Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico

LINS, Filipe C. A. et al. Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico. In: CONGRESSO BRASILEIRO DE PESQUISA E DESENVOLVIMENTO EM PETRÓLEO E GÁS, 5. 2009, Fortaleza, CE. Anais... Fortaleza: CBPDPetro, 2009.

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

Dynamic stationary response of reinforced plates by the boundary element method

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state ( membrane) and for the out-of-plane state ( bending). These uncoupled systems are joined to formamacro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).

Traveling waves in the Lethargic Crab Disease

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

New steps on Sobolev orthogonality in two variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa-Holm equation

In this Letter we investigate Lie symmetries of a (2 + 1)-dimensional integrable generalization of the Camassa-Holm (CH) equation. Through the similarity reductions we obtain four different (1 + 1)-dimensional systems of partial differential equations in which one of them turns out to be a (1 + 1)-dimensional CH equation. We establish their integrability by providing the Lax pair for all of them. Further, we present a brief analysis for some types of particular solutions which include the cuspon, peakon and soliton solutions for the two-dimensional generalization of the CH equation. (C) 2000 Published by Elsevier B.V. B.V.

On the extended applications of Homogenous Balance Method

In this paper, we study the travelling wave reductions for certain (2 + 1)- and (3 + 1)-dimensional physically important nonlinear evolutionary equations by using the recently proposed Homogenous Balance Method (HBM). Through this analysis we explore certain new solutions for the equations we have studied. (C) 2001 Published by Elsevier B.V.

Symmetry analysis of an integrable reaction-diffusion equation

In this paper, we investigate the invariance and integrability properties of an integrable two-component reaction-diffusion equation. We perform Painleve analysis for both the reaction-diffusion equation modelled by a coupled nonlinear partial differential equations and its general similarity reduced ordinary differential equation and confirm its integrability. Further, we perform Lie symmetry analysis for this model. Interestingly our investigations reveals a rich variety of particular solutions, which have not been reported in the literature, for this model. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Homoclinic bifurcations in reversible Hamiltonian systems

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u(iv) + au - u +f(u, b) = 0 as a model, where fis an analytic function and a, b real parameters. These equations are important in several physical situations such as solitons and in the existence of finite energy stationary states of partial differential equations, but no assumptions of any kind of discrete symmetry is made and the analysis here developed can be extended to others Hamiltonian systems and successfully employed in situations where standard methods fail. We reduce the problem of computing these orbits to that of finding the intersection of the unstable manifold with a suitable set and then apply it to concrete situations. We also plot the homoclinic values configuration in parameters space, giving a picture of the structural distribution and a geometrical view of homoclinic bifurcations. (c) 2005 Published by Elsevier B.V.

Non-local interactions and the dynamics of dispersal in immature insects

A simple mathematical model is developed to explain the appearance of oscillations in the dispersal of larvae from the food source in experimental populations of certain species of blowflies. The life history of the immature stage in these flies, and in a number of other insects, is a system with two populations, one of larvae dispersing on the soil and the other of larvae that burrow in the soil to pupate. The observed oscillations in the horizontal distribution of buried pupae at the end of the dispersal process are hypothesized to be a consequence of larval crowding at a given point in the pupation substrate. It is assumed that dispersing larvae are capable of perceiving variations in density of larvae buried at a given point in the substrate of pupation, and that pupal density may influence pupation of dispersing larvae. The assumed interaction between dispersing larvae and the larvae that are burrowing to pupate is modeled using the concept of non-local effects. Numerical solutions of integro-partial differential equations developed to model density-dependent immature dispersal demonstrate that variation in the parameter that governs the non-local interaction between dispersing and buried larvae induces oscillations in the final horizontal distribution of pupae. (C) 1997 Academic Press Limited.

The application of interpolating MLS approximations to the analysis of MHD flows

The element-free Galerkin method (EFGM) is a very attractive technique for solutions of partial differential equations, since it makes use of nodal point configurations which do not require a mesh. Therefore, it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometry problems. However, the imposition of boundary conditions is not straightforward, since the EFGM is based on moving-least-squares (MLS) approximations which are not necessarily interpolants. This feature requires, for instance, the introduction of modified functionals with additional unknown parameters such as Lagrange multipliers, a serious drawback which leads to poor conditionings of the matrix equations. In this paper, an interpolatory formulation for MLS approximants is presented: it allows the direct introduction of boundary conditions, reducing the processing time and improving the condition numbers. The formulation is applied to the study of two-dimensional magnetohydrodynamic flow problems, and the computed results confirm the accuracy and correctness of the proposed formulation. (C) 2002 Elsevier B.V. All rights reserved.

On the integrable perturbations of the Camassa-Holm equation

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure. © 2000 American Institute of Physics.

Analytical/numerical hybrid solution for one-dimensional ablation problem

Ablation is a thermal protection process with several applications in engineering, mainly in the field of airspace industry. The use of conventional materials must be quite restricted, because they would suffer catastrophic flaws due to thermal degradation of their structures. However, the same materials can be quite suitable once being protected by well-known ablative materials. The process that involves the ablative phenomena is complex, could involve the whole or partial loss of material that is sacrificed for absorption of energy. The analysis of the ablative process in a blunt body with revolution geometry will be made on the stagnation point area that can be simplified as a one-dimensional plane plate problem, hi this work the Generalized Integral Transform Technique (GITT) is employed for the solution of the non-linear system of coupled partial differential equations that model the phenomena. The solution of the problem is obtained by transforming the non-linear partial differential equation system to a system of coupled first order ordinary differential equations and then solving it by using well-established numerical routines. The results of interest such as the temperature field, the depth and the rate of removal of the ablative material are presented and compared with those ones available in the open literature.

Simulations of incompressible fluid flows by a least squares finite element method

In this work simulations of incompressible fluid flows have been done by a Least Squares Finite Element Method (LSFEM) using velocity-pressure-vorticity and velocity-pressure-stress formulations, named u-p-ω) and u-p-τ formulations respectively. These formulations are preferred because the resulting equations are partial differential equations of first order, which is convenient for implementation by LSFEM. The main purposes of this work are the numerical computation of laminar, transitional and turbulent fluid flows through the application of large eddy simulation (LES) methodology using the LSFEM. The Navier-Stokes equations in u-p-ω and u-p-τ formulations are filtered and the eddy viscosity model of Smagorinsky is used for modeling the sub-grid-scale stresses. Some benchmark problems are solved for validate the numerical code and the preliminary results are presented and compared with available results from the literature. Copyright © 2005 by ABCM.

Detecção de bordas em imagens digitais através de um processo de difusão anisotrópica não linear

The edges detection model by a non-linear anisotropic diffusion, consists in a mathematical model of smoothing based in Partial Differential Equation (PDE), alternative to the conventional low-pass filters. The smoothing model consists in a selective process, where homogeneous areas of the image are smoothed intensely in agreement with the temporal evolution applied to the model. The level of smoothing is related with the amount of undesired information contained in the image, i.e., the model is directly related with the optimal level of smoothing, eliminating the undesired information and keeping selectively the interest features for Cartography area. The model is primordial for cartographic applications, its function is to realize the image preprocessing without losing edges and other important details on the image, mainly airports tracks and paved roads. Experiments carried out with digital images showed that the methodology allows to obtain the features, e.g. airports tracks, with efficiency.