Ce travail de thèse, propose un schéma numérique d'ordre élevé, distribuantle résidu (RD) pour l'approximation d'un problème hydro-sédimentairehyperbolique non conservatif, couplant les modèles de Grass et de Saint-Venant. Il fait appel à des méthodes de Runge-Kutta à variation totale diminuanteet de stabilisation (méthode de décentrement amont, dit Upwind),avec ou sans adjonction de limiteurs et présente de bonnes propriétés.L'une des facettes importantes de ce qui a été réalisée, repose sur la conceptionet le développement d'un programme Python 2D-espace, sous la formed'un logiciel faisant appel à un ensemble de modules créés pour l'occasion.Le développement du code de calcul, qui se propose d'approcher la solutiondu problème hydro-sédimentaire, a été e_ectué avec une orientation Objetet pour être e_cace sur calculateur parallèle (utilisant le parallélisme multithreadsOpenMP). L'une des particularités du schéma numérique dans cecadre, est liée à son application à des quadrangles.Un programme 1D-espace, qui se présente également sous forme de logiciel,a aussi été mis en place. Pour des raisons de portabilité et d'e_catité, il aété écrit multilangages (Python-Fortran : via numpy.ctypes pour Python etvia l'interface standard de Fortran pour C). Le schéma RD avec ou sansadjonction de limiteurs de _ux, a été implémenté à la manière d'un schémaprédicteur-correcteur. Des comparaisons avec d'autres schémas ont été e_ectuées a_n de montrer son e_cacité, son ordre de précision élevé a été mis enévidence, et la C-propriété a été testée. Les tests ont révélé que, pour le casd'un transport d'un pro_l sédimentaire parabolique, c'est le limiteur de _uxMUSCL MinMod, qui est le plus adapté parmi ceux testés.Dans le cas scalaire, des tests numériques ont été réalisés a_n de validerle second ordre de précision. / The present work, proposes a high order Residual Distribution (RD) numericalscheme to solve the non conservative hyperbolic problem, coupling Shallow Water and Grass equations. It uses Total Value Diminishing Runge Kutta and stabilisation Upwind methods, with or without limiters. It also has some good properties.A part of the work realised in this thesis, is about the conception and the developpement of a 2D-space Python program, under the form of a software,using a set of moduls created for the occasion. the code developpement, whichis said to approach the _uid-sediment model, coupling Shallow-Water and sedimentequations, has been made with an Object orientation and in orderto be e_cient on parallel architecture (using multithreads OpenMP parallelism). One of the features of the scheme in this case, is due to its application on quadrangles.A 1D-space program, also writen as a software, has been estabished. In order to be portable and e_cient, It has been developped multilinguals (Python- Fortran : by numpy.ctypes for Python and by standart interface FORTRAN for C). The RD scheme with or without Flux Limiters, has been implemented like predictor-corrector one. Comparisons with other schemes results have been realised, in order to show its e_ciency, moreover its high order accuracy has been focus on, and the C-proprerty has been tested. The tests show that MUSCL MinMod _ux limiters, is the most adaptated for a dune test case, between all tested.In the scalar case, numerical tests have been realised, for validating the secondorder of accuracy.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-04-06T20:35:55Z No. of bitstreams: 1 ILIANA DE OLIVEIRA GUIMARÃES - TESE PPG-CEMat 2014..pdf: 50160837 bytes, checksum: 767ec5c57ef7319ccbd6b2d10571ff53 (MD5) / Made available in DSpace on 2018-04-06T20:35:55Z (GMT). No. of bitstreams: 1 ILIANA DE OLIVEIRA GUIMARÃES - TESE PPG-CEMat 2014..pdf: 50160837 bytes, checksum: 767ec5c57ef7319ccbd6b2d10571ff53 (MD5) Previous issue date: 2014-08-29 / Capes / O processo Bayer, utilizado para a obtenção de alumina, usa bauxita como matériaprima. Este processo abrange quatro estágios: digestão, clarificação, precipitação e calcinação. O resíduo gerado na etapa de calcinação é um produto com pequeno tamanho de partícula, conhecido como ESP dust. Esta pesquisa teve como objetivo desenvolver membranas cerâmicas tubulares utilizando em sua composição o ESP dust, um pó de alumina do precipitador eletrostático, e uma argila bentonítica. Inicialmente, foi realizada a caracterização dos precursores. Foram analisadas duas amostras do resíduo, uma do resíduo bruto e outra do resíduo calcinado a 1200°C. Essas amostras apresentaram um alto teor de alumina nas suas composições químicas. As fases gibbsita e α-alumina foram identificadas no resíduo bruto e, após sua calcinação, a gibbsita foi totalmente transformada em α-alumina. Observou-se que não houve alterações significativas no tamanho e morfologia das partículas após a calcinação, mas durante este processo, as partículas tornaram-se porosas, provavelmente devido às mudanças de fase cristalina da alumina e a saída de água dos cristais. Dentre vinte formulações diferentes testadas para produzir membranas cerâmicas, quatro composições apresentaram os melhores resultados com relação ao processamento por extrusão: duas composições com o resíduo bruto e duas com o resíduo calcinado. Neste trabalho, as membranas tubulares compostas pelo resíduo de alumina e pela argila bentonítica foram produzidas por extrusão e foram sinterizadas a 900, 1000 e 1100°C. Foi observado que as membranas produzidas apresentaram superfícies com poros distribuídos. A porosidade aparente variou entre 47,70% (composição com 60% de resíduo calcinado e 40% de argila bentonítica sinterizada a 1000°C) e 58,40% (composição com 70% de resíduo bruto e 30% de argila bentonítica sinterizada a 1000°C). Foram realizados ensaios de fluxo tangencial com água deionizada em pressões de 1,0; 1,5 e 2,0 Bar. O maior fluxo permeado (909,24L/h.m2) foi observado para as membranas feitas da composição contendo 70% de resíduo bruto e 30% de argila bentonítica sinterizadas a 1100°C, aplicando pressão de 1 Bar. / The Bayer process uses bauxite as raw material to obtain alumina. This process includes four stages: digestion, clarification, precipitation and calcination. The waste generated during the calcination step is a product with small particle size, known as ESP dust. This research aimed to develop tubular ceramic membranes using in its composition the ESP dust, an alumina powder from electrostatic precipitator, and a bentonite clay. Initially, the characterization of the precursors was performed. Two samples were studied, one from crude residue and other from calcined residue at 1200°C. These samples showed a high content of alumina in chemical compositions. The gibbsite and α-alumina phases were identified in crude residue and after calcination gibbsite was completely transformed into α-alumina. Were observed no significant changes in particles size and morphology after calcination, but during this process, the particles become porous, probable due changes in crystalline phase of alumina and the water outlet of crystals. Among twenty different formulations tested to produce ceramic membranes, four compositions showed better results with regard to the extrusion processing: two compositions with crude residue and two with calcined residue. In this paper, tubular membranes produced from alumina residue and bentonite clay were sintered at 900, 1000 and 1100°C. It was observed that the produced membranes had surfaces with distributed pores. The apparent porosity was between 47.70% (composition with 60% of calcined residue and 40% of bentonite clay sintered at 1000°C) and 58.40% (composition with 70% of crude residue and 30% of bentonite clay sintered at 1000°C). Tangential flow tests were performed with deionized water at pressures of 1.0; 1.5 and 2.0 Bar. Higher permeate flow rate (909,24L/h.m2) was observed for membranes made of a composition containing crude residue (70%) and bentonite clay (30%) sintered at 1100°C, applying pressure of 1 bar.

Nous nous intéressons dans cette thèse, à l’étude des méthodes itératives pour la résolutiond’équations matricielles de grande taille : Lyapunov, Sylvester, Riccati et Riccatinon symétrique.L’objectif est de chercher des méthodes itératives plus efficaces et plus rapides pour résoudreles équations matricielles de grande taille. Nous proposons des méthodes itérativesde type projection sur des sous espaces de Krylov par blocs Km(A, V ) = Image{V,AV, . . . ,Am−1V }, ou des sous espaces de Krylov étendus par blocs Kem(A, V ) = Image{V,A−1V,AV,A−2V,A2V, · · · ,Am−1V,A−m+1V } . Ces méthodes sont généralement plus efficaces et rapides pour les problèmes de grande dimension. Nous avons traité d'abord la résolution numérique des équations matricielles linéaires : Lyapunov, Sylvester, Stein. Nous avons proposé une nouvelle méthode itérative basée sur la minimisation de résidu MR et la projection sur des sous espaces de Krylov étendus par blocs Kem(A, V ). L'algorithme d'Arnoldi étendu par blocs permet de donner un problème de minimisation projeté de petite taille. Le problème de minimisation de taille réduit est résolu par différentes méthodes directes ou itératives. Nous avons présenté ainsi la méthode de minimisation de résidu basée sur l'approche global à la place de l'approche bloc. Nous projetons sur des sous espaces de Krylov étendus Global Kem(A, V ) = sev{V,A−1V,AV,A−2V,A2V, · · · ,Am−1V,A−m+1V }. Nous nous sommes intéressés en deuxième lieu à des équations matricielles non linéaires, et tout particulièrement l'équation matricielle de Riccati dans le cas continu et dans le cas non symétrique appliquée dans les problèmes de transport. Nous avons utilisé la méthode de Newtown et l'algorithme MINRES pour résoudre le problème de minimisation projeté. Enfin, nous avons proposé deux nouvelles méthodes itératives pour résoudre les équations de Riccati non symétriques de grande taille : la première basée sur l'algorithme d'Arnoldi étendu par bloc et la condition d'orthogonalité de Galerkin, la deuxième est de type Newton-Krylov, basée sur la méthode de Newton et la résolution d'une équation de Sylvester de grande taille par une méthode de type Krylov par blocs. Pour toutes ces méthodes, les approximations sont données sous la forme factorisée, ce qui nous permet d'économiser la place mémoire en programmation. Nous avons donné des exemples numériques qui montrent bien l'efficacité des méthodes proposées dans le cas de grandes tailles. / In this thesis, we focus in the studying of some iterative methods for solving large matrix equations such as Lyapunov, Sylvester, Riccati and nonsymmetric algebraic Riccati equation. We look for the most efficient and faster iterative methods for solving large matrix equations. We propose iterative methods such as projection on block Krylov subspaces Km(A, V ) = Range{V,AV, . . . ,Am−1V }, or block extended Krylov subspaces Kem(A, V ) = Range{V,A−1V,AV,A−2V,A2V, · · · ,Am−1V,A−m+1V }. These methods are generally most efficient and faster for large problems. We first treat the numerical solution of the following linear matrix equations : Lyapunov, Sylvester and Stein matrix equations. We have proposed a new iterative method based on Minimal Residual MR and projection on block extended Krylov subspaces Kem(A, V ). The extended block Arnoldi algorithm gives a projected minimization problem of small size. The reduced size of the minimization problem is solved by direct or iterative methods. We also introduced the Minimal Residual method based on the global approach instead of the block approach. We projected on the global extended Krylov subspace Kem(A, V ) = Span{V,A−1V,AV,A−2V,A2V, · · · ,Am−1V,A−m+1V }. Secondly, we focus on nonlinear matrix equations, especially the matrix Riccati equation in the continuous case and the nonsymmetric case applied in transportation problems. We used the Newton method and MINRES algorithm to solve the projected minimization problem. Finally, we proposed two new iterative methods for solving large nonsymmetric Riccati equation : the first based on the algorithm of extended block Arnoldi and Galerkin condition, the second type is Newton-Krylov, based on Newton’s method and the resolution of the large matrix Sylvester equation by using block Krylov method. For all these methods, approximations are given in low rank form, wich allow us to save memory space. We have given numerical examples that show the effectiveness of the methods proposed in the case of large sizes.