dinâmica de Fluido Computacional através do método de volumes finitos. As seguintes variáveis como temperatura de reação constante e variável, reator tubular sem e com deflectores, temperatura de alimentação, diâmetro de reator, processo adiabático e exotérmico, calor de reação constante e velocidade axial completamente desenvolvida foram investigados. Os efeitos de conversão de monômero, área transversal interna, temperatura axial, concentração do polímero, radicais e iniciador, outros corno densidade de polímero e monômero, perda de carga e queda de pressão foram determinados e simulados. Os produtos foram caracterizados com Número de Partículas (nucleação homogênea e heterogênea), distribuição de peso molecular, tamanho de partículas de polímero e distribuição de viscosidade. Estes resultados foram validados com resultados da literatura sob condição igualou aproximada. Os resultados sob condições não isotérmicas foram melhores que os resultados isotérmicos em termos de caracterização do polímero. Isso mostra que o desenho alternativo proposto (com deflectores) permite obter o polímero com propriedades melhores em termos de número de partículas, distribuição de peso molecular, distribuição do tamanho de partículas e viscosidade / Abstract: Deterministic model and emulsion homopolymerization process of styrene are applied in continuous tubular reactor without and with internal angular baffles under isothermic and no isothermic conditions. The modeling and simulation results were approximate to steady state, one-dimensional model, cylindrical coordinate, fully developed laminar plug flow, Smith-Ewart model to estimate the monomer conversion, Arrhenius chemical kinetics as laminar finite-rate model to compute chemical source. The objective is to model, simulate and to analyze the emulsion homopolymerization reactor performance of styrene with internal-inc1ined angular baffles, and to compare with continuous tubular reactor. The experimental and mathematical-deductive methods were applied to obtain results, by means of computational programming, using Computational Fluid Dynamics (program code), finite volume method. The following variables such as constant and variable reaction temperature, tubular reactor without and with baffles, feed temperature, reactor diameter, adiabatic and exothermic process, constant reaction heat and fully developed axial velocity were investigated. The monomer conversion, internal transversal are a, axial temperature, concentration of polymer, radicals and initiator, others as density of polymer and monomer, head loss and pressure drop effects were determined and simulated. The products were characterized by partic1es number (homogeneous and heterogeneous nuc1eation), molecular weight distribution, polymer partic1es size and polymer viscosity distribution. These results were validated with literature results under same or approximate condition. The results under no isothermic conditions were better than isothermic results in terms of polymer characterization. It is shown that the proposed alternative design (with baffles) allow to obtain the polymer with better properties in terms of number of partic1es, molecular weight distribution, particle size distribution and viscosity / Doutorado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química

Les transferts de chaleur par convection forcée turbulente dans une conduite plane partiellement remplie par un milieu poreux sont étudiés numériquement. L’étude concerne l’analyse de l’encrassement dans un canal plan représentatif d’un échangeur de chaleur à plaques. Un fluide, ayant un fort pouvoir encrassant, est considéré en régime turbulent. L’objectif de cette étude est de proposer une technique qui repose sur l’utilisation de matériaux fibreux comme capteur de particules pouvant réduire les méfaits de l’encrassement. Cela consiste à essayer de réduire la résistance d’encrassement en agissant sur les propriétés thermiques du dépôt. L’étude de la cinétique de l’encrassement permet de déterminer la loi de variation de l’épaisseur du dépôt au cours du temps. Cette équation est couplée aux équations de conservation. Un modèle de conductivité thermique effective (fluide, dépôt, fibres poreuses) a été choisi et le phénomène de colmatage de la matrice poreuse est considéré. L’apport du milieu poreux sur les performances de l’échangeur est analysé / A numerical study is carried out to investigate the forced convection heat transfer induced by a turbulent flow in a parallel plate channel partly filled with a porous or fibrous material. The study involves the analysis of fouling in a plate heat exchanger, represented by a parallel plate channel with a high fouling potential liquid flow in turbulent regime. The objective is to come out with a technical solution that relies on the use of fibrous materials capability to capture deposited particles, and therefore to reduce the fouling impacts within heat exchangers. This solution focuses on reducing the fouling resistance on wall surfaces by modifying the thermal properties of the deposit. The deposit thickness evolution is obtained through a kinetics model of fouling, which is coupled to the conservation equations. An effective thermal conduction model (liquid, deposit, porous material) is selected in order to account for fouling within the porous matrix. The benefits of porous material on heat exchanger performance are analyzed

Diploma thesis is focused on modeling rotor downwash generated by the main rotor of helicopter and analyzing its effects on the roof structure. Theoretical definition of rotor downwash flow is described in the first part of the text. Governing equations of computational fluid dynamics are briefly explained as well as boundary layer and finite volume method. Next part inquires into numerical simulation of rotor downwash based on height of rotor above the roof, shape of roof plane and climatic conditions. Results are compared with climatic load values provided by actual Czech construction standard in the end of the text.

<p align="justify">This work deals with the development of numerical methods for compressible flow simulation with application to the interaction of fluid flows and structural bodies.</p><p><p><p align="justify">First, we develop numerical methods based on multidimensional upwind residual distribution (RD) schemes. Theoretical results for the stability and accuracy of the methods are given. Then, the RD schemes for unsteady problems are extended for computations on moving meshes. As a second approach, cell centered and vertex centered finite volume (FV) schemes are considered. The RD schemes are compared to FV schemes by means of the 1D modified equation and by the comparison of the numerical results for scalar problems and system of Euler equations. We present a number of two and three dimensional steady and unsteady test cases, illustrating properties of the numerical methods. The results are compared with the theoretical solution and experimental data.</p><p><p><p align="justify">In the second part, a numerical method for fluid-structure interaction problems is developed. The problem is divided into three distinct sub-problems: Computational Fluid Dynamics, Computational Solid Mechanics and the problem of fluid mesh movement. The problem of Computational Solid Mechanics is formulated as a system of partial differential equations for an anisotropic elastic continuum and solved by the finite element method. The mesh movement is determined using the pseudo-elastic continuum approach and solved again by the finite element method. The coupling of the problems is achieved by a simple sub-iterative approach. Capabilities of the methods are demonstrated on computations of 2D supersonic panel flutter and 3D transonic flutter of the AGARD 445.6 wing. In the first case, the results are compared with the theoretical solution and the numerical computations given in the references. In the second case the comparison with experimental data is presented.</p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

The interaction between fluids and structures, which is an interdisciplinary problem, has gained importance in a wide range of scientific and engineering applications. Thanks to new advances in computer technology, the numerical analysis of multiphysics phenomena has aroused growing interest. Fluid-structure interactions have been numerically and experimentally studied by many researchers and published by several books, papers, and review papers. Hou et al. (2012) [3] have also published a review paper entitled “Numerical methods for fluid-structure interaction”, which provides useful knowledge about different approaches for FSI analysis. The key challenge encountered in any numerical FSI analysis is the coupling between the two independent domains with clear distinctions. For example, a structure domain requires discretizing by a Lagrangian mesh where the mesh is fixed to the mass and follows the mass motion. In fact, the Lagrangian mesh is able to deform and follows an individual structural mass as it moves through space and time. Nonetheless, the fluid mesh remains intact within the space, where the fluid flows as time passes. The numerical approaches with regard to FSI phenomena can be divided into two main categories, namely the monolithic approach and the partitioned approach. In the former, a single system equation for the whole problem is solved simultaneously by a unified algorithm; however, in the latter, the fluid and the structure are discretized with their proper mesh and solved separately by different numerical algorithms. When a fluid flow interacts with a structure, the pressure load arising from the fluid flow is exerted on the structure, followed by deformations, stresses, and strains of the structure. Depending on the resulting deformation and the rate of the variations, a one-way or two-way coupling analysis can be conducted. Fluid-structure interaction (FSI) is characterized by the interaction of some movable or deformable structure with an internal or surrounding fluid flow. In a fluid-structure interaction (FSI), the laws that describe fluid dynamics and structural mechanics are coupled. There is also another classification for FSI problems on the basis of mesh methods: conforming methods and non-conforming methods. In the first method, the interface condition is regarded as a physical boundary (interface boundary) moving during the solution time, which imposes the mesh for the fluid domain to be updated in conformity with the new position for the interface. In contrast, the implementation of the second method eliminates a need for the fluid mesh update on the account of the fact that the interface requirement is enforced by constraints on the system equations instead of the physical boundary motion. In this work, we study numerically and experimentally the fluid-structure interaction comprising a flexible slender shaped structure, free surface flow and potentially interacting rigid structures, categorized in flood protection applications, whereas more emphasis is given to numerical analysis. Objectives of this study are defined in detail as follows: The initial aim is the numerical analysis of the behavior of a down-scale membrane loaded by hydrostatic pressures, where the numerical results have to be validated against available experimental data. A further case which has to be investigated is how the full scale flexible flood barrier behaves when approached and impacted by an accelerated massive flotsam. The numerical model has to be built so as to replicate the same physical phenomenon investigated experimentally. It enables a comparison between the numerical and experimental analyses to be drawn. A more complicated case where the flexible down-scale membrane interacts with a propagated water wave is a further target area to study. Moreover, an experimental investigation is required to validate the numerical results by way of comparison. The ultimate goal is to perform a similitude analysis upon which a correlation between the full-scale prototype and the down-scale model can be formed. The implementation of the similarity laws enables the behavior of the full scale prototype to be quantitatively assessed on the basis of the available data for the down-scale model. In addition, in order to validate the accuracy of the similitude analysis, numerical analyses have to be carried out.:Contents Zusammenfassung I ABSTRACT IV Nomenclature X 1 Introduction 1 1.1 Work overview 2 1.2 Literature review 3 1.2.1 The non-conforming methods 6 1.2.2 The conforming (partitioned) approaches 11 1.2.2.1 Interface data transfer 16 1.2.2.2 Accuracy, stability and efficiency 16 1.2.2.3 Modification of interface conditions: Robin transmission conditions 18 1.3 Concluding remarks 19 2 Methodology-numerical methods for fluid-structure interaction analysis (FSI) 20 2.1 Single FV framework 21 2.1.1 The prism layer mesher 24 2.1.2 Turbulence modeling 24 2.2 Preparation of the standalone Abaqus model 27 2.2.1 Damping by bulk viscosity 28 2.2.2 Coulomb friction damping 29 2.2.3 Rayleigh damping 29 2.2.4 Determination of the Rayleigh damping parameters based on the Chowdhury procedure 29 2.2.5 The frequency response function (FRF) measurement 30 2.2.6 The half-power bandwidth method 31 2.3 Explicit partitioned coupling 33 2.4 Implicit partitioned coupling 39 2.5 Overset mesh 40 2.6 Concluding remarks 42 3 Verification and validation of the structural model 44 3.1 Numerical model setup of the down-scale membrane 44 3.2 Comparing similarity between numerical and experimental results 46 3.2.1 Hypothesis test terminology 46 3.2.2 Curve fitting 47 3.2.3 Similarity measures between two curves 48 3.3 Results (down-scale membrane) 52 3.3.1 Similarity tests for the contact length 54 3.3.2 Similarity tests for the slope 58 3.3.3 Similarity tests for the displacement in Y direction 60 3.4 Concluding remarks 63 4 Numerical model setup of the original membrane for impact analysis 66 4.1 Structure domain 67 4.2 Fluid domain 72 4.2.1 Standard mesh and results 74 4.2.2 Overset mesh 80 4.3 Co-simulation model setup and results 88 4.4 Concluding remarks 96 5 Numerical wave generation 100 5.1 Theoretical estimation of the waves 107 5.2 Numerical wave tank setup 110 5.3 Results 114 5.4 Concluding remarks 119 6 Validity of the model with dynamic pressure 121 6.1 Wave tank 123 6.2 Structure domain 127 6.3 Fluid domain 130 6.4 Co-simulation model setup 136 6.5 Experimental approach 137 6.6 Results 141 6.6.1 Similarity tests for the displacement of the membrane in X direction 156 6.6.2 Similarity tests for the displacement of the membrane in Y direction 160 6.6.3 Similarity tests for the displacement of the membrane in Z direction 164 6.7 Concluding remarks 168 7 Similarity 171 7.1 Motivation 171 7.2 Governing equations 174 7.3 Buckingham Pi theorem 175 7.4 Dimensionless numbers 175 Similitude requirement 177 7.5 Simulation setup 178 7.6 Results 179 7.7 Concluding remarks 191 8 Summary, conclusions and outlook 192 List of figures 199 List of tables 209 References 210

On considère le problème d’advection-diffusion stationnaire v(∇u, ∇v)+( β•∇u, v) = (f, v) et non stationnaire d/dt (u(t), v) + v(∇u, ∇v)+( β•∇u, v) = (g(t), v), ainsi que le problème d’advection (β•∇u, v) = (f, v) sur un domaine polygonal borné du plan. Le terme de diffusion est approché par des éléments de Crouzeix Raviart et le terme de convection par une méthode upwind sur des volumes barycentriques finis avec un maillage triangulaire. Pour le problème stationnaire d’advection-diffusion, la L²-stabilité (c’est-à-dire indépendante du coefficient de diffusion v) est démontrée pour la solution du problème approché obtenue par cette méthode d’éléments finis et de volumes finis. Pour cela une condition sur la géométrie doit être satisfaite. Des exemples de maillages sont donnés. Toujours avec cette condition géométrique sur le maillage, une inégalité de stabilité (où la discrétisation en temps n’est pas couplée à une condition sur la finesse du maillage) est obtenue pour le cas non-stationnaire. La discrétisation en temps y est faite par un schéma d’Euler implicite. Une majoration de l’erreur, proportionnelle au pas en temps et à la finesse du maillage, est ensuite proposée et exprimée explicitement en fonction des données du problème. Pour le problème d’advection, une approche utilisant la théorie des graphes est utilisée pour obtenir l’existence et l’unicité de la solution, ainsi que le résultat de stabilité. Comme pour la stabilité du problème d’advection-diffusion, une condition géométrique - qui est équivalente pour les points intérieurs du maillage à celle du problème d’advection-diffusion - est nécessaire. / We consider the stationary linear convection-diffusion equation v(∇u, ∇v)+( β•∇u, v) = (f, v), the time dependent d/dt (u(t), v) + v(∇u,∇v)+( β•∇u, v)= (g(t), v) equation and the linear advection equation (β•∇u, v) = (f, v) on a two dimensional bounded polygonal domain. The diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements, and the convection term by upwind barycentric finite volumes on a triangular grid. For the stationary convection-diffusion problem, L²-stability (i.e. independent of the diffusion coefficient v) is proven for the approximate solution obtained by this combined finite-element finite-volume method. This result holds if the underlying grid satisfies a condition that is fulfilled, for example, by some structured meshes. Using again this condition on the grid, stability is shown for the time dependent convection-diffusion equation (without any link between mesh size and time step). An implicit Euler approach is used for the time discretization. It is shown that the error associated with this scheme decays linearly with the mesh size and the time step. This result holds without any link between mesh size and time step. The dependence of the corresponding error bound on the diffusion coefficient is completely explicit. For the stationary advection equation, an approach using graph theory is used to obtain existence, uniqueness and stability. As in the stationary linear convection-diffusion equation, the underlying grid must satisfy some geometric condition. / Gegenstand der Arbeit ist die zweidimensionale stationäre Konvektion-Diffusionsgleichung v(∇u, ∇v)+( β•∇u, v) = (f, v), die zeitabhängige Konvektion-Diffusionsgleichung d/dt (u(t), v) + v(∇u,∇v)+( β•∇u, v)= (g(t), v), sowie die Konvektionsgleichung (β•∇u, v) = (f, v). Der Diffusionsterm ist diskretisiert mittels Crouzeix-Raviart stückweise lineare Finite Elemente. Das Gebiet ist in Dreiecke unterteilt und der Konvektionsterm ist mittels einer upwind Methode auf Baryzentrische Finite Volumenelemente definiert. Für die stationäre Konvektion-Diffusionsgleichung, wird (d.h. von v unabhängige) L²-Stabilität der numerischen Lösung bewiesen. Voraussetzung dafür, ist die Erfüllung gewisser geometrischer Bedingungen an die Unterteilung des Gebiets. Beispiele von Unterteilungen die diese Bedingungen erfüllen, werden gegeben. Wieder an dieser geometrischen Bedingung geknüpft, wird Stabilität (d.h. die Zeitdiskretisierung ist entkoppelt von der Netzweite) für die zeitabhängige Konvektion-Diffusionsgleichung, bewiesen. Für die Zeitableitung wird dabei eine Implizite Euler Diskretisierung verwendet. Eine obere Schranke für den Diskretisierungsfehler, proportional zum Zeitdiskretisierungsparameter und zur Netzfeinheit, ausgedrückt als Funktion der Daten der Differenzialgleichung, wird gezeigt. Für die Konvektionsgleichung wird ein graphentheoretischer Zugang verwendet, der es ermöglicht Existenz, Eindeutigkeit und Stabilität, zu bekommen. Für die Stabilität, werden ähnliche geometrische Bedingungen an die Unterteilung des Gebiets gestellt, wie beim stationären Konvektion-Diffusionsproblem.

This master’s thesis is dealing with analysis of fluid flow pulse in a flexible tube representing e.g. an artery in a human body. In ANSYS program, 3D simulations were performed, and these are so-called interrelated FSI analysis. In Maple software, 1D simulations of fluid flow in the tube were performed for various thin-walled and thick-walled variants. The aim is using these programs to determine the flow rates and pressures in the tube, its wall deformation and stress. Therefore, the theoretical part deals mainly with basic equations of flow dynamics, linear and nonlinear models and rotationally symmetric vessels. In the computational part are described individual procedures in the mentioned programs.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.