Made available in DSpace on 2014-07-29T16:02:21Z (GMT). No. of bitstreams: 1 dissertacao gisele.pdf: 849978 bytes, checksum: 6707e4fe01d67af874b9cc826b72dfab (MD5) Previous issue date: 2007-11-29 / Transitional shock waves arises in solution of initial values problems for non linear systems of conservation laws that are not strictly hyperbolic. These waves are discontinuous solutions that posses viscous profile but do not conform to the Lax characteristic criterion, where inequalities between the shock propagation speed and the characteristic speeds must to be satisfied. These waves arise as transition between wave groups associated with distinct characteristic families. In this work we studied transitional shock waves for a system of two conservation laws with quadratic fux functions and positive defined viscosity matrix. In particular, we studied the transitional shock waves with viscous profile defined by orbits laying on straightlines. We show from examples, for systems with quadratic fux functions and viscosity matrix chosen in a convenience way, that is necessary to use transitional shock waves to solve the Riemann problem (initial data constant by parts) for these systems. / Ondas de choque transicionais aparecem nas soluções de problemas de valores iniciais para sistemas não lineares de leis de conservação não estritamente hiperbólicos . São soluções descontínuas que possuem perfil viscoso mas não satisfazem o critério de entropia de Lax, onde certas desigualdades entre a velocidade de propagação do choque e as velocidades características são satisfeitas. Estas ondas aparecem como transição entre grupos de ondas associados com diferentes famílias características. Neste trabalho estudamos as ondas de choque transicionais para um sistema de duas leis de conservação com função de fluxo quadratica e matriz de viscosidade definida positiva. Em particular estudamos os choques transicionais com perfil viscoso definidos por orbitas sobre um segmento de reta. Mostramos através de exemplos, para sistemas com funções de fluxo quadráticas e matrizes de viscosidade escolhidas de modo conveniente, que e necessário usar as ondas de choques transicionais para resolver o problema de Riemann (dados iniciais constantes por partes) para estes sistemas.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-03-27T18:18:55Z No. of bitstreams: 1 stiwharrisonherrerataipe.pdf: 5886256 bytes, checksum: 4fa85d1d9808790a2f5c85bb6c6c8d8d (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-03-28T16:44:29Z (GMT) No. of bitstreams: 1 stiwharrisonherrerataipe.pdf: 5886256 bytes, checksum: 4fa85d1d9808790a2f5c85bb6c6c8d8d (MD5) / Made available in DSpace on 2018-03-28T16:44:30Z (GMT). No. of bitstreams: 1 stiwharrisonherrerataipe.pdf: 5886256 bytes, checksum: 4fa85d1d9808790a2f5c85bb6c6c8d8d (MD5) Previous issue date: 2018-01-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho estamos interessados em estudar, mediante simulações computacionais, se o aquecimento eletromagnético é capaz de melhorar o deslocamento do óleo pela água. Nesta direção, nos baseamos nos resultados obtidos pela equipe da TU Delft da Holanda, que desenvolveu experimentos de laboratório que demonstravam a distribuição da temperatura em um meio poroso, onde o óleo está sendo deslocado pela injeção de água, gerada por aquecimento eletromagnético. Para tanto, definimos o modelo matemático que governa o problema em questão regido por equações diferenciais parciais das leis de conservação de massa e energia. Assim, partindo da caracterização do contínuo e estendendo a lei de Darcy para o caso multifásico, através da introdução do conceito de permeabilidades relativas dos fluidos, derivamos um sistema acoplado de equações diferenciais parciais com coeficientes variáveis e termos não lineares formulados em função da velocidade de Darcy para o escoamento bifásico (água, óleo) aquecido por ondas eletromagnéticas. O modelo matemático é discretizado utilizando o método de diferenças finitas no tempo e no espaço e a técnica Splitting. Dessa forma dividimos o sistema de equações diferencias parciais em dois subsistemas. O primeiro subsistema consiste em resolver a parte difusiva e reativa e o segundo subsistema tem por objetivo a resolução do termo convectivo. O método numérico desenvolvido é validado por simulações computacionais que visam a comparação com os resultados obtidos experimentalmente e com soluções semi-analíticas, para este problema, que foram derivadas pelo método do princípio de Duhamel. Além disso, o método proposto quando aplicado para o caso geral da simulação do escoamento bifásico com aquecimento eletromagnético demonstrou um ganho de 1.67%, se comparado ao método sem aquecimento. / In this work we are interested in studying, through computational simulations, if the electromagnetic heating is able to improve the displacement of the oil by water. In this direction, we rely on the results obtained by the TU Delft team from the Netherlands, which developed laboratory experiments that demonstrated the temperature distribution in a porous medium where the oil is being displaced by the injection of water generated by electromagnetic heating. For this, we define the mathematical model that governs the problem in question governed by partial differential equations of the laws of conservation of mass and energy. Thus, starting from the characterization of the continuum and extending Darcy’s law to the multiphase case, by introducing the concept of relative permeabilities of fluids, we derive a coupled system of partial differential equations with variable coefficients and non-linear terms formulated as a function of the velocity of Darcy for two-phase flow (water, oil) heated by electromagnetic waves. The mathematical model is discretized using the finite difference method in time and space and the Splitting technique. In this way we divide the system of partial differential equations into two subsystems. The first subsystem consists of solving the diffusive and reactive part and the second subsystem aims to solve the convective term. The numerical method developed is validated by computational simulations aimed at the comparison with the results obtained experimentally and with semi-analytical solutions, for this problem, which were derived by the Duhamel principle method. In addition, the proposed method when applied to the general case of simulation of the biphasic flow with electromagnetic heating demonstrated a gain of 1.67%, when compared to the non-heating method.

Orientador: Yuri Dimitrov Bozhkov / Tese (doutorado) ¿ Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-21T22:59:33Z (GMT). No. of bitstreams: 1 Silva_KenioAlexsomdeAlmeida_D.pdf: 5129062 bytes, checksum: 0bae8b75b0ea90b8799bc1dd7496d766 (MD5) Previous issue date: 2013 / Resumo: Nesta tese estudamos o conceito novo de equações diferenciais não - linearmente auto-adjuntas para duas classes gerais de equações evolutivas de segunda ordem quase lineares. Uma vez que essas equações não provêm de um problema variacional, não podemos obter leis de conservação via o Teorema de Noether. Por isto aplicamos tal conceito e o Novo Teorema sobre Leis de Conservação de Nail H. Ibragimov, o qual possibilita-nos a determinação de leis de conservação para qualquer equação diferencial. Obtivemos em ambas as classes, equações não - linearmente auto-adjuntos e leis de conservação para alguns casos particularmente importantes: a) as equações do fluxo de Ricci geométrico, do fluxo de Ricci 2D, do fluxo de Ricci modificada e a equação do calor não-linear, na primeira classe; b) as equações do fluxo geométrico hiperbólico e do fluxo geométrica hiperbólica modificada, na segunda classe de equações evolutivas / Abstract: In this thesis we study the new concept of nonlinear self-adjoint deferential equations for two general classes of quasilinear 2D second order evolution equations. Since these equations do not come from a variational problem, we cannot obtain conservation laws via the Noether's Theorem. Therefore we apply this concept and the New Conservation Theorem of Nail H. Ibragimov, which enables one to establish the conservation laws for any deferential equation. We obtain in classes, nonlinear self-adjoint equations and conservation laws for important particular cases: a) the Ricci flow geometric equation, Ricci flow 2D equation, the modified Ricci flow equation and the nonlinear heat equation in the first class; b) the hyperbolic geometric flow equation and the modified hyperbolic geometric flow equation in the second class of evolution equations / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Nous considérons deux modèles EDP-EDO couplés: un pour modéliser des goulots d’étranglementmobiles et l’autre pour décrire la distribution du trafic sur une bretelle d’accès. Le premier modèle a étéintroduit pour décrire le mouvement d’un bus, qui roule à une vitesse inférieure à celle des autresvoitures, en réduisant la capacité de la route et générant ainsi un goulot d’étranglement. Une loi deconservation scalaire avec une contrainte mobile sur le flux décrit le trafic et une EDO décrit latrajectoire du bus. Nous présentons un résultat d’existence des solutions du modèle et nous proposonsune méthode numérique “front/capturing" et une méthode basée sur une technique de reconstructiondes ondes de chocs. Dans la deuxième partie, nous introduisons un nouveau modèle macroscopique dejonction pour les bretelles d’autoroute. Nous considérons le modèle de trafic de Lighthill-Whitham-Richards sur une jonction composée d’une voie principale, une bretelle d’accès et une bretelle de sortie,toutes reliées par un nœud. Une loi de conservation scalaire décrit l’évolution de la densité des véhiculessur la voie principale et une EDO décrit l’évolution de la longueur de la file d’attente sur la bretelled’accès. La définition de la solution du problème de Riemann à la jonction est basée sur la résolutiond’un problème d’optimisation linéaire et sur l’utilisation d’un paramètre de priorité. Ensuite, ce modèleest étendu aux réseaux et discrétisé en utilisant un schéma de Godunov qui prend en compte les effetsde la bretelle d’accès. Enfin, nous présentons un modèle d’optimisation de la circulation sur les ronds points. / In this thesis we consider two coupled PDE-ODE models. One to model moving bottlenecks and theother one to describe traffic flow at junctions. First, we consider a strongly coupled PDE-ODE systemthat describes the influence of a slow and large vehicle on road traffic. The model consists of a scalarconservation law accounting for the main traffic evolution, while the trajectory of the slower vehicle isgiven by an ODE depending on the downstream traffic density. The moving constraint is expressed byan inequality on the flux, which models the bottleneck created in the road by the presence of the slowerDépôt de thèse – Donnéescomplémentairesvehicle. We prove the existence of solutions to the Cauchy problem for initial data of bounded variation.Moreover, two numerical schemes are proposed. The first one is a finite volume algorithm that uses alocally nonuniform moving mesh. The second one uses a reconstruction technique to display thebehavior of the vehicle. Next, we consider the Lighthill-Whitham-Richards traffic flow model on ajunction composed by one mainline, an onramp and an offramp, which are connected by a node. Theonramp dynamics is modeled using an ordinary differential equation describing the evolution of thequeue length. The definition of the solution of the Riemann problem at the junction is based on anoptimization problem and the use of a right of way parameter. The numerical approximation is carriedout using a Godunov scheme, modified to take into account the effects of the onramp buffer. Aftersuitable modification, the model is used to solve an optimal control problem on roundabouts. Two costfunctionals are numerically optimized with respect to the right of way parameter.

Orientador: Igor Leite Freire / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-27T16:11:39Z (GMT). No. of bitstreams: 1 Sampaio_JulioCesarSantos_D.pdf: 2598760 bytes, checksum: b1332349b50fc600ddddb7596fd4b5a4 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho estudamos simetrias de Lie e a teoria de leis de conservação desenvolvida por Ibragimov nos últimos 10 anos. Leis de conservação para várias equações sem Lagrangeanas clássicas foram estabelecidas / Abstract: In this work we study Lie point symmetries and the theory on conservation laws developed by Ibragimov in the last 10 years. Conservation laws for several equations without classical Lagrangians were established / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-01-13T13:01:30Z No. of bitstreams: 1 juliocesaragustinsangay.pdf: 1652010 bytes, checksum: 099a3e652e69be1b05f68b24adb6a5a4 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-01-25T17:30:12Z (GMT) No. of bitstreams: 1 juliocesaragustinsangay.pdf: 1652010 bytes, checksum: 099a3e652e69be1b05f68b24adb6a5a4 (MD5) / Made available in DSpace on 2016-01-25T17:30:12Z (GMT). No. of bitstreams: 1 juliocesaragustinsangay.pdf: 1652010 bytes, checksum: 099a3e652e69be1b05f68b24adb6a5a4 (MD5) Previous issue date: 2015-05-29 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho realizamos um estudo do método de complementaridade mista para problemas parabólicos não lineares, devido ao fato de que alguns podem ser escritos como problema de complementaridade mista e aparecem em muitas aplicações como fluxo de líquidos em um meio poroso, difusão, fluxo de calor envolvendo mudança de fases. Estes tipos de problemas apresentam dificuldades para obter as soluções analíticas. Estuda-se leis de conservação e os tipos de soluções associadas ao Problema de Riemann, essencialmente leis de balanço que expressam o fato de que alguma substância é conservada. O estudo desta teoria é importante pois frequentemente as leis de conservação aparecem quando nos problemas parabólicos são desprezados os termos difusivos de segunda ordem. Estudaremos um método numérico que permita a busca de uma solução aproximada da solução exata, o qual é uma variação do método de Newton para resolver sistemas não lineares que estão baseados num esquema de diferenças finitas implícito e um algoritmo de complementaridade mista não linear, FDA-MNCP. O método tem a vantagem de fornecer uma convergência global em relação ao método de diferenças finitas como o método de Newton que só tem convergência local. A teoria é aplicada ao modelo de combustão in-situ, que pode ser reescrito na forma de problema de complementaridade mista, além disso faremos uma comparação com o método FDA-NCP. / In this work, we study the mixed complementarity method for nonlinear parabolic problems, because some can be written as mixed complementarity problems and appear in many applications such as fluid flow in porous media, diffusion, heat flow wrapping phase change. These types of problems have difficulty obtaining the analytical solution. We study the conservation laws and the types of solutions associated with the Riemann Problem, these types of laws are essentially balance laws that express the fact that some substance is balanced. The study of this theory is important because the conservation laws often appear when the parabolic problems are neglected the diffusive terms of second order. We will study a numerical method that allows finding an approximate solution of the exact solution, which is a variation of the Newton’s method for solving nonlinear systems based on an implicit finite difference scheme and a nonlinear algorithm mixed complementarity, FDA-MNCP. The method has the advantage of provide a global convergence in relation to the finite difference method and method of Newton that only has local convergence. The theory is applied to model in-situ combustion, which can be rewritten in the form of mixed complementarity also we do a comparison with the FDA-NCP method.

<p>&nbsp;U okviru ove doktorske disertacije posmatrani su zakoni održanja sa funkcijom fluksa koja ima prekid u x = 0, pri čemu delovi fluksa levo i desno od x = 0 imaju smo po jedan ekstrem. U prvoj glavi se može naći pregled osnovnih pojmova, definicija i teorema. U drugoj&nbsp; glavi su opisani hiperbolični sistemi zakona održanja, slaba re&scaron;enja, kao&nbsp;<br />i numerički postupci za njihovo re&scaron;avanje. U trećoj glavi su predstavljeni&nbsp; diskretni profili darnih talasa. U četvrtoj glavi su opisani zakoni održanja&nbsp; sa prekidnom funkcijom fluksa i ukratko su predstvaljeni rezultati drugih autora iz ove oblasti. U petoj glavi je najpre analizirana tzv. jednačina sa dva fluksa u slučaju kada oba dela fluksa levo i desno od&nbsp; x = 0 imaju minimum, a pri tome se seku u najvi&scaron;e jednoj tačci unutar intervala. Primenom regularizacije na intervalu [&minus;<em>&epsilon;, &epsilon;</em>], za<em> &epsilon;</em> &gt; 0 dovoljno malo, dokazano je postojanje diskretnih udarnih profila za postupak Godunova za zakone održanja sa promenljivom funkcijom fluksa. Definisan je i odgovarajući diskretan uslov entropije, a postojanje entropijskog diskretnog&nbsp; udarnog profila je postavljen kao kriterijum za dopustivost udarnih talasa. Potom je analizirana ista jednačina u slucaju kada deo fluksa levo&nbsp; od x = 0 ima maksimum, a deo fluksa desno od x = 0 minimum, dok se oba dela fluksa seku na&nbsp; krajevima posmatranog intervala. U ovom slučaju, uop&scaron;ten je uslov entropije. U okviru ove glave je prikazano nekoliko numeričkih primera za oba opisana slučaja. Numerički rezultati&nbsp; su dobijeni kori&scaron;cenjem softvera razvijenog za potrebe ove teze u pro<br />gramskom paketu <em>Mathematica</em>.</p> / <p>We consider conservation laws with a flux discontinuity at x = 0, where the flux parts from both left and right hand side of x = 0 have at most one extreme on the&nbsp; observed &nbsp;domain. The first chapter provides elementary definitions and theorems..The second chapter refers to hyperbolic systems of conservation laws, their solutions, and&nbsp; numerical procedures. The third chapter is devoted to discrete&nbsp; shock profiles. The fourth chapter describes conservation laws with discontinuous flux functions and provides basic information upon known results in this field. In the&nbsp; fifth chapter, we first &nbsp;analyse the two-flux equation when both flux parts have a minimum and cross at most&nbsp;&nbsp;&nbsp; at one point in the interior of the domain. Using a flux regularization on the interval [&minus;&epsilon;,&nbsp;&nbsp; &epsilon;], for &epsilon; &gt; 0 small enough, we show the existence of discrete shock profiles for Godunov&rsquo;s scheme for conservation laws with discontinuous flux functions. We also define a discrete entropy condition accordingly, and use the existence of an entropy discrete shock profile as an entropy criterion for shocks. Then we analyse the same problem in the case when the flux part on the left of x = 0 has a maximum and the part on the right of x = 0 has a minimum, whereas the fluxes cross at the edges of the interval. We derive a more general discrete entropy condition in this case. We provide several numerical examples in both of the above mentioned flux cases. All the&nbsp; presented numerical results are obtained using a program written in Mathematica. Finally, in chapter six, we prove the existence of&nbsp; singular shock waves in the case when the graph of one of the flux parts is above the graph of the other one on the entire domain. For that purpose, we use the shadow wave technique. At the end of this chapter, we provide a numerical verification of the obtained singular solution.</p>

<p>U doktorskoj disertaciji posmatrani su Rimanovi problemi kod strogo i slabo hiperboličnih&nbsp;nelinearnih sistema PDJ. U uvodu je predstavljena jednačina zakona održanja u jednoj prostornoj&nbsp;dimenziji i definisani su Ko&scaron;ijevi i Rimanovi problemi. U drugoj glavi, date su osnovne osobine&nbsp;nelinearnih hiperboličnih zakona održanja, uvedeni supojmovi stroge hiperboličnosti i slabog re&scaron;enja&nbsp;zakona održanja. Definisani su Rankin-Igono i entropijski uslovi kao i op&scaron;te re&scaron;enje Rimanovog problema&nbsp;(za dovoljno male početne uslove). U trećoj glavi detaljno je obja&scaron;njena Glimova diferencna &nbsp;&scaron;ema. Metod&nbsp;praćenja talasa predstavljen je u četvrtoj glavi. Pokazano je da se ovom metodom, za dovoljno male&nbsp;početne uslove, dobija stabilno i jedinstveno re&scaron;enje koje u svakom vremenu ima ograničenu totalnu&nbsp;varijaciju. U petoj glavi, posmatrana je jednačina protoka izentropnog gasa u Lagranžovim koordinatama.&nbsp;Uz pretpostavku da je početni uslov ograničen i da ima ograničenu totalnu varijaciju, pokazano je da&nbsp;Ko&scaron;ijev problem ima jedinstveno slabo re&scaron;enje ako je totalna varijacija početnog uslova pomnožena sa &nbsp;0&lt;&epsilon;&lt;&lt; 1 dovoljno mala. Slabo re&scaron;enjedobijeno je metodom praćenja talasa. U glavi &scaron;est ispitana je&nbsp;interakcija dva delta talasa koji su posmatrani kao specijalna vrsta shadowtalasa. U glavi sedam,&nbsp;pokazano je da za proizvoljno velike početne uslove, re&scaron;enje Rimanovog problema jednodimenzionalnog&nbsp;Ojlerovog zakona održanja gasne dinamikepostoji, daje jedinstveno i entropijski dopustivo, uz drugačiju<br />ocenu snaga elementarnih talasa. Data je numerička verifikacija interakcije dva delta talasa kori&scaron;ćenjem&nbsp;metode praćenja talasa.</p> / <p>In this doctoral thesis, Riemann problems for strictly and weakly nonlinear hyperbolic PDE&nbsp;systems were observed. In the introduction, conservation laws in one spatial dimension were presented&nbsp;and the Cauchy and Riemann problems were defined. In the second chapter, the basic properties of&nbsp;nonlinear hyperbolic conservation laws were intorduced, as well as the terms such as strictly hyperbolic&nbsp;system and weak solution of conservation law. Also, Rankine -Hugoniot and entropy conditions were<br />introduced and the general solution to the Riemann problem (for sufficiently small initial conditions) were&nbsp;defined. Glimm&rsquo;s difference scheme was explained in the third chapter. The wave front tracking method&nbsp;was introduced in the fourth chapter. It was shown that, using this method, for sufficiently small initial&nbsp;conditions, it could be obtained a unique solution with bounded total variation for t &ge;0. In the fifth&nbsp;chapter, the Euler equations for isentropic fluid inLagrangian coordinates were observed. Under the&nbsp;assumption that the initial condition was bounded and had bounded total variation, it was shown that the&nbsp;Cauchy problem had a weak unique solution, provided that the total variation of initial condition&nbsp;multiplied by 0&lt;&epsilon;&lt;&lt;1 was sufficiently &nbsp;small. Weak solution was obtained by applying the wave front&nbsp;tracking method. In the sixth chapter, the interaction of two delta shock waves were examined. Delta&nbsp;shock waves were regarded as special kind of shadowwaves. In the chapter seven, it was shown that for&nbsp;arbitrarily large initial conditions, solution to the Riemann problem of one-dimensional Euler&nbsp;conservation laws of gas dynamics existed, it was unique and admissible. New bounds on the strength of&nbsp;elementary waves in the wave front tracking algorithm were given. The numerical verification of two&nbsp;delta shock waves interaction via wave front tracking method was given at the end of the thesis.</p>

<p>Doktorska disertacija posve&para;cena je re&middot;savanju nelinearnih hiperboli&middot;cnih skalarnih zakona odr&middot;zanja u heterogenim sredinama, prou&middot;cavanjem osobina kompaktnosti re&middot;senja familija aproksimativnih jedna&middot;cina. Ta&middot;cnije, u cilju dobijanja re&middot;senja u = u(t; x) problema @ t u + divx f (t; x; u) = 0;uj t=0 = u 0(x); gde su promenljive x 2 R d i t 2 R+<br />, posmatramo familije problema koji na neki na&middot;cin aproksimiraju po&middot;cetni problem, a koje znamo da re&middot;simo, i ispitujemo familije dobijenih re&middot;senja koja zovemo aproksimativna re&middot;senja. Cilj nam je da poka&middot;zemo da je dobijena familija u nekom smislu prekompaktna,<br />tj. da ima konvergentan podniz &middot;cija granica re&middot;sava po&middot;cetni problem.</p> / <p>Doctoral theses is dedicated to solving nonlinear hyperbolic scalar conservation laws in heterogeneous media, by studying compactness properties of the family of solutions to approximate problems. More precise, in order to obtain solution u = u(t; x) to the problem @ t u + divx f (t; x; u) = 0; uj t=0 = u 0 (x); (4.18) where x 2 R d and t 2 R+<br />, we study the solutions of the families of problems that, in some way, approximate previously mentioned problem, which we know how to solve. We call those solutions approximate solutions. The aim is to show that the obtained family is in some sense precompact, i.e. has convergent subsequence that solves the problem (4.18).</p>

No description available.