Gas metal arc is a high-efficiency and widely used heat source for metal processing applied predominantly in welding and additive manufacturing. In this study, it was applied to welding. It offers high productivity, low production and investment cost, as well as suffers from some drawbacks such as humping or undercut when welding large parts that are curved and impose changing the orientation of the welding torch along the joint path. Deeper process understanding was therefore sought to mitigate these drawbacks. The difficulty is then the non-lineardependence of the process to the welding parameters and material properties. Besides, visual observation of this process is also difficult. For instance, the elevated temperature and the intense radiative emission from the electric arc, smoke, spatter, as well as the non-transparency of the processed alloy can hinder in-process observation or limit it. Process simulation provides a complementary means to reach process knowledge. It was thus the approach used in this study. For this, a thermo-fluid melt pool model that can predict melting and solidification, track free surface deformation, metal transfer, and coalescence with the melt pool was developed. Two main research questions were identified and addressed.The first one led to studying the effect of the substrate orientation during multilayer welding of a V-groove joint with INVAR and gas metal arc. It was foundthat the force balance in the melt pool changes significantly when the workpieceorientation is changed, resulting in distinct melt flow patterns, melt pool and bead geometries, and in some conditions defect initiation such as humping, undercut, and lack of fusion. As a result, multi-layer welding with flat substrate and downhill welding of a 20◦ inclined substrate are recommended with these process conditions. On the contrary, welding of a side inclined substrate and uphill welding of a 20◦ inclined substrate are not recommended. The second question gave rise to the comparative investigation of the three electromagnetic force models commonly used when modelling a melt pool produced by an electric arc. The underlying modelling assumptions were retrieved and investigated. It was found that each of these three models predicts a different melt flow pattern, different heat convection, melt pool shape, free surface oscillation, and interaction with the transferred metal drops, and thus result in different bead geometry. All these models can be adjusted to predict the penetration depth, however, only the most complete of them is recommended for developing a predictive melt pool model. For this, it is proposed as a future work to improve this model through predicting an electromagnetic force that takes also into account the local deformation of the free surface. / Gasmetallbåge är en effektiv och allmänt använd värmekälla vid svetsning och additiv tillverkning. I denna studie tillämpas den på svetsning. Den erbjuder hög produktivitet, låg kostnad vid inköp och användning, såväl som vissa nackdelarsom ojämn "bucklig" svetssträng och smältdiken vid svetsning av stora komponenter som är krökta och medför att svetsbrännarens orientering ändras utmed fogen. Bättre processförståelse eftersträvas därför för att mildra dessa nackdelar. En utmaning är processens icke-linjära beroende av svetsparametrarna och materialegenskaperna. Dessutom är experimentell optisk övervakning svår. Till exempel kan den höga temperaturen och den intensiva elektromagnetiska strålningen från ljusbågen, rök, sprut, såväl som legeringens ogenomskinlighet, förhindra observation under processen eller begränsa den. Processimulering erbjuder en komplementär metod för att nå processkunskap. Det är alltså detta tillvägagångssätt som används i denna studie. För detta har en modell av värme och materialflödena i smältan utvecklats som kan prediktera smältning och stelning, spåra smältytans deformation, metallflöde och koalescens med smältan.Två huvudsakliga forskningsfrågor har identifierats och adresserats. Den första studerade gravitationens påverkan vid flersträngs-, gasmetallbågsvetsning av V-fogar i INVAR. Olika svetslägen har visat sig ha en betydande påverkan på kraftbalanserna i svetssmältan vilket resulterar i distinkta smältflöden, smält- och svetsförbandgeometrier, och under vissa förhållanden svetsdefekter såsom ojämn "bucklig" svetssträng, smältdiken och bindfel. Som ett resultat rekommenderas horisontellt och 20◦ fallande läge vid flersträngssvetsning, medan 20◦ stigande och sidolutande inte rekommenderas. Den andra frågan undersökte inverkan av de tre huvudsakliga modellerna för den elektromagnetiska kraften som idag används vid svetssimuleringar. För modelleringen har antaganden lagts fram och undersökts. Det visade sig att de tre modellerna predikterar olika flödesmönster i smältan, olika värmekonvektion, smältgeometri, ytvågor och interaktion med de överförda metalldropparna, och därmed också predikterar olika svetsstränggeometrier. Alla tre modeller kan justeras för att prediktera svetspenetrationen, men endast den mest kompletta av dessa rekommenderas för sant prediktiv modellering. Det föreslås också att ytterligare förbättra den mest kompletta modellen så att det elektromagnetiska kraftfältet följer deformationen av den fria smältytan. / <p>Submitted papers or manuscripts have been excluded from the fulltext file. </p>

[pt] O deslocamento de um líquido em um tubo capilar pela injeção de um gás ocorre em muitas situações, tais como na recuperação avançada de petróleo, no revestimento de conversores catalíticos e na moldagem assistida por injeção de gás. Geralmente o líquido deslocado é uma solução polimérica ou uma dispersão, que é não Newtoniana. Forças viscoelásticas alteram o balanço de forças em várias partes do escoamento e, conseqüentemente, alteram a eficiência do deslocamento, isto é, mudam a quantidade de líquido deixada na parede do capilar. Modelos de tais escoamentos devem se basear em teorias que levem em consideração o comportamento diferenciado de líquidos com microestrutura complexa, tanto no cisalhamento quanto na extensão. Além do mais, escoamentos de deslocamento envolvem uma superfície livre, e o domínio no qual as equações diferenciais são resolvidas é desconhecido a priori, fazendo parte da solução. Estas duas características tornam o problema extremamente complexo. Este problema foi estudado aqui tanto experimentalmente quanto teoricamente. Os experimentos consistiram da visualização do escoamento e medição da massa deslocada pela passagem de uma bolha de gás através de um tubo capilar preenchido por um líquido viscoelástico. Várias soluções de baixo peso molecular de Polietileno Glicol (PEG) e de alto peso molecular de Óxido de Polietileno (PEO) em água foram usadas a fim de avaliar os efeitos do comportamento viscoelástico no escoamento. As propriedades reológicas das soluções foram avaliadas tanto em cisalhamento quanto em extensão. Na análise teórica, o escoamento com superfície livre bidimensional próximo µa interface gás- líquido foi modelado usando três equações diferenciais constitutivas distintas que aproximam o comportamento viscoelástico de soluções poliméricas diluídas, as quais são os modelos Oldroyd-B, FENE-P e FENE-CR, juntamente com as equações de conservação de massa e de quantidade de movimento linear. O sistema de equações foi resolvido pelo Método dos Elementos Finitos. O sistema de equações algébricas não-lineares resultante foi resolvido pelo método de Newton. Os resultados mostram o efeito do caráter viscoelástico do líquido na forma da superfície livre e a espessura do filme líquido deixado na parede. / [en] Displacement of a liquid in a capillary tube by gas injection occurs in many situations, like enhanced oil recovery, coating of catalytic converters and gas-assisted injection molding. Generally the liquid being displaced is a polymeric solution or dispersion, which is not Newtonian. Viscoelastic forces alter the force balance in various parts of the flow and consequently change the amount of liquid left attached to the capillary wall. Models of such flows must rely on theories that can account for the different behavior of microstructured liquids in simple shear and extensional flow. Moreover, displacement flows involve a free surface, and the domain where the differential equations are posed is unknown a priori being part of the solution. These two characteristics make the problem extremely complex. This problem was analyzed here both by experiments and theory. The experiments consisted of flow visualization and measurement of mass displaced by a gas bubble in a capillary tube filled with a viscoelastic liquid. Various solutions of low molecular weight Polyethylene Glycol (PEG) and high molecular weight Polyethylene Oxide (PEO) in water were used in order to evaluate the effect of viscoelastic behavior on the flow. The rheological properties of the solutions were evaluated both in simple shear and predominantly extensional flows. In the theoretical analysis, the two- dimensional free surface flow near the gas-liquid interface was modelled using three different differential constitutive equations that approximate viscoelastic behavior of dilute polymer solutions, namely Oldroyd-B, FENE-P and FENE-CR, together with momentum and continuity equations. The equation system was solved with the Finite Element Method. The resulting non- linear system of algebraic equations was solved by Newton`s method. The results show the effect of the viscoelastic character of the liquid on the free surface shape and the film thickness attached to the capillary wall.

Dans la production d'électricité, un des leviers centraux pour réduire les détériorations et les pertes causées par l'humidité dans les turbines à vapeur est l'étude des films liquides. Ces films minces, sont créés par la déposition de gouttes et sont fortement cisaillés. Des gouttes peuvent ensuite être arrachées du film. A l'heure actuelle, aucun modèle complet et valide n'existe pour décrire ce phénomène. Un modèle 2D à formulation intégrale associé à des lois de fermetures a été dérivé pour représenter ce film. Comparé aux équations classiques de Saint-Venant, le modèle prend en compte davantage d'effets : le transfert de masse, l'impact des gouttes, le cisaillement à la surface libre, la tension de surface, le gradient de pression et la rotation. Une analyse des propriétés du modèle (hyperbolicité, entropie, conservativité, analyse de stabilité linéaire, invariance par translation et par rotation) est réalisée pour juger de la pertinence du modèle. Un nouveau code 2D est implémenté dans un module de développement libre du code EDF Code Saturne et une méthode de volumes finis pour un maillage non-structure a été développée. La vérification du code est ensuite effectuée avec des solutions analytiques dont un problème de Riemann. Le modèle, qui dégénère en modèle classique de Saint-Venant pour le cas d'un film tombant sur un plan inclinée, est validé par l'expérience de Liu and Gollub, 1994, PoF et comparé à des modèles de références (Ruyer-Quil and Manneville, 2000, EPJ-B et Lavalle, 2014, PhD thesis). Un autre cas d'étude met en scène un film cisaillé en condition basse-pression de turbine à vapeur et, est validé par l'expérience de Hammitt et al., 1981, I. Enfin, le code film est couplé aux données 3D du champ de vapeur autour d'un stator d'une turbine basse-pression du parc EDF, issues de Blondel, 2014, PhD thesis. Cette application industrielle montre la faisabilité d'une simulation d'un film en condition réelle du turbine à vapeur. / In the electricity production, one central key to reduce damages and losses due to wetness in steam turbines is the study of liquid films. These thin films are created by the deposition of droplets and are highly sheared. This film may then be atomized into coarse water. At the moment, no comprehensive and validated model exists to describe this phenomenon. A 2D model based on a integral formulation associated with closure laws is developed to represent this film. Compared to classical Shallow-Water equation, the model takes into account additional effect : mass transfer, droplet impact, shearing at the free surface, surface tension, pressure gradient and the rotation. The model properties (hyperbolicity, entropy, conservativity, linear stability, Galilean invariance and rotational invariance) has been analyzed to judge the pertinence of the model. A new 2D code is implemented in a free module of the code EDF Code Saturne and a finite volume method for unstructured mesh has been developed. The verification of the code is then carried out with analytical solutions including a Riemann problem. The model, which degenerates into classical Shallow-Water equations for the case of a falling liquid film on a inclined plane, is validated by the experiment of Liu and Gollub, 1994, PoF and compared to reference models (Ruyer-Quil and Manneville, 2000, EPJ-B et Lavalle, 2014, PhD thesis). Another study depicts a sheared film under low-pressure steam turbine conditions and is validated by the experiment of Hammitt et al., 1981, FiI. Lastly, the code film is coupled to 3D steam data around a fixed blade of a BP100 turbine, from Blondel, 2014, PhD thesis. This industrial application shows the feasibility of liquid film's simulation in real steam turbine condition.

Cette thèse s'inscrit dans l'étude des modèles asymptotiques aux équations des ondes de surface dans le régime modulationnel. Le problème des ondes de surface consiste à décrire le mouvement - sous l'influence de la gravitation et éventuellement de tension de surface - d'un fluide dans un domaine délimité par la surface libre du fluide et par un fond fixe. Dans l'étude de ce problème, on s'intéresse en particulier aux ondes se propageant à la surface du fluide.Dans le régime modulationnel, on considère l'évolution des ondes de surface sous forme de paquets d'ondes de faible amplitude se propageant dans une direction. Il est bien connu que la motion de l'enveloppe du paquet d'onde sur une échelle de temps d'ordre t = O(1/ϵ²), où ϵ est un petit paramètre désignant l'amplitude, est décrite approximativement par des systèmes d'équations appelés systèmes de Benney-Roskes (BR) / Davey-Stewartson (DS). Ces systèmes sont donnés par une équation de type Schrödinger cubique couplée à une équation d'ondes. L'approximation classique de BR / DS est bien établie et a été largement étudiée au cours des dernières décennies. Récemment, David Lannes a introduit une version à "dispersion exacte" de ces systèmes. Contrairement aux équations de BR / DS standard, les systèmes à dispersion exacte préservent la relation de dispersion des équations des ondes de surface. On devrait obtenir ainsi une description plus riche du vrai comportement dynamique des ondes de surface que dans le cas de l'approximation classique.Le systèmes de BR / DS à dispersion exacte sont étudiés dans cette thèse. La première partie est consacrée à la déduction formelle des systèmes de BR / DS en tant que modèles asymptotiques aux équations des ondes de surface. Nous donnons en outre un résultat sur la consistance de cette approximation.Ensuite, nous étudions le problème de Cauchy pour le système de BR à dispersion exacte. En fait, afin de justifier la consistance de l'approximation de BR avec les équations exactes, on doit prouver que ce système est bien posé (en espace de Sobolev) sur une échelle de temps d'ordre O(1/ϵ). Ceci est un problème ouvert même dans le cas classique, du moins pour le système de dimension 1 + 2. De même, nous ne pouvons pas démontrer l'existence de solutions en temps long pour le système de BR à dispersion exacte, mais nous obtenons un théorème d'existence locale (t = O(1)) à condition que la tension de surface soit assez forte. Si nous nous restreignons au système de dimension 1+1, nous pouvons enlever la contrainte sur la tension de surface. L'idée de la preuve d'existence locale, qui est inspirée par un travail de Schochet-Weinstein, est d'écrire le système de BR comme un système symétrique hyperbolique quasi-linéaire perturbé par un terme dispersif ne contribuant pas à l'énergie du système. Ainsi, nous pouvons appliquer les méthodes standard de résolution des systèmes hyperboliques.En modifiant le terme non-linéaire du système de BR de dimension 1+1 sans changer l'ordre de consistance, nous obtenons un système qui est bien posé sur l'échelle de temps appropriée O(1/ϵ). Cependant, cette démarche ne peut pas être généralisée au cas de dimension 1+2.Dans le dernier chapitre de cette thèse, nous donnons quelques résultats sur les systèmes de Davey-Stewartson à dispersion exacte. Pour les systèmes de DS, il est suffisant de démontrer qu'ils sont bien posés localement afin de justifier leur consistance avec les équations des ondes de surface. La théorie d'existence de solutions est assez complète pour le système de DS classique. Dans le cas de dispersion exacte cependant, les équations paraissent mal posées généralement, si bien que l'existence locale ne peut être démontrée pour l'instant que pour quelques cas particuliers simples. / This thesis is concerned with asymptotic models to the water wave equations in the modulational regime. The water wave equations describe the motion - under the influence of gravity and possibly surface tension - of an inviscid fluid in a domain which is bounded by a fixed bottom from below and the free surface of the fluid from above. In the study of the water wave problem, one is in particular interested by waves propagating on the surface of the fluid.In the modulational regime, one considers the evolution of surface waves under the form of small amplitude wave packets traveling in one direction. It is well known that the evolution of the wave packet envelope on the long time scale t = O(1/ϵ²), where ϵ is a small parameter denoting the amplitude of the wave, is approximately governed by a set of equations known as the Benney-Roskes (BR) / Davey-Stewartson (DS) systems. These systems are essentially given by a cubic Schrödinger-type equation coupled to a wave equation. The classical BR / DS approximation is well established and has been largely studied in the past decades. Recently, David Lannes has introduced a "full dispersion" version of these systems. In contrast to the standard BR / DS equations, the full dispersion systems preserve the linear dispersion relation of the full water wave equations, and should therefore give a richer description of the original wave dynamics than the classical approximation.The full dispersion BR / DS systems are studied in this thesis. In the first part, we formally derive the full dispersion BR / DS approximation from the water wave equations both in the case of zero and positive surface tension. The formal derivation is completed by a consistency result.We then study well-posedness in Sobolev space of the full dispersion BR system. In order to justify consistency of the BR approximation with the full water wave equations, one needs to show that the BR system is well posed on a time scale of order O(1/ϵ). This is an open problem even in the classical case, at least for the 1 + 2 dimensional system. We also do not obtain well-posedness on the long time scale for the full dispersion BR system, but we can show that it is locally well-posed in the case of sufficiently strong surface tension, and additionally in the zero surface tension case if we restrict ourselves to the 1+1 dimensional system. The proof is inspired by a paper of Schochet-Weinstein, and is based on writing the full dispersion BR system as a quasilinear symmetric hyperbolic system with dispersive perturbation, where the dispersive terms do not contribute to the energy. We can therefore apply classical solution methods for hyperbolic systems.By modifying the nonlinear part of the 1+1 dimensional full dispersion BR system without changing consistency, we obtain a system that is well-posed on the appropriate O(1/ϵ) time scale. This approach however does not generalize to the 1+2 dimensional case.In the last chapter of the thesis, we give some results on the full dispersion DS systems, which are obtained as special limits of the full dispersion BR system. For these systems, it is sufficient to prove local well-posedness in order to show consistency with the water wave equations. For the standard DS systems, local well-posedness theory is quite complete. For the full dispersion systems, the analysis is complicated by some nonlocal operators and the equations seem to be generally ill-posed. There are however some simple cases where local well-posedness can be shown. We also discuss some modifications of the full dispersion DS system that might allow to solve it for a larger range of parameters.

Neste trabalho são apresentados os resultados do desenvolvimento e teste de esquemas upwind de alta resolução para o controle da difusão numérica em leis de conservação gerais e problemas em dinâmica dos fluidos. Em particular, são derivados dois novos esquemas: o ALUS (Adaptive Linear Upwind Scheme) e o TOPUS (Third-Order Polynomial Upwind Scheme). Esses esquemas são testados no transporte de escalares, em equações 1D tipo convecção-difusão, em sistemas hiperbólicos 1D, nas equações de Euler 2D da dinâmica dos gases e nas equações de Navier-Stokes incompressíveis 2D/3D. Os esquemas são então associados a uma modelagem algébrica não linear para a simulação de problemas de escoamentos incompressíveis turbulentos 2D com/sem superfícies livres / In this work, results of the development and testing of high-resolution upwind schemes for controlling of the numerical diffusion for general conservation laws and fluid dynamics problems are presented. In particular, two new high-resolution upwind schemes are derived, namely, the ALUS (Adaptive Linear Upwind Scheme) and the TOPUS (Third-Order Polynomial Upwind Scheme). These schemes are tested in scalar transport, 1D convection-diffusion equations, 1D hyperbolic systems, 2D Euler equations of the gas dynamics, and in 2D/3D incompressible Navier-Stokes equations. The schemes are then combined with a nonlinear Reynolds stress algebraic equation model for the simulation of 2D incompressible turbulent flows with/without free surfaces

Apesar de as EDPS que modelam leis de conservação e problemas em dinâmica dos fluídos serem bem estabelecidas, suas soluções numéricas continuam ainda desafiadoras. Em particular, há dois desafios associados à computação e ao entendimento desses problemas: um deles é a formação de descontinuidades (choques) e o outro é o fenômeno turbulência. Ambos os desafios podem ser atribuídos ao tratamento dos termos advectivos não lineares nessas equações de transporte. Dentro deste canário, esta tese apresenta o estudo do desenvolvimento de um novo esquema \"upwind\" de alta resolução e sua associação com modelagem da turbulência. O desempenho do esquema é investigado nas soluções da equação de advecção 1D com dados iniciais descontínuos e de problemas de Riemann 1D para as equações de Burgers, Euler e águas rasas. Além disso, são apresentados resultados numéricos de escoamentos incompressíveis 2D e 3D no regime laminar a altos números de Reynolds. O novo esquema é então associado à modelagem \'capa\' - \'epsilon\' da turbulência para a simulação numérica de escoamentos incompressíveis turbulentos 2D e 3D com superfícies livres móveis. Aplicação, verificação e validação dos métodos numéricos são também fornecidas / Althought the PDEs that model conservation laws and fluid dynamics problems are well established, their numerical solutions have presented a continuing challenge. In particular, there are two challenges associated with the computation and the understanding of these problems, namely, formation of shocks and turbulence. Both challenges can be attributed to the nonlinear advection terms of these transport equations. In this scenario, this thesis presents the study of the development of a new high-resolution upwind scheme and its association with turbulence modelling. The performance of the scheme is investigated by solving the 1D advection equation with discontinuous initial data 1D Riemann problems for Burgers, Euler and shallow water equations. Besides, numerical results for 2D and 3D incompressible laminar flows at high Reynolds number are presented. The new scheme is then associated with the \'capa - \' epsilon\' turbulence model for the simulation of 2D and 3D incompressible turbulent flows with moving free surfaces. Application, verification and validation of the numerical methods are also provided

Uma parte significativa dos escoamentos encontrados em aplicações tecnológicas é caracterizada por envolver altos números de Reynolds, principalmente aqueles em regime turbulento e com superfície livre. Obter soluções numéricas representativas para essa classe de problemas é extremamente difícil, devido à natureza não-linear das equações diferenciais parciais envolvidas nos modelos. Conseqüentemente, o tema tem sido uma das principais preocupações da comunidade científica moderna em dinâmica de fluidos computacional. Aproximações de primeira ordem para os termos convectivos são as mais adequadas para amortecer oscilações que estão associadas às aproximações de alta ordem não-limitadas. Todavia, elas introduzem dissipação artificial nas representações discretas comprometendo os resultados numéricos. Para minimizar esse efeito não-físico e, ao mesmo tempo, conseguir aproximações incondicionalmente estáveis, é indispensável adotar uma estratégia que combine aproximações de primeira ordem com as de ordem mais alta e que leve em conta a propagação de informações físicas. Os resultados dessa composição são os esquemas "upwind" limitados de alta ordem. Em geral, espera-se que esses esquemas sejam apropriados para a representação das derivadas convectivas nos modelos de turbulência kappa-varepsilon. No contexto de diferenças finitas, a presente tese dedica-se à solução numérica das equações de Navier-Stokes no regime de números de Reynolds elevados. Em particular, ela contém uma análise de algoritmos monotônicos e antidifusivos e modelos de turbulência kappa-varepsilon para a simulação de escoamentos incompressíveis envolvendo superfícies livres. Esquemas de convecção são implementados nos códigos GENSMAC para proporcionar um tratamento robusto dos termos convectivos nas equações de transporte. Duas versões do modelo kappa-varepsilon de turbulência são implementadas nos códigos GENSMAC, para problems bidimensionais e com simetria radial, para descrever os efeitos da turbulência sobre o escoamento médio. Resultados numéricos de escoamentos com simetria radial são comparados com resultados experimentais e analíticos. Simulações numéricas de problemas tridimensionais complexos são apresentadas para avaliar o desempenho de esquemas "upwind". Finalmente, os modelos de turbulência kappa-varepsilon são utilizados para a simulação de escoamentos confinados e com superfícies livres. / A considerable part of fluid flows encountered in technological applications is characterised by involving high-Reynolds numbers, especially those in turbulent regime and with free-surface. It is extremely difficult to obtain representative numerical solutions for this class of problems, due to the non-linear nature of the partial differential equations involved in the models. Consequently, this subject has been one of main concerns in the modern computational fluid dynamics community. First-order approximation to the convective terms is one of the most appropriate to smooth out oscilations/instabilities which are associated with high-order unlimited approximation. However, it introduces numerical dissipation in the discrete representation jeopardizing the numerical results. In order to minimize this non-physical effect and, at the same time, to obtain unconditionally stable approximation, it is essential to adopt a strategy that combines first and high-order approximations and takes into account the propagation of physical information. The results of this composition are the high-order bounded upwind techniques. In general, it is expected that these algorithms are satisfactory for the representation of the convective derivatives in the kappa-varepsilon turbulence model. In the context of finite-difference, the present thesis deals with the numerical solution of the Navier-Stokes equations at high-Reynolds number regimes. In particular, it contains an analysis of monotonic and anti-difusive convection schemes and kappa-varepsilon turbulence models for the simulation of free-surface fluid flows. Upwinding methods are implemented into the GENSMAC codes to provide a robust treatment of the convective terms in the transport equations. Two versions of the K-Epsilon turbulence model are implemented into the two-dimensional and axisymmetric GENSMAC codes, in order to describe the turbulent effects on the average flow. Numerical results of axisymmetric flows are compared with experimental and analytical results. Numerical simulations of complex three-dimensional problems are presented to assess the performance of high-order bounded upwind schemes. Finally, the K-Epsilon turbulence models are employed in the simulation of confined and free-surface flows.

Apesar de as EDPS que modelam leis de conservação e problemas em dinâmica dos fluídos serem bem estabelecidas, suas soluções numéricas continuam ainda desafiadoras. Em particular, há dois desafios associados à computação e ao entendimento desses problemas: um deles é a formação de descontinuidades (choques) e o outro é o fenômeno turbulência. Ambos os desafios podem ser atribuídos ao tratamento dos termos advectivos não lineares nessas equações de transporte. Dentro deste canário, esta tese apresenta o estudo do desenvolvimento de um novo esquema \"upwind\" de alta resolução e sua associação com modelagem da turbulência. O desempenho do esquema é investigado nas soluções da equação de advecção 1D com dados iniciais descontínuos e de problemas de Riemann 1D para as equações de Burgers, Euler e águas rasas. Além disso, são apresentados resultados numéricos de escoamentos incompressíveis 2D e 3D no regime laminar a altos números de Reynolds. O novo esquema é então associado à modelagem \'capa\' - \'epsilon\' da turbulência para a simulação numérica de escoamentos incompressíveis turbulentos 2D e 3D com superfícies livres móveis. Aplicação, verificação e validação dos métodos numéricos são também fornecidas / Althought the PDEs that model conservation laws and fluid dynamics problems are well established, their numerical solutions have presented a continuing challenge. In particular, there are two challenges associated with the computation and the understanding of these problems, namely, formation of shocks and turbulence. Both challenges can be attributed to the nonlinear advection terms of these transport equations. In this scenario, this thesis presents the study of the development of a new high-resolution upwind scheme and its association with turbulence modelling. The performance of the scheme is investigated by solving the 1D advection equation with discontinuous initial data 1D Riemann problems for Burgers, Euler and shallow water equations. Besides, numerical results for 2D and 3D incompressible laminar flows at high Reynolds number are presented. The new scheme is then associated with the \'capa - \' epsilon\' turbulence model for the simulation of 2D and 3D incompressible turbulent flows with moving free surfaces. Application, verification and validation of the numerical methods are also provided

In this work we review 12 years of developments in the field of residual based discretizations for hyperbolic problems and their application to the solution of the shallow water equations. Fundamental concepts related to the topic are recalled and he construction of second and higher order schemes for steady problems is presented. The generalization to time dependent problems by means of multi-step implicit time integration, space-time, and genuinely explicit techniques is thoroughly discussed. Finally, the issues of C-property, super consistency, and wetting/drying are analyzed in this framework showing the power of the residual based approach.

Das Ziel der vorliegenden Arbeit ist die Entwicklung von partikelbasierenden Strömungs- und Transportmodellen zur Charakterisierung von kleinskaligen Strömungsprozessen in gesättigten und ungesättigten Poren- und Kluftsystemen. Aufgrund der unzureichenden Prozessbeschreibung von ungesättigter Strömung in Doppelkontinuummodellen mittels der Richardsgleichung und van Genuchten Parametern werden innovative Methoden präsentiert um die zugrunde liegenden hochdynamischen Strömungs- und Transportprozesse zu erfassen. Die Simulation von Strömung und Transport in ungesättigten geklüfteten Aquiferen bildet immer noch ein höchst anspruchsvolles Aufgabenfeld aufgrund von skalenübergreifenden Diskontinuitäten, welche oftmals die Definition eines globalen repräsentativen Einheitsvolumens nicht zulassen. Des Weiteren können die hydraulischen Eigenschaften und potentiellen Parameterräume von geklüfteten Aquiferen oftmals nur durch integrale Ansätze, wie z.B. Pump- und Slugtests, Zeitreihenanalysen von Quellschüttungen und Tracertests ermittelt werden. Doppelkontinuummodelle bieten hierfür einen ausgewogenen Ansatz hinsichtlich der erforderlichen Felddaten und der resultierenden prädiktiven Modellqualität. Der erste Teil dieser Arbeit evaluiert den Doppelkontinuumansatz, welcher die Simulation von Strömung mittels der Richardsgleichung und van Genuchten Parametern in zwei, durch einen linearen Austauschterm gekoppelten, Kontinua ermöglicht. Ganglinien von Karstquellen weisen eine charakteristischen steilen Abfall nach Niederschlagsereignissen auf, der durch das Modell erfolgreich reproduziert werden kann. Das Röhrensystem bildet die hydraulische Brücke zur Karstquelle und nimmt potentialabhängige Wassermengen des geklüfteten Matrixsystems auf. Um die Simulation von schneller Grundwasserinfiltration durch das Röhrenkontinuum innerhalb der ungesättigten Zone zu vermeiden wurde die entsprechende Randbedingung an die untere Grenze des Kontinuums gesetzt. Ein genereller Nachteil des Doppelkontinuumsansatz ist die potentielle Mehrdeutigkeit von Modellergebnissen. Der duale Parameterraum in Kombination mit schwierig zu ermittelnden Parametern, führt zur Existenz von mehr als einem kalibrierten Modell, wie durch mehrdimensionale Sensitivitätsanalysen aufgezeigt wird.  Insbesondere in Karstaquiferen bilden Diskontinuitäten, wie z.B. Lösungsdolinen, Klüfte und Störungssysteme, bevorzugte hydraulische Elemente für schnelle vertikale Grundwasserneubildungsprozesse, die oftmals nicht durch volumeneffektive Modellansätze erfasst werden können. Der Hauptteil dieser Arbeit befasst sich daher mit der Entwicklung von zwei Smoothed Particle Hydrodynamics (SPH) Modellen um ein adäquates numerisches Werkzeug zur partikelbasierenden Simulation von kleinskaligen Strömungen mit freien Oberflächen und Transportprozessen bereitzustellen. SPH Modelle ermöglichen eine Eulersche Beschreibung eines Strömungsfelds auf Basis der Navier-Stokes Gleichung und Partikelbewegung mittels klassischer Newtonscher Mechanik. Der gitterlose Modellansatz ermöglicht flexible Simulationen von hochdynamischen Phasengrenzen in ungesättigten Klüften und Porenräumen. Das erste SPH Modell wird eingesetzt um durch Oberflächenspannung dominierte Tropfen- und Filmströmungen auf glatten und rauhen Kluftoberflächen zu simulieren. Charakteristische dimensionslose Kennzahlen werden über einen weiten Bereich von Benetzungswinkeln und Reynoldszahlen bestimmt. Modellergebnisse weisen einen hervorragende Übereinstimmung mit dimensionslosen Skalierungsfunktionen auf und kritische Kontaktwinkel folgen der zu erwartenden Entnetzungsdynamik. Die Entstehung von adsorbierten Filmen auf trockenen Oberflächen wird für einen breiten Parameterraum bestimmt. Des Weiteren wird der Einfluss von befeuchteten Oberflächen auf die Geschwindigkeitszunahme von Tropfenströmung aufgezeigt und so die Bedeutung der Koexistenz verschiedener Strömungsmodi gezeigt. Der Effekt von Oberflächenrauhigkeit auf Tropfenströmung wird für verschiedene Rauhigkeiten ermittelt und eine deutliche Geschwindigkeitsabnahme demonstriert. Um die makroskopische Kontinuumsbeschreibung der Navier-Stokes Gleichung und atomistische Effekte eines klassischen Partikelsystems der statistischen Mechanik zu kombinieren wurde ein zweites mesoskopisches SPH Modell entwickelt. Diese neue Diskretisation der vollständig gekoppelten Landau-Lifshitz-Navier-Stokes und Advektions- Diffusionsgleichung ermöglicht die Simulation von Strömung und Transport bei gleichzeitiger Berücksichtigung von Fluktuationsdynamiken, welche sich korrekt der Systemskala anpassen. Die Verbindung von klassischer Fickscher Diffusion und thermodynamischen Fluktuationen wird hierbei durch einen effektiven Diffusionskoeffizienten beschrieben. Numerische Experimente zeigen die Präzision des Modells. Grenzflächen zwischen zwei Fluiden unterschiedlicher Konzentration weisen eine korrekte Wellenzahldivergenz entsprechend aktuellen Laborergebnissen auf.