Made available in DSpace on 2014-06-12T18:33:15Z (GMT). No. of bitstreams: 2 arquivo8700_1.pdf: 540197 bytes, checksum: e74b5744a487d8c40b6fa2123078eda1 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2007 / Universidade Federal de Sergipe / Discutimos existência e unicidade de soluções clássicas para a equações de Burgers com viscosidade e para o sistema de Navier-Stokes em duas e três dimensões espaciais. Provamos existência e unicidade de soluções locais no tempo para cada um dos modelos estudados. Além disso, para a equação de Burgers e para as equações de Navier-Stokes bidimensionais, utilizamos estimativas a priori para garantir a existência global de soluções. Indicamos por que o método não pode ser aplicado para o caso tridimensional

We investigate the use of the Method of Fundamental Solutions (MFS) for the numerical solution of elliptic problems arising in engineering. In particular, we examine harmonic and biharmonic problems with boundary singularities, certain steady-state free boundary flow problems and inhomogeneous problems. The MFS can be viewed as an indirect boundary method with an auxiliary boundary. The solution is approximated by a linear combination of fundamental solutions of the governing equation which are expressed in terms of sources located outside the domain of the problem. The unknown coefficients in the linear combination of fundamental solutions and the location of the sources are determined so that the boundary conditions are satisfied in a least squares sense. The MFS shares the same advantages of the boundary methods over domain discretisation methods. Moreover, it is relatively easy to implement, it is adaptive in the sense that it takes into account sharp changes in the solution and/or in the geometry of the domain and it can easily incorporate complicated boundary conditions.

A modal finite element method is presented for the steady state and transient analyses of the plane flow of incompressible Newtonian fluid. The governing restricted functional is discretized with a high precision triangular stream function finite element. Eigenvalue analysis is carried out on the resulting discretized problem, under the assumption that the nonlinear convective term is equal to zero. After truncating at various levels of approximation to obtain a reduced number of modes, the transformation to the new vector space, spanned by these modes is performed. Advantage is taken of the ..symmetric and the antisymmetric properties of the modes in order to simplify the calculations. The Lagrange multipliers technique is employed to {incorporate the nonhomo-geneous boundary conditions. The steady state analysis is carried out by utilizing the Newton-Raphson iterative procedure. The algorithm for transient analysis is based upon backward finite differences in time. Numerical results are presented for the fully developed plane Poiseuille flow, the flow in a square cavity, and the flow over a circular cylinder problems. These resultscfor the steady state are compared with the results obtained by direct finite element approach on the same grids and the results obtained by finite differences technique. It is concluded that the number of modes, which are to be retained in the analysis in order to achieve reasonable results, increases with the refinement of the finite element grid. Furthermore, the choice of modes to be used depends on the problem. Finally it is established, that this new modal method yields good results in the range of moderate Reynolds numbers with about 50% or less of the modes of the problem. This, in turn, means that the time integrations can be performed on a greatly reduced number of equations and hence potential savings in computer time are significant. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Orientador: Jose Luiz Boldrini / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-19T10:51:31Z (GMT). No. of bitstreams: 1 Damazio_PedroDanizete_M.pdf: 1522946 bytes, checksum: 4199e3d0be77a05285779aadb0bddd3a (MD5) Previous issue date: 1994 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática

No description available.

Neste trabalho estudamos a existência de soluções de equações do tipo Navier-Stokes com retardo na força externa e no termo n~ao linear. Usando a teoria de semigrupos estudamos a existência de soluções para um problema da forma \'d. SUP. dt u(t) - v\'delta\'u(t) + (F(t, \'u IND.t\'). abla)u(t) + abla p = g(t, \'u IND.t\'), em \'OMEGA\' x (0, T), div u(t) = 0 em \'OMEGA\' x (0, T), u(0, x) = \'u POT.0 (x) x PERTENCE a \' OMEGA\', u(t, x) = 0 t > 0, X \'PERTENCE A\' \' PARTIAL\' \'OMEGA\', u(t, x) =\\phi (t, x) t \'PERTENCE A\' (- \'INFINITO\', 0) x \'PERTENCE A\' \'OMEGA\', onde F9t, \'uIND.t) = INT.IND.t SUP. -\' INFINITO\' \' ALFA1(s-t)u(s)ds + u(t-r), g(t, \'u IND.t\') = INT. SUP. t IND. - INFINITO \'BETA\' (s-t)u(s)ds. Similarmente, usando a tecnica de aproximac~oes de Galerkin, estudamos o problema anterior com F(.) e g(.) dadas por f(t; \'u INDS.t\') = u(t-r(t)); e g(t; \'u IND.t\') = G(u(t-\'rô\' (t))), para alguma função G apropriada. Neste caso, também estudamos a estabilidade de soluções estacionarias / In this work we stuy the existence of solutions for a Navier-Stokes typt equations with delay in the external force and in the nonlinear term. Using the semi-group theory we study the existence of solution for a problem in the form \'d. SUP. dt u(t) - v\'delta\'u(t) + (F(t, \'u IND.t\'). abla)u(t) + abla p = g(t, \'u IND.t\'), ijn \'OMEGA\' x (0, T), div u(t) = 0 in \'OMEGA\' x (0, T), u(0, x) = \'u POT.0 (x) x \'IT BELONGS \' OMEGA\', u(t, x) = 0 t > 0, X \'IT BELONGS\' \'PARTIAL\' \'OMEGA\', u(t, x) =\\phi (t, x) t \'IT BELONGS\' (- \'INFINITY\', 0) x \'IT BELONGS\' \'OMEGA\', where F(t, \'u .t) = INT.IND.t SUP. -\' INFINITY\' \' ALFA(s-t)u(s)ds + u(t-r), g(t, \'u IND.t\') = INT. SUP. t IND. - INFINITY \'BETA\' (s-t)u(s)ds. On another hand using the Galerkin appreoximations method we study the same with F(.) e g(.) given by f(t; \'u INDS.t\') = u(t-r(t)); and g(t; \'u IND.t\') = G(u(t-\'rô\' (t))), for some G appropriated. In thiis case, we study also the stability of stanionary solutions

No description available.

Neste trabalho estudamos a existência de soluções de equações do tipo Navier-Stokes com retardo na força externa e no termo n~ao linear. Usando a teoria de semigrupos estudamos a existência de soluções para um problema da forma \'d. SUP. dt u(t) - v\'delta\'u(t) + (F(t, \'u IND.t\'). abla)u(t) + abla p = g(t, \'u IND.t\'), em \'OMEGA\' x (0, T), div u(t) = 0 em \'OMEGA\' x (0, T), u(0, x) = \'u POT.0 (x) x PERTENCE a \' OMEGA\', u(t, x) = 0 t > 0, X \'PERTENCE A\' \' PARTIAL\' \'OMEGA\', u(t, x) =\\phi (t, x) t \'PERTENCE A\' (- \'INFINITO\', 0) x \'PERTENCE A\' \'OMEGA\', onde F9t, \'uIND.t) = INT.IND.t SUP. -\' INFINITO\' \' ALFA1(s-t)u(s)ds + u(t-r), g(t, \'u IND.t\') = INT. SUP. t IND. - INFINITO \'BETA\' (s-t)u(s)ds. Similarmente, usando a tecnica de aproximac~oes de Galerkin, estudamos o problema anterior com F(.) e g(.) dadas por f(t; \'u INDS.t\') = u(t-r(t)); e g(t; \'u IND.t\') = G(u(t-\'rô\' (t))), para alguma função G apropriada. Neste caso, também estudamos a estabilidade de soluções estacionarias / In this work we stuy the existence of solutions for a Navier-Stokes typt equations with delay in the external force and in the nonlinear term. Using the semi-group theory we study the existence of solution for a problem in the form \'d. SUP. dt u(t) - v\'delta\'u(t) + (F(t, \'u IND.t\'). abla)u(t) + abla p = g(t, \'u IND.t\'), ijn \'OMEGA\' x (0, T), div u(t) = 0 in \'OMEGA\' x (0, T), u(0, x) = \'u POT.0 (x) x \'IT BELONGS \' OMEGA\', u(t, x) = 0 t > 0, X \'IT BELONGS\' \'PARTIAL\' \'OMEGA\', u(t, x) =\\phi (t, x) t \'IT BELONGS\' (- \'INFINITY\', 0) x \'IT BELONGS\' \'OMEGA\', where F(t, \'u .t) = INT.IND.t SUP. -\' INFINITY\' \' ALFA(s-t)u(s)ds + u(t-r), g(t, \'u IND.t\') = INT. SUP. t IND. - INFINITY \'BETA\' (s-t)u(s)ds. On another hand using the Galerkin appreoximations method we study the same with F(.) e g(.) given by f(t; \'u INDS.t\') = u(t-r(t)); and g(t; \'u IND.t\') = G(u(t-\'rô\' (t))), for some G appropriated. In thiis case, we study also the stability of stanionary solutions

Orientador: Lucas Catão de Freitas Ferreira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T15:06:30Z (GMT). No. of bitstreams: 1 Alves_BrunoFerreira_M.pdf: 943114 bytes, checksum: 70e3cdb3ee60ae3ed29a79cfeded3f59 (MD5) Previous issue date: 2012 / Resumo: Estudamos as equações de Navier-Stokes (NS) em...Observação: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital / Abstract: We study the Navier-Stokes equations (NS) in...Note: The complete abstract is available with the full electronic document / Mestrado / Matematica / Mestre em Matemática

Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática / This thesis is focused on the Navier{Stokes system for incompressible uids with either Dirichlet or nonlinear Navier{slip boundary conditions. For these systems, we exploit some ideas in the context of the control theory and inverse source problems. The thesis is divided in three parts. In the rst part, we deal with the local null controllability for the Navier{Stokes system with nonlinear Navier{slip conditions, where the internal controls have one vanishing component. The novelty of the boundary conditions and the new estimates with respect to the pressure term, has allowed us to extend previous results on controllability for the Navier{ Stokes system. The main ingredients to build our result are the following: a new regularity result for the linearized system around the origin, and a suitable Carleman inequality for the adjoint system associated to the linearized system. Finally, xed point arguments are used in order to conclude the proof. In the second part, we deal with an inverse source problem for the N- dimensional Stokes system from local and missing velocity measurements. More precisely, our main result establishes a reconstruction formula for the source F(x; t) = (t)f(x) from local observations of N ����� 1 components of the velocity. We consider that f(x) is an unknown vectorial function, meanwhile (t) is known. As a consequence, the uniqueness is achieved for f(x) in a suitable Sobolev space. The main tools are the following: connection between null controllability and inverse problems throughout a result on null controllability for the N- dimensional Stokes system with N ����� 1 scalar controls, spectral analysis of the Stokes operator and Volterra integral equations. We also implement this result and present several numerical experiments that show the feasibility of the proposed recovering formula. Finally, the last chapter of the thesis presents a partial result of stability for the Stokes system when we consider a source F(x; t) = R(x; t)g(x), where R(x; t) is a known vectorial function and g(x) is unknown. This result involves the Bukhgeim-Klibanov method for solving inverse problems and some topics in degenerate Sobolev spaces.