Experimental studies have been conducted on the topic of the interaction of compressiblevortex rings on stationary surfaces. Throughout the campaign experimentswere carried out at pressure ratios of ! 4, 8, and 12. In the classical set up of airas both the driver and driven gas, these corresponded to theoretical incident Machnumbers Ms of 1.34, 1.54, and 1.61.Experiments were conducted on vortex rings impinging on a stationary surfacelocated at three (increasing) distances (1.66, 3.33, and 5.00 inner diameters) fromthe shock tube exit and on a stationary surface at a set distance but at three anglesinclinations (75, 60, and 45deg at 3.33 inner diameters). Results of the impingementof a vortex ring on a stationary solid surface perpendicular to the flow showed asymmetrical impingement process. A boundary layer is generated over the surfacewith an associated increase in pressure. An increase in velocity due to the radialexpansion causes the pressure over the surface to decrease. This expansion leads tothe development of azimuthal wave instabilities along the core. Pressure was seen toincrease with an increase in incident Mach number value. The variation in distanceresulted in an increase in pressure with an increase in distance. This counter-intuitiveresult can be explained by the higher translational velocity at impingement, alongwith the absence of the initial radial expansion of the counter-rotating vortex rings. The variation in surface angle inclination introduced several degrees of asymmetry. One core of the vortex ring impinges first on the surface due to its closerproximity to it, while the other core is still free to propagate. This process generatesan asymmetric boundary layer over the surface, and a higher rate of stretching ofthe lower core, resulting in its dissipation. At higher incident Mach numbers, theembedded rearward facing shock is reflected and propagates perpendicularly to thesurface. At the inclination angles of 60 and 45deg, the counter-rotating vortex ringsare fully deflected upwards and orbit around the main vortex. This phenomenonresult in a significant difference in pressure distribution between the upper and lowersections of the surface.

The purpose of this paper is to consider the impulse formulations of the Euler equations for incompressible and compressible fluids. Different gauges are considered. In particular, the Kuz'min gauge provides an interesting case as it allows the fluid impulse velocity to describe the evolution of material surface elements. This result affords interesting physical interpretations of the Kuz'min invariant. Some exact solutions in the impulse formulation are studied. Finally, generalizations to compressible fluids are considered as an extension of these results. The arrangement of the paper is as follows: in the first chapter we will give a brief explanation on the importance of the study of fluid impulse. In chapters two and three we will derive the Kuz'min, E & Liu, Maddocks & Pego and the Zero gauges for the evolution equation of the impulse density, as well as their properties. The first three of these gauges have been named after their authors. Chapter four will study two exact solutions in the impulse formulation. Physical interpretations are examined in chapter five. In chapter six, we will begin with the generalization to the compressible case for the Kuz'min gauge, based on Shivamoggi et al. (2007), and we will derive similar results for the remaining gauges. In Chapter seven we will examine physical interpretations for the compressible case.

We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solidand fluidmechanics.For manyof these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model.Most notably, the use of least-squares principles leads to a variational unconstrained minimization problem where stability conditions such as inf-sup conditions (typically arising in mixed methods using weak form Galerkin finite element formulations) never arise. In addition, the least-squares based finite elementmodelalways yields a discrete system ofequations witha symmetric positive definite coeffcientmatrix.These attributes, amongst manyothers highlightedand detailed in this work, allow the developmentofrobust andeffcient finite elementmodels for problems of practical importance. The research documented herein encompasses least-squares based formulations for incompressible and compressible viscous fluid flow, the bending of thin and thick plates, and for the analysis of shear-deformable shell structures.

Hot mix asphalt (HMA) is a composite material that exhibits a nonlinear response that is dependent on temperature, type of loading and strain level. The properties of HMA are highly influenced by the type and amount of the constituents used and also depend on its internal structure. In such a material the variable effects of the compaction process assume a central importance in determining material performance. It is generally accepted that the theoretical knowledge about material behavior during compaction is limited and it is therefore hard to predict and manage (the effect of) a compaction process. This work makes an attempt to address such a specific need by developing a continuum model that can be adapted for simulating the compaction of hot mix asphalt (HMA) using the notion of multiple natural configurations. A thermodynamic framework is employed to study the non-linear dissipative response associated with HMA by specifying the forms for the stored energy and the rate of dissipation function for the material; a viscoelastic compressible fluid model is developed using this framework to model the compaction of hot mix asphalt. It is further anticipated that the present work will aid in the development of better constitutive models capable of capturing the mechanics of processes like compaction both in the laboratory and in the field. The continuum model developed was implemented in the finite element method, which was employed to setup a simulation environment for hot mix asphalt compaction. The finite element method was used for simulating compaction in the laboratory and in various field compaction projects.

In this thesis we collect the study of two problems in the Calculus of Variations and Partial Differential Equations. Our first group of results concern the analysis of minimizers in a variational model describing the shape of liquid drops and crystals under the influence of gravity, resting on a horizontal surface. Making use of anisotropic symmetrization techniques and an analysis of fine properties of minimizers within the class of sets of finite perimeter, we establish existence, convexity and symmetry of minimizers. In the case of smooth surface tensions, we obtain uniqueness of minimizers via an ODE characterization. In the second group of results discussed in this thesis, which is joint work with A. Vasseur, we treat a problem in compressible fluid dynamics, establishing a uniform bound from below on the temperature for a variant of the compressible Navier-Stokes-Fourier system under suitable hypotheses. This system of equations forms a mathematical model of the motion of a compressible fluid subject to heat conduction. Building upon the work of (Mellet, Vasseur 2009), we identify a class of weak solutions satisfying a localized form of the entropy inequality (adapted to measure the set where the temperature becomes small) and use a form of the De Giorgi argument for L[superscript infinity] bounds of solutions to elliptic equations with bounded measurable coefficients. / text

We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solidand fluidmechanics.For manyof these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model.Most notably, the use of least-squares principles leads to a variational unconstrained minimization problem where stability conditions such as inf-sup conditions (typically arising in mixed methods using weak form Galerkin finite element formulations) never arise. In addition, the least-squares based finite elementmodelalways yields a discrete system ofequations witha symmetric positive definite coeffcientmatrix.These attributes, amongst manyothers highlightedand detailed in this work, allow the developmentofrobust andeffcient finite elementmodels for problems of practical importance. The research documented herein encompasses least-squares based formulations for incompressible and compressible viscous fluid flow, the bending of thin and thick plates, and for the analysis of shear-deformable shell structures.

[pt] O presente trabalho tem como principal objetivo resolver numericamente o escoamento de líquidos e gases isotérmicos ou não, no regime transiente em tubulações industriais com área variável. Pretende-se ainda, investigar os campos de velocidade,pressão e temperatura na presença de vazamentos na tubulação. O código computacional implementado resolve as equações de conservação de massa, quantidade de movimento linear e da energia na sua forma conservativa. Este enfoque permite obter resultados importantes, dentre os quais pode- se destacar a capacidade de reproduzir as perturbações nos campos de velocidade e pressão, uma vez iniciado o vazamento do fluido num determinado instante de tempo e em qualquer ponto da tubulação. Para a solução numérica do escoamento unidimensional em coordenadas retangulares utilizou-se o método de volumes finitos. A discretização espacial foi realizada baseada no método - upwind - e para a discretização temporal utilizou- se o método totalmente implícito. As equações de conservação de massa e quantidade de movimento linear são resolvidas diretamente, através da solução de uma matriz hepta-diagonal. A seguir resolvese a equação da energia por um algoritmo para matrizes tri- diagonais. Como as equações são não lineares, um processo iterativo é necessário. Para validar o metodologia empregada, são efetuados vários testes com casos registrados na literatura e resolvidos problemas que apresentam solução analítica. Uma comparação entre o enfoque conservativo e não conservativo é apresentada. Finalmente,investiga-se a resposta do campo de pressão e velocidade para a presença de vazamentos na tubulação. / [en] The main objective of the present work is to solve numerically the flow of liquid and gases isothermal or not, in the transient regime, in industrial pipes with variable area. It also has as objective to investigate the velocity, pressure and temperature field in the presence of fluid leak in the pipe. The numerical code was implemented to solve the conservation of mass, momentum, and energy in its conservative form. This approach is very convenient to study the perturbations in the velocity and temperature fields, once a leakage is detected in some point along the point, in a certain time. The numerical solution for the one-dimensional flow in rectangular coordinates is obtained by the finite volume method. The spatial discretization is based on the upwind method and totally implicit time integration is employed. The conservation of mass and linear momentum are directly solved through an hepta-diagonal matrix algorithm, followed by the solution of the energy equation by a three-diagonal algorithm. Since the conservation equations are non- linear, an iterative procedure is necessary. To validate the methodology presented, several tests of different case tests available in the literature were solved, as well as tests with analytical solution. A comparison between the conservative and non-conservative approach is presented. Finally, some test cases with leakage are examined. / [es] El presente trabajo tiene como principal objetivo resolver numéricamente el flujo de líquidos y gases isotérmicos o no, en régimen transitorio, en tuberías industriales con área variable. Se pretenden investigar los campos de velocidad, presión y temperatura en presencia de escape en la tubería. El código computacional implementado resuelve las ecuaciones de conservación de masa, cantidad de movimiento lineal y de la energía en su forma conservativa. Este enfoque permite obtener resultados importantes, dentro de los cuales cabe destacar la capacidad de reproducir las perturbaciones en los campos de velocidad y presión, una vez iniciado el escape del fluido en un determinado instante de tiempo y en cualquier punto de la tubería. Para la solución numérica del flujo unidimensional en coordenadas rectangulares se utilizó el método de volúmenes finitos. La discretización espacial se realizó a través del método - upwind - y para la discretización en el tiempo, se utilizó el método totalmente implícito. Las ecuaciones de conservación de masa y de cantidad de movimiento lineal se resuelven directamente, a través de la solución de una matriz heptadiagonal. A seguir se resuelve la ecuación de la energía por un algoritmo para matrizes tri-diagonales. Como las ecuaciones son no lineales, se necesita un proceso iterativo. Para evaluar la metodología utilizada, se efectúan varios experimentos con casos registrados en la literatura y se resuelven algunos problemas que presentan solución analítica. Se presenta una comparación entre el enfoque conservativo y no conservativo. Finalmente, se investiga la respuesta del campo de presión y velocidad en presencia de escapes en la tubería.

Lorsqu'un phénomène de détonation survient dans des milieux confinés comme un bâtiment présentant un système de galeries, l'onde de choc générée se propage et peut engendrer des dégâts matériels et humains considérables. En effet, l’onde de choc en se propageant dans ces systèmes de canaux confinés va interagir avec les obstacles qu’elle rencontre (humains et matériels), et va provoquer de très fortes élévations de la pression localement. Ce phénomène peut être très destructeur pour les structures et létale pour les humains. L'objectif de cette étude, expérimentale et numérique, est donc d'étudier la propagation d'une onde de choc dans différents systèmes de canaux afin de comprendre son comportement et de proposer des solutions pour en atténuer les dégâts. L’étude s’articule autour de deux grands axes. Le premier étudie de manière très académique la propagation d’une onde de choc au travers de cinq configurations différentes ; deux sans variation de section (un coude à 45$^{\circ}$ et un coude à 90$^{\circ}$), et trois avec variation de section (un divergent, un élargissement brusque et une bifurcation en « Y »). L’influence de la singularité sur la pression réfléchie en fond de configuration est étudiée ainsi que les mécanismes physiques complexes qui se produisent derrière l’onde de choc le long de la singularité. Le deuxième axe étudie l’atténuation de la pression réfléchie par l’ajout de piège (cavités) le long du système étudié. Une étude paramétrique montre que la position ainsi que la taille et la forme du piège ont un impact sur l’atténuation de l’onde de choc. / In the search for protection from explosions phenomena, a variety of underground shelters were studied to minimize the risks related to the propagation of shock waves in closed areas. Indeed, the blast effect could be really destructive for equipment and humans encountering the shock wave propagation, because of the high elevation of the local pressure it generates. Thus, the propagation of a shock wave through various canal systems is both experimentally and numerically studied. This study is based on two topics. The first part is focused on the study of the propagation of a shock wave through five various configurations ; two whithout aera change (a 45$^{\circ}$ bend duct and a 90$^{\circ}$ bend), and three configurations whith a sectional enlargement (a divergent, an abrupt area change and a « Y » bifurcation). The impact of the geometry on the end wall reflected pressure is studied as well as some complex physical mechanisms that occur behind the incident shock wave. The second part explores the mitigation of the pressure level in the device with the addition of traps (cavities) along the studied configuration. A parametric study based on the shape and size of the cavities, shows that these parameters have a considerable impact on the pressure level in the duct system.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-25T16:40:40Z No. of bitstreams: 1 DÉSIO RAMIREZ DA ROCHA SILVA - DISSERTAÇÃO PPGMAT 2010..pdf: 641903 bytes, checksum: 9b0b6f008468c08a7a9d581e14ef0d13 (MD5) / Made available in DSpace on 2018-07-25T16:40:41Z (GMT). No. of bitstreams: 1 DÉSIO RAMIREZ DA ROCHA SILVA - DISSERTAÇÃO PPGMAT 2010..pdf: 641903 bytes, checksum: 9b0b6f008468c08a7a9d581e14ef0d13 (MD5) Previous issue date: 2010-09 / CNPq / Capes / Neste trabalho, baseado numa seqüência de artigos de David Ho , é provado um teorema sobre a existência de uma solução fraca para um problema de valor inicial envolvendo as equações de Navier-Stokes para o caso de um escoamento unidimensional de um fluido compressível. São consideradas como hipóteses básicas a ausência de forças externas e que a pressão seja uma função contínua positiva crescente da densidade, cuja derivada também seja contínua. Quanto aos dados iniciais, estes podem possuir descontinuidades do tipo salto, não necessariamente pequenos, podendo se comportar inclusive como funções constantes por partes, em particular dados de Riemann. Tal teorema é provado baseado numa seqüência de lemas e proposições que fornecem estimativas para soluções aproximadas suaves obtidas a partir de dados regularizados. A solução nal é obtida por um processo de passagem ao limite das soluções aproximadas / In this work, based on a serie of papers by David Ho , it is proved a theorem on the existence of a weak solution to the initial value problem for the Navier-Stokes equations for a one space dimension ow of a compressible uid. It is assumed the absence of external forces and that the pressure is a continuous positive increasing function of density with the derivative also continuous. Concerning the initial data, they are allowed to have large jump discontinuities, such as piecewise constant functions, in particular Riemann data. The proof of the theorem is based on a sequence of lemmas and propositions which give estimates on the approximate smooth solutions obtained under regularized data. The nal solution is obtained by a limit process on the approximate solutions.

The main purpose of this work is to prove short-time structural stability of compressible vortex sheets with surface tension. The main result can be summarised as follows. Assume we start with an initial vortex-sheet configuration which consists of two inviscid fluids with density bounded below flowing smoothly past each other, where a strictly positive fixed coefficient of surface tension produces a surface tension force across the common interface, balanced by the pressure jump. We assume the fluids are modelled by the compressible Euler equations in three space dimensions with a very general equation of state relating the pressure, entropy and density in each fluid such that the sound speed is positive. Then, for a short time, which may depend on the initial configuration, there exists a unique solution of the equations with the same structure, that is, two fluids with density bounded below flowing smoothly past each other, where the surface tension force across the common interface balances the pressure jump. The mathematical approach consists of introducing a carefully chosen artificial viscosity-type regularisation which allows one to linearise the system so as to obtain a collection of transport equations for the entropy, pressure and curl together with a parabolic-type equation for the velocity. We prove a high order energy estimate for the non-linear equations that is independent of the artificial viscosity parameter which allows us to send it to zero. This approach loosely follows that introduced by Shkoller et al in the setting of a compressible liquid-vacuum interface. Although already considered by Shkoller et al, we also make some brief comments on the case of a compressible liquid-vacuum interface, which is obtained from the vortex sheets problem by replacing one of the fluids by vacuum, where it is possible to obtain a structural stability result even without surface tension.