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In this paper, artificial neural networks are used for predicting single fiber efficiency in the process of removing smaller particles from gas stream by fiber filters. For this, numerical simulations are obtained of a classic model of literature for fiber efficiency, which is numerically solved along with the convection diffusion equation in polar coordinates for particle concentration, with associated initial and boundary conditions. A sufficient number of examples from two numerical simulations are employed to construct a database, from which parameters of a novel neural model are adjusted. This model is constructed based on the back propagation algorithm in order to map two features, namely Peclet number and packing density, which are extracted from the numerical simulations into the corresponding single fiber efficiency. The results indicate that the developed neural model can be trained in a reasonable computational time and is capable of estimating single fiber efficiency from examples of the test set with a maximum error of 1.7%.

SUMMARY A bounded upwinding scheme for numerical solution of hyperbolic conservation laws and Navier–Stokes equations is presented. The scheme is based on convection boundedness criterion and total variation diminishing stability criteria and developed by employing continuously differentiable functions. The accuracy of the scheme is verified by assessing the error and observed convergence rate on 1-D benchmark test cases. A comparative study between the new scheme and conventional total variation diminishing/convection boundedness criterion-based upwind schemes to solve standard nonlinear hyperbolic conservation laws is also accomplished. The scheme is then examined in the simulation of Newtonian and non-Newtonian fluid flows of increasing complexity; a satisfactory agreement has been observed in terms of the overall behavior. Finally, the scheme is used to study the hydrodynamics of a gas-solid flow in a bubbling fluidized bed. Copyright © 2013 John Wiley & Sons, Ltd.

Made available in DSpace on 2018-12-11T17:07:23Z (GMT). No. of bitstreams: 0 Previous issue date: 2016-11-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Plant species can be classified into heterobaric and homobaric, depending on whether their leaves present bundle sheath extensions (BSEs) (heterobaric) or not (homobaric). Incidences of the two leaf types seem to be related to growth environment and the light stratification. The Brazilian Cerrado and seasonal semideciduous forests are contrasting environments mainly with regard to irradiance and air humidity. However, studies comparing the distributions of homobaric and heterobaric species in these vegetation types are lacking. We investigate the presence/absence of leaf BSEs across diverse habits (herbs, shrubs and trees) in a seasonal semideciduous forest, cerrado sensu stricto (open physiognomy) and cerradão (forest physiognomy) to evaluate the influence of plant habit and growth environment on the distribution of homobaric and heterobaric species. Leaves from 131 species in 54 angiosperm families were analysed using standard methods of light microscopy. The distribution of the different leaf types in each environment was analysed using the χ2 test and Fisher's exact test (P

SUMMARY This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the Navier–Stokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient. Copyright © 2012 John Wiley & Sons, Ltd.

The fluid flow of the liquid phase in the sol-gel-dip-coating process for SnO2 thin film deposition is numerically simulated. This calculation yields useful information on the velocity distribution close to the substrate, where the film is deposited. The fluid modeling is done by assuming Newtonian behavior, since the linear relation between shear stress and velocity gradient is observed. Besides, very low viscosities are used. The fluid governing equations are the Navier–Stokes in the two dimensional form, discretized by the finite difference technique. Results of optical transmittance and X-ray diffraction on films obtained from colloidal suspensions with regular viscosity, confirm the substrate base as the thickest part of the film, as inferred from the numerical simulation. In addition, as the viscosity increases, the fluid acquires more uniform velocity distribution close to the substrate, leading to more homogenous and uniform films.

This article deals with the study of the development and application of the high-order upwind ADBQUICKEST scheme, an adaptative bounded version of the QUICKEST for unsteady problems (Commun. Numer. Meth. Engng 2007; 23:419-445), employing both linear and nonlinear convection term discretization. This scheme is applicable to a wide range of computational fluid dynamics problems, where transport phenomena are of special importance. In particular, the performance of the scheme is assessed through an extensive numerical simulation study of advection-diffusion problems. The scheme, implemented in the context of finite difference methodology, combines a good approximation of shocks (or discontinuities) with a good approximation of the smooth parts of the solutions. In order to assess the performance of the scheme, seven problems are solved, namely (a) advection of scalars; (b) non-linear viscous Burgers equation; (c) Euler equations of gas dynamics; (d) Newtonian flow in a channel; (e) axisymmetric Newtonian jet flow; (f) axisymmetric non-Newtonian (generalized Newtonian) flow in a pipe; and (g) collapse of a fluid column. The numerical experiments clearly show that the scheme provides more consistent solutions than those found in the literature. From the study, the flexibility and robustness of the ADBQUICKEST scheme is confirmed by demonstrating its capability to solve a variety of linear and nonlinear problems with and without discontinuous solutions.

This work presents a numerical method for solving three-dimensional (3D) viscoelastic unsteady free surface flows governed by the Oldroyd-B constitutive equation. It is an extension of the two-dimensional (2D) technique introduced by Tome et al. [M.F. Tome, N. Mangiavacchi, J.A. Cuminato, A. Castelo, S. McKee, A numerical technique for solving unsteady viscoelastic free surface flows, J. Non-Newt. Fluid Mech. 106 (2002) 61–106]. The governing equations are solved by a finite difference method on a 3D-staggered grid. Marker particles are employed to describe the fluid providing both visualization and the location of the free surface. The numerical technique is validated by using an exact solution of the flow of an Oldroyd-B fluid inside a 3D-pipe. Numerical results include the simulation of the transient extrudate swell and jet buckling.

In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC technique dates back to the early 1960s at the Los Alamos Laboratories and this article starts with a historical review, and then a brief discussion of related techniques. Improvements since the early days of MAC (and the Simplified MAC - SMAC) include automatic time-stepping, the use of the conjugate gradient method to solve the Poisson equation for the corrected velocity potential, greater efficiency through stripping out the virtual particles (markers) other than those near the free surface, and more accurate approximations of the free surface boundary conditions, the addition of bounded high accuracy upwinding for the convected terms (thereby being able to solve higher Reynolds number flows), and a (dynamics) flow visualization facility. More recently, effective techniques for surface and interfacial flows and, in particular, for accurately tracking the associated surface(s)/interface(s) including moving contact angles have been developed. This article will concentrate principally on a three-dimensional version of the SMAC method. It will eschew both code verification and model validation; instead it will emphasize the applications that the MAC method can solve, from multiphase flows to rheology.

In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynoldsκ-ɛmodel and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005)) is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994)) methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of theFreeflowsimulation system (Castello et al. (2000)). A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.

This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier-Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110:171-186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199-210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions.

The present work is concerned with a semi-implicit modification of the GENSMAC method for solving the two-dimensional time-dependent incompressible Navier-Stokes equations in primitive variables formulation with a free surface. A projection method is employed to uncouple the velocity components and pressure, thus allowing the solution of each variable separately (a segregated approach). The viscous terms are treated by the implicit backward method in time and a centered second order method in space, and the nonlinear convection terms are explicitly approximated by the high order upwind variable-order nonoscillatory scheme method in space. The boundary conditions at the free surface couple the otherwise segregated velocity and pressure fields. The present work proposes a method that allows the segregated solution of free surface flow problems to be computed by semi-implicit schemes that preserve the stability conditions of the related coupled semi-implicit scheme. The numerical method is applied to both the simulation of free surface and to confined flows. The numerical results demonstrate that the present technique eliminates the parabolic stability restriction required by the original explicit GENSMAC method, and also found in segregated semi-implicit methods with time-lagged boundary conditions. For low Reynolds number flows, the method is robust and very efficient when compared to the original GENSMAC method.

This work presents a numerical technique for solving three-dimensional generalized Newtonian free surface flows. It is an extension to three dimensions of the technique introduced by Tome et al. [M.F. Tome, B. Duffy, S. McKee, A numerical technique for solving unsteady non-Newtonian free surface flows, J. Non-Newtonian Fluid Mech. 62 (1996) 9–34] but additionally includes many other features. The governing equations are solved by a finite difference method on a staggered grid. It uses marker particles to describe the fluid; these particles provide the location and visualization of the fluid free surface. As currently implemented, the present method can simulate generalized Newtonian flow in which the viscosity is modelled using the Cross model. The numerical technique presented in this paper is validated by using exact solutions for the flow of a Cross model fluid inside a pipe and convergence is demonstrated by means of grid refinement for the problem of a spreading drop. Numerical results showing the flow of a generalized Newtonian fluid jet impinging onto a flat surface and that of a jet buckling are given.

A method for simulating incompressible, imiscible, unsteady, Newtonian, multi-fluid flows with free surfaces is described. A sharp interface separates fluids of different density and viscosity. Surface and interfacial tensions are also considered and the required curvature is geometrically approximated at the fronts by a least squares quadratic fitting. To remove small undulations at the fronts, a mass-conserving filter is employed. The numerical method employed to solve the Navier-Stokes equations is based on the GENSMAC-3D front-tracking method. The velocity field is computed using a finite-difference scheme on an Eulerian grid. The free-surface and the interfaces are represented by an unstructured Lagrangian grid moving through an Eulerian grid. The method was validated by comparing the numerical results with analytical results for a number of simple problems. Complex numerical simulations show the capability and emphasize the robustness of this new method.

In this article recent advances in the MAC method will be reviewed. The MAC technique dates back to the early sixties at the Los Alamos Laboratories and this paper starts with a historical review, and then a summary of related techniques. Improvements since the early days of MAC (and the Simplified MAC-SMAC) include automatic time-stepping, the use of the conjugate gradient method to solve the Poisson equation for the corrected velocity potential, greater efficiency through stripping out all particles (markers) other than those near the free surface, more accurate approximations of the free surface boundary conditions, the addition of a bounded high accuracy upwinding for the convected terms (thereby being able to solve higher Reynolds number flows), and a (dynamic) flow visualization facility. This article will concentrate, in the main, on a three-dimensional version of the SMAC method. It will show how to approximate curved boundaries by considering one configurational example in detail; the same will also be done for the free surface. The article will avoid validation, but rather focus on many of the examples and applications that the MAC method can solve from turbulent flows to rheology. It will conclude with some speculative comments on the future direction of the methodology.

This paper presents a finite difference technique for solving incompressible turbulent free surface fluid flow problems. The closure of the time-averaged Navier-Stokes equations is achieved by using the two-equation eddy-viscosity model: the high-Reynolds k- (standard) model, with a time scale proposed by Durbin; and a low-Reynolds number form of the standard k- model, similar to that proposed by Yang and Shih. In order to achieve an accurate discretization of the non-linear terms, a second/third-order upwinding technique is adopted. The computational method is validated by applying it to the flat plate boundary layer problem and to impinging jet flows. The method is then applied to a turbulent planar jet flow beneath and parallel to a free surface. Computations show that the high-Reynolds k- model yields favourable predictions both of the zero-pressure-gradient turbulent boundary layer on a flat plate and jet impingement flows. However, the results using the low-Reynolds number form of the k- model are somewhat unsatisfactory.

Submitted by Guilherme Lemeszenski (guilherme@nead.unesp.br) on 2013-08-22T18:44:04Z No. of bitstreams: 1 S1807-03022012000300009.pdf: 2559270 bytes, checksum: 42bebf967000663ebee3e420e61a5204 (MD5) Made available in DSpace on 2013-08-22T18:44:04Z (GMT). No. of bitstreams: 1 S1807-03022012000300009.pdf: 2559270 bytes, checksum: 42bebf967000663ebee3e420e61a5204 (MD5) Previous issue date: 2012-01-01 Made available in DSpace on 2013-09-30T18:36:00Z (GMT). No. of bitstreams: 2 S1807-03022012000300009.pdf: 2559270 bytes, checksum: 42bebf967000663ebee3e420e61a5204 (MD5) S1807-03022012000300009.pdf.txt: 46733 bytes, checksum: c6b21e70a7d469782af3ab7612e0900c (MD5) Previous issue date: 2012-01-01 Submitted by Vitor Silverio Rodrigues (vitorsrodrigues@reitoria.unesp.br) on 2014-05-20T13:48:12Z No. of bitstreams: 2 S1807-03022012000300009.pdf: 2559270 bytes, checksum: 42bebf967000663ebee3e420e61a5204 (MD5) S1807-03022012000300009.pdf.txt: 46733 bytes, checksum: c6b21e70a7d469782af3ab7612e0900c (MD5) Made available in DSpace on 2014-05-20T13:48:12Z (GMT). No. of bitstreams: 2 S1807-03022012000300009.pdf: 2559270 bytes, checksum: 42bebf967000663ebee3e420e61a5204 (MD5) S1807-03022012000300009.pdf.txt: 46733 bytes, checksum: c6b21e70a7d469782af3ab7612e0900c (MD5) Previous issue date: 2012-01-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena. Mathematical subject classification: Primary: 06B10; Secondary: 06D05. USP Departamento de Matemática Aplicada e Estatística Instituto de Ciências Matemáticas e de Computação UNESP Departamento de Matemática Computação Universidade Estadual Júlio de Mesquita Filho Instituto de Biociências de Botucatu - UNESP Departamento de Bioestatística UNESP Departamento de Matemática Computação Universidade Estadual Júlio de Mesquita Filho Instituto de Biociências de Botucatu - UNESP Departamento de Bioestatística FAPESP: 09/16954-8 FAPESP: 09/15892-9 FAPESP: 10/16865-2 CNPq: 305447/2010-6 CNPq: 306808/2011-0 CNPq: 472945/2011-4 CAPES: PECPG1462/08-3

A practical high resolution upwind differencing scheme for the numerical solution of convection-dominated transport problems is presented. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving the 1D/2D scalar advection equations, 1D inviscid Burgers’ equation, 1D scalar convection–diffusion equation, 1D/2D compressible Euler’s equations, and 2D incompressible Navier–Stokes equations. The numerical results displayed good agreement with other existing numerical and experimental data.

This paper deals with the numerical solution of complex fluid dynamics problems using a new bounded high resolution upwind scheme (called SDPUS-C1 henceforth), for convection term discretization. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite volume/difference methodologies, either into the CLAWPACK software package for compressible flows or in the Freeflow simulation system for incompressible viscous flows. The performance of the proposed upwind non-oscillatory scheme is demonstrated by solving two-dimensional compressible flow problems, such as shock wave propagation and two-dimensional/axisymmetric incompressible moving free surface flows. The numerical results demonstrate that this new cell-interface reconstruction technique works very well in several practical applications.

This paper addresses the problem of obtaining numerical solutions of shallow water equations with source term when f ux limiters (ARORA-ROE, ADBQUICKEST, TOPUS, SUPERBEE andMINMOD)in upwindschemesare used. The numerical results show that these high-resolution upwindschemesprovidebetterresults thanthose obtain e

In this work, a new high resolution TVD scheme for unsteady flows with shock waves is presented. The performance of the scheme is investigated for solving Burgers and Euler’s equations. In particular, 1D shock tubes, 1D inviscid turbulence (Burgers equation) and 2D supersonic/transonic flows are simulated.The numerical results show good agreement with numerical and experimental data.

In this paper, a turbulent fluid flow of a non-Newtonian aqueous solution in a tubular membrane is numerically studied. The effects of several physical parameters on the concentration profile are investigated. The mathematical model, in cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transport equations. The suction velocity is described by Darcy’s law (resistance-in-series model). The turbulence model utilized is the Prandtl mixing length and the equations with the associated boundary conditions are discretized by a finite-difference scheme on a staggered grid system. The convective terms are approximated by a new high-resolution upwind scheme. In order to demonstrate the capabilities of the numerical model, various test cases are presented. The numerical results compare favorably with the experimental data and the analytical solutions.

Neste trabalho, esquemas “upwind” modernos de alta ordem e limitados sao analisados/implementados no ambiente de simulacao Freeflow-2D. O objetivo e a simulacao numerica bidimensional de escoamentos de fluidos incompressiveis a altos valores do numero de Reynolds. Em conjunto com condicoes iniciais e de contorno, as equacoes de conservacao sao resolvidas no contexto de variaveis primitivas e pelo metodo de diferencas finitas. Para mostrar a capacidade do codigo atual, sao apresentados resultados numericos para o escoamento de Poiseuille, o escoamento numa expansao brusca e o escoamento de um jato livre sobre uma superficie rigida impermeavel.

The present work is concerned with a study of numerical schemes for solving two-dimensional time-dependent incompressible free-surface fluid flow problems. The primitive variable flow equations are discretized by the finite difference method. A projection method is employed to uncouple the velocity components and pressure, thus allowing the solution of each variable separately (a segregated approach). The diffusive terms are discretized by Implicit Backward and Crank- Nicolson schemes, and the non-linear advection terms are approximated by the high order upwind VONOS (Variable-Order Non-oscillatory Scheme) technique. In order to improved numerical stability of the schemes, the boundary conditions for the pressure field at the free surface are treated implicitly, and for the velocity field explicitly. The numerical schemes are then applied to the simulation of the Hagen-Poiseuille flow, and container filling problems. The results show that the semi-implicit techniques eliminate the stability restriction in the original explicit GENSMAC method.

Implicit schemes are studied with the purpose of introducing them in the two-dimensional GENSMAC method, for the numerical solution of unsteady newtonian incompressible flows. By using the fractional-step approach, the Freeflow2D simulation system is employed to solve the conservation equations. The viscous terms in the Navier-Stokes equations are implicitly treated via the Implicit Backward (IR), Crank-Nicolson (CN) and Adams-Bashforth/Crank-Nicolson (AB/CN) schemes. The convective terms are explicitly treated by the upwind differencing Variable Order Non-Oscillatory Scheme (VONOS) scheme. For channel and impinging jet flows, the numerical techniques are robust and produce results that compare very well with the analytical solutions.

This work is concerned with the development of a numerical technique for solving free surface flows of a Maxwell fluid. The governing equations for the flow of a Maxwell type fluid together with appropriate boundary conditions are given. The free surface stress conditions are treated in details. A novel formulation for calculating the extra stress components on rigid boundaries is given. The numerical technique presented in this work employs the finite difference method on a staggered grid and employs the ideas of the MAC (Marker-and-Cell) method. Numerical results demonstrating that this numerical technique can solve viscoelastic flows governed by the Maxwell model are presented. Moreover, validation results are presented.

O objetivo do presente trabalho e estender o ambiente de simulacao FreeFlow-3D para a solucao numerica de problemas de escoamentos incompreessiveis, com superficies livres e com influencia de temperatura.

O bom desempenho do algoritmo numerico e o pre-requisito essencial para a simulacao de escoamentos em regime turbulento.

Uma parte significativa dos escoamentos encontrados em aplicações tecnológicas é caracterizada por envolver altos números de Reynolds, principalmente aqueles em regime turbulento e com superfície livre. Obter soluções numéricas representativas para essa classe de problemas é extremamente difícil, devido à natureza não-linear das equações diferenciais parciais envolvidas nos modelos. Conseqüentemente, o tema tem sido uma das principais preocupações da comunidade científica moderna em dinâmica de fluidos computacional. Aproximações de primeira ordem para os termos convectivos são as mais adequadas para amortecer oscilações que estão associadas às aproximações de alta ordem não-limitadas. Todavia, elas introduzem dissipação artificial nas representações discretas comprometendo os resultados numéricos. Para minimizar esse efeito não-físico e, ao mesmo tempo, conseguir aproximações incondicionalmente estáveis, é indispensável adotar uma estratégia que combine aproximações de primeira ordem com as de ordem mais alta e que leve em conta a propagação de informações físicas. Os resultados dessa composição são os esquemas "upwind" limitados de alta ordem. Em geral, espera-se que esses esquemas sejam apropriados para a representação das derivadas convectivas nos modelos de turbulência kappa-varepsilon. No contexto de diferenças finitas, a presente tese dedica-se à solução numérica das equações de Navier-Stokes no regime de números de Reynolds elevados. Em particular, ela contém uma análise de algoritmos monotônicos e antidifusivos e modelos de turbulência kappa-varepsilon para a simulação de escoamentos incompressíveis envolvendo superfícies livres. Esquemas de convecção são implementados nos códigos GENSMAC para proporcionar um tratamento robusto dos termos convectivos nas equações de transporte. Duas versões do modelo kappa-varepsilon de turbulência são implementadas nos códigos GENSMAC, para problems bidimensionais e com simetria radial, para descrever os efeitos da turbulência sobre o escoamento médio. Resultados numéricos de escoamentos com simetria radial são comparados com resultados experimentais e analíticos. Simulações numéricas de problemas tridimensionais complexos são apresentadas para avaliar o desempenho de esquemas "upwind". Finalmente, os modelos de turbulência kappa-varepsilon são utilizados para a simulação de escoamentos confinados e com superfícies livres. A considerable part of fluid flows encountered in technological applications is characterised by involving high-Reynolds numbers, especially those in turbulent regime and with free-surface. It is extremely difficult to obtain representative numerical solutions for this class of problems, due to the non-linear nature of the partial differential equations involved in the models. Consequently, this subject has been one of main concerns in the modern computational fluid dynamics community. First-order approximation to the convective terms is one of the most appropriate to smooth out oscilations/instabilities which are associated with high-order unlimited approximation. However, it introduces numerical dissipation in the discrete representation jeopardizing the numerical results. In order to minimize this non-physical effect and, at the same time, to obtain unconditionally stable approximation, it is essential to adopt a strategy that combines first and high-order approximations and takes into account the propagation of physical information. The results of this composition are the high-order bounded upwind techniques. In general, it is expected that these algorithms are satisfactory for the representation of the convective derivatives in the kappa-varepsilon turbulence model. In the context of finite-difference, the present thesis deals with the numerical solution of the Navier-Stokes equations at high-Reynolds number regimes. In particular, it contains an analysis of monotonic and anti-difusive convection schemes and kappa-varepsilon turbulence models for the simulation of free-surface fluid flows. Upwinding methods are implemented into the GENSMAC codes to provide a robust treatment of the convective terms in the transport equations. Two versions of the K-Epsilon turbulence model are implemented into the two-dimensional and axisymmetric GENSMAC codes, in order to describe the turbulent effects on the average flow. Numerical results of axisymmetric flows are compared with experimental and analytical results. Numerical simulations of complex three-dimensional problems are presented to assess the performance of high-order bounded upwind schemes. Finally, the K-Epsilon turbulence models are employed in the simulation of confined and free-surface flows.

In the present work we describe a method which allows the incorporation of surface tension into the GENSMAC2D code. This is achieved on two scales. First on the scale of a cell, the surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is estimated by fitting a least square circle to the free surface using the tracking particles in the cell and in its close neighbors. On a sub-cell scale, short wavelength perturbations are filtered out using a local 4-point stencil which is mass conservative. An efficient implementation is obtained through a dual representation of the cell data, using both a matrix representation, for ease at identifying neighbouring cells, and also a tree data structure, which permits the representation of specific groups of cells with additional information pertaining to that group. The resulting code is shown to be robust, and to produce accurate results when compared with exact solutions of selected fluid dynamic problems involving surface tension.

Nesta dissertação é estudada a classe dos métodos de Runge-Kutta e também do tipo Rosenbrock para a solução de Equações Diferenciais Ordinárias. Atenção especial é dedicada aos métodos de Rosenbrock-Wanner (ROW) métodos, os quais são extensões dos métodos clássicos de Rosenbrock. Um procedimento é apresentado para a obtenção dos métodos de Rosenbrock-Wanner de quarta ordem A-estáveis e um método com estas propriedades é mostrado. Isto é confirmado por resultados numéricos. Todo o estudo, aqui apresentado, baseia-se na teoria dos grafos ao estilo de J.C.Butcher. This work is concerned with Runge-Kutta and Rosenbrock methods for numerical solution of Ordinary Differential Equations. Special attention is devoted to an extension of the classical Rosenbrock method, namely the Rosenbrock-Wanner (ROW) methods. A procedure for obtaining forth order A-stable ROW methods is presented and a method with these properties is exhibited. This is confirmed by numerical results. The whole study is based on graphs theory in Butcher\'s like style.

Uma família de esquemas upwind denominada FUS-RF (Family of Upwind Scheme via Rational Functions), que é derivada via funções racionais e dependentes de parâmetros, é proposta para o cálculo de soluções aproximadas de equações de conservação. A fim de ilustrar a capacidade dos novos esquemas, vários resultados computacionais para sistemas hiperbólicos de leis de conservação são apresentados. Esses testes mostram a inflluência dos parâmetros escolidos sobre a qualidade dos resultados numéricos. Fazendo o uso de alguns testes de padrões, comparação dos novos limitadores de fluxo correspondentes com o esquema bem estabelecido van Albada e esquema atual EPUS (Eight-degree Polynomial Upwind Scheme) é também realizada. Os testes numéricos realizados em transporte de escalares e problemas de dinâmica dos gases confirmam que alguns esquemas da família FUS-RF são não oscilatórios e fornecem resultados confiáveis quando perfis descontínuos são transportados. Um esquema particular dessa nova família de esquemas upwind é então selecionado e utilizado para resolver escoamentos complexos com superfícies livres móveis A family of upwind schemes named as FUS-RF (Family of Upwind Scheme via Rational Functions), which is derived via rational functions and dependent of parameters, is proposed for computing approximated solutions of conservation equations. In order to illustrate the capability of the new schemes, several computational results for system of hyperbolic conservation laws are presented. These results clarify the influence of the chosen parameters on the quality of the numerical calculations. Using some standard test cases, comparison of the new corresponding limiters with the well established van Albada and the recently introduced EPUS (Eight-degree Polynomial Upwind Scheme) limiters is also done. Numerical tests on both scalar and gas dynamics problems confirm that some schemes of the FUS-RF family are non-oscillatory and yield sharp results when solving profiles with discontinuities. A particular upwind scheme of this new family is then slected and used for solving complex incompressible moving free surface flows

Neste trabalho são apresentados os resultados do desenvolvimento e teste de esquemas upwind de alta resolução para o controle da difusão numérica em leis de conservação gerais e problemas em dinâmica dos fluidos. Em particular, são derivados dois novos esquemas: o ALUS (Adaptive Linear Upwind Scheme) e o TOPUS (Third-Order Polynomial Upwind Scheme). Esses esquemas são testados no transporte de escalares, em equações 1D tipo convecção-difusão, em sistemas hiperbólicos 1D, nas equações de Euler 2D da dinâmica dos gases e nas equações de Navier-Stokes incompressíveis 2D/3D. Os esquemas são então associados a uma modelagem algébrica não linear para a simulação de problemas de escoamentos incompressíveis turbulentos 2D com/sem superfícies livres In this work, results of the development and testing of high-resolution upwind schemes for controlling of the numerical diffusion for general conservation laws and fluid dynamics problems are presented. In particular, two new high-resolution upwind schemes are derived, namely, the ALUS (Adaptive Linear Upwind Scheme) and the TOPUS (Third-Order Polynomial Upwind Scheme). These schemes are tested in scalar transport, 1D convection-diffusion equations, 1D hyperbolic systems, 2D Euler equations of the gas dynamics, and in 2D/3D incompressible Navier-Stokes equations. The schemes are then combined with a nonlinear Reynolds stress algebraic equation model for the simulation of 2D incompressible turbulent flows with/without free surfaces

Reatores de leito fluidizado circulante são caracterizados por escoamentos altamente heterogêneos e instáveis. Devido a isso, operam em regimes pseudo-estacionários ou estatisticamente permanentes, onde os parâmetros do escoamento oscilam em torno de valores médios bem definidos. Neste trabalho estuda-se o comportamento de uma solução numérica para um escoamento típico de reatores de leito fluidizado circulante na região estatisticamente permanente. A simulação numérica foi realizada com o modelo de dois fluidos. A partir dos dados de simulação são estabelecidas médias e auto-correlações para as várias variáveis de interesse, considerando-se diferentes tempos de simulação ou diferentes tempos de observação. A partir destes resultados discute-se a questão do tempo mínimo de simulação necessário para que os resultados temporais médios sejam representativos do processo. Embora os resultados sugiram que 10 segundos de fluidização sejam suficientes para a geração de resultados médios temporais representativos, uma demonstração mais rigorosa permanece por ser executada. Circulating fluidized bed reactors are characterized by highly heterogenic and instable flow. Due to this flow, the reactors operate under either pseudo-stationary or statistically permanent patterns, where the flowing parameters vary among well defined average values. This paper aims to study the behavior of a numeric solution for a typical flow of circulating fluidized bed reactors in the statistically permanent region. The numeric simulation was performed with the two-fluid model. From the simulation data both average and self-correlations are established for several variables of interest, considering either different simulation time or different observation time. From these results, the minimum simulation time necessary is discussed, so that the average temporal results can be considered representative in the process. Although the results suggest 10 seconds of fluidization are enough to generate the average temporal results, a more rigorous demonstration is supposed to be executed.

Estudos aplicados ao processo de filtração tangencial têm sido o objetivo de muitos trabalhos devido a sua ampla capacidade de adequação aos mais diversos processos industriais. Os mecanismos de transferência associados a esse processo envolvem basicamente o escoamento em tubos permeáveis (ou membranas) com fenômenos de transferência de massa presentes junto à superfície. Esta tese de doutorado apresenta uma modelagem numérica capaz de representar o escoamento de fluidos newtonianos e não-newtonianos em tubos permeáveis aplicada ao processo de filtração tangencial, para os regimes de escoamento laminar e turbulento. No regime turbulento, utilizou-se o modelo de comprimento de mistura de Prandtl. O modelo numérico envolveu as equações de conservação da massa, da quantidade de movimento e das espécies químicas, acopladas a adequadas condições de fronteira. Em particular, por se tratar de um modelo numérico, analisou-se a discretização dos termos convectivos por meio da implementação de três esquemas: WACEB, CUBISTA e QUICKEST adaptativo. Os resultados produzidos pela implementação dos esquemas convectivos foram analisados por meio de comparações com resultados analíticos e experimentais da literatura, para regimes de escoamento laminar e turbulento. De acordo com as comparações realizadas, o esquema QUICKEST adaptativo apresentou melhor desempenho na modelagem desse escoamento. Diversas simulações numéricas geraram resultados, os quais foram comparados com expressões analíticas e dados experimentais da literatura e com dados produzidos pelo laboratório do Núcleo de Engenharia Térmica e Fluidos (NETeF) da USP São Carlos. Verificou-se, assim, que o modelo matemático produziu resultados compatíveis com o fenômeno estudado, tendo-se, portanto, uma ferramenta para descrição do problema convectivo mássico do escoamento em tubos permeáveis. Studies applied to the crossflow filtration process have been the goal of several researches due to its large capacity for adaptation to the various industrial processes. The mechanism of transfer associated with this process basically involves fiows in permeable tubes (or membranes) with the phenomenon of mass transfer on the surface. This doctoral thesis presents a numerical modeling able to represent the fiow of Newtonian and non-Newtonian fiuids in permeable tubes applied to the process of crossflow filtration, in laminar and turbulent flow regimes. In the turbulent regime the Prandtl mixing length model was used. The numerical model involved the mass conservation, momentum conservation and mass transport equations coupled to the appropriate boundary conditions. In particular, as it is a numerical model, the discretization of convective terms was analyzed through the implementation of three schemes: WACEB, CUBISTA and adaptative QUICKEST. The results produced by the implementation of the convective schemes were analyzed through comparisons with experimental and analytical results from the literature, for laminar and turbulent flow regImes. According to the comparisons made, adaptative QUICKEST scheme showed the best performance in the modeling in this flow. Several numerical simulations generated results, which were compared with experimental data and analytical expressions of the literature and with data produced by the laboratory of the Center of Thermal Thermal and Fluids Engineering (NETeF) of the EESC- USP/São Cados. It was possible to verify, that the mathematical model produced results consistent with the phenomenon studied, and can be considered a tool for the description of the mass convective problem flow in permeavel tubes.

Este trabalho é dedicado à análise e implementação de esquemas "upwind" de alta ordem modernos e o modelo de turbulência k-epsilon padrão no Freeflow-2D; um ambiente integrado para simulação numérica em diferenças finitas de problemas de escoamentos incompressíveis com superfícies livres. O propósito do estudo é a simulação de escoamentos de fluidos newtonianos incompressíveis, bidimensionais, confinados e/ou com superfícies livres e a altos valores do número de Reynolds. O desempenho do código Freeflow-2D atual é avaliada na simulação do escoamento numa expansão brusca e de um jato livre incidindo perpendicularmente sobre uma superfície rígida impermeável. O código é então aplicado na simulação de um jato planar turbulento em uma porção de fluido com superfície livre e estacionário. Os resultados numéricos obtidos são comparados com dados experimentais, soluções analíticas e soluções numéricas de outros trabalhos. This work is devoted to the analysis and implementation of modern high-order upwind schemes and the standard k-epsilon turbulence model into the Freeflow-2D; a finite difference integrated environment for the numerical simulation of incompressible free surface flow problems. The purpose of this study is the two-dimensional simulation of high-Reynolds incompressible newtonian confined and/or free surface flows. The performance of the current Freeflow-2D code is assessed by applying it to the simulation of flow over a backward facing step and of an impinging free jet onto an impermeable rigid surface. The code is then applied to a turbulent planar jet into a pool. The numerical results are compared with experimental data, analytical solution, and numerical simulations of other works.

Três esquemas de captura de descontinuidade são apresentados para simular hiperbólicos de leis de conservação e equações de Navier-Stokes incompressíveis, a saber: FDHERPUS (Five Degree Hermite Upwind Scheme); RUS (Rational Upwind Scheme); e CSPUS (Cubic Spline Polynomial Upwind Scheme). Esses esquemas são baseados nos critérios de estabilidade CBC e TVD e implementados nos contextos das metodologias diferenças finitas e volumes finitos. A precisão local dos esquemas é verificada acessando o erro e a taxa de convergência em problemas testes de referência. Um estudo comparativo entre os esquemas estudados (incluido o WENO5) e o esquema bem estabelecido de van Albada, para resolver leis de conservação lineares e não lineares, é também realizado. O esquema de convecção que fornece melhores resultados em leis de conservação hiperbólicas é então examinado na simulação de escoamentos de fluidos newtonianos com superfícies livres móveis de complexidade crescente; resultados satisfatórios têm sido observados em termos do comportamento global Three shock capturing schemes for numerical solution of hyperbolic conservation laws and incompressible Navier-Stokes equations are presented, namely: FDHERPUS (Five Degree Hermite Polynomial Upwind Scheme); RUS (Rational Upwind Scheme); and CSPUS ( Cubic Spline Polynomial Upwind Scheme). These schemes are based on CBC and TVD stability criteria and implemented in the context of finite volume methodologies. The local observed accuracy of the schemes is verified by assessing the error and convergence rate on benchmark test cases. A comparative study between the schemes (including WENO5) and the well established van. Albada scheme to solve standard linear and nonlinear hyperbolic conservation laws is also accomplished. The scheme that has provided better results in hyperbolic conservation laws is then examined in the simulation of Newtonian moving free surface flows of increasing complexity, satisfactory agreement has been observed in terms of the overall behavior

Nesta tese é apresentado um esquema novo de alta resolução upwind (denominado TDPUS-C3) para reconstrução de fluxos numéricos para leis de conservação não lineares e problemas relacionados em DFC. O esquema é baseado nos critérios de estabilidade CBC e TVD e desenvolvido utilizando condições de diferenciabilidade \'C POT. 3\'. Além disso, é realiozada a implementação da associação do esquema TDPLUS-C3 com a modelagem de turbulência RNG \'\\kappa - \\epsilon\'. O propósito é obter soluções numéricas de sistemas hiperbólicos de leis de conservação para dinâmica dos gases e equações de Navier-Stokes para escoamento incompreensível de fluidos newtonianos e não newtonianos (viscoelásticos). Fazendo o uso do esquema TDPUS-C3, a precisão global dos métodos numéricos é verificada acessando o erro em problemas teste (benchmark) 1D e 2D. Um estudo comparativo entre os resultados do esquema TDPUS-C3 e os esquemas upwind convencionais para leis de conservação hiperbólicas complexas é também realizado. A Associação das modelagens numéricas (upwinding mais RNG \'\\kappa - \\epsilon\') é , então, examinada na simulação de escoamentos turbulentos de fluidos newtonianos envolvendo superfícies livres móveis, usando a metodologia URANS. No geral, em termos do comportamento global, concordância satisfatória é observada In this thesis, a new high-resolution upwind scheme (named TDPUS-C3) for reconstruction of numerical fluxes for nonlinear conservation laws and related CFD problems in presented. The scheme is based on CBC and TVD stability criteria and developed by employing differentiability condictions (\'C POT. 3\'). In additon, the implementation of an association of the TDPUS-C3 scheme with the RNG \'\\kappa - \\epsilon\' turbulence modelling is also performed. The purpose is to obtain numerical solutions of systems of hyperbolic conservation laws for gas dynamics and Navier-Stokes equations for incompressible flow of Newtonian and non-Newtonian (viscoelstic) fluids. By using the TDPUS-C3 scheme, the global accuracy of the numerical methods is verified by assessing the error on 1D and 2D benchmark test cases. A comparative study between the TDPUS-C3 scheme and convectional upwind schemes to solve standard and complex hyperbolic conservation laws is also accomplished. The association of the numerical modelling (upwinding plus RNG \'\\kappa - epsilon\') is then examined in the simulation of turbulent Newtonian fluid flows involving moving free surfaces, by using URANS methodology. Overall, satisfactory agreement is found in terms of the overall behaviour

Neste trabalho aplicamos a formulação semi-discreta, caracterizada pela combinação de aproximações distintas para as variáveis temporal e espacial, onde a variável temporal é discretizada utilizando métodos implícitos multi-estágios e a espacial usando métodos de elementos finitos,para a obtenção de soluções numéricas para as equações 1D de convecção-difusão-reação e de Burgers, cujas soluções analíticas são conhecidas.Métodos multi-estágios são obtidos através dos aproximantes de Padé. Em particular, neste trabalho consideramos os métodos implícitos multi-estágios de segunda ordem, R11, e de quarta ordem, R22, na discretização temporal. Quanto à discretização espacial, utilizamos três formulações do método de elementos finitos, ou seja, mínimos quadrados (MEFMQ), Galerkin (MEFG) e streamline-upwind Petrov-Galerkin (SUPG). Apresentamos análises quanto à influência dos números de Péclet e de Courant-Friedrichs-Lewy, da influência da malha e dos aproximantes de Padé R11 e R22 nas formulações MEFMQ, MEFG e SUPG. Apresentamos uma análise do erro utilizando a norma L2, comparando as soluções numéricas com a solução analítica das equações avaliadas. Verificamos que o método implícito multi-estágio de quarta ordem, R22, quando adicionado aos MEFMQ, MEFG e SUPG aumentou a região de convergênciadas soluções numéricas das equações e que o MEFMQ apresentou uma melhor performance, quando comparado as formulações MEFG e SUPG. In this work we apply the semidiscrete formulation, characterized by the combination of distinct approaches to the time and space variables, where the time variable is discretized using implicits multi-stages methods and space variable is discretized using finite element methods, for obtaning numerical solutions for the 1D convection-diffusion-reation and Burgers equations, whose analytical solutions are known. Multi-stage methods are obtained through of Padé approximants. In particular, in this work we consider of the implicit multi-stage method of second-order R11 and of fourth-order R22, for time discretization. As for space discretization, we use three formulations of the finite elements methods, namely, least square (LSFEM), Galerkin (GFEM) and streamline-upwind Petrov-Galerkin (SUPG). We present analysis of the influence of the Péclet and Courant-Friedrichs-Lewy numbers, of the influence of the grid, of the Padé approximants R11 and R22 in the formulations LSFEM, GFEM and SUPG. We present a analysis of the error using the L2-norm, comparing the numerical solutions with analytical solutions. We verify that of the implicit multi-stage method of second-order when combined with the LSFEM, GFEM and SUPG, increased region of convergence of the numerical solutions, and that LSFEM presented a better performace when compared to the GFEM and SUPG formulations.

Este trabalho de pesquisa é dedicado ao desenvolvimento, análise e implementação de um novo esquema upwind de alta resolução (denominada PFDPUS) para a aproximação de termos convectivos em leis de conservação e problemas relacionados em mecânica dos fluídos. Usando variáveis normalizadas de Leonard, o equema PFDPUS é baseado em uma função polinomial por partes que satisfaz os critérios de estabilidade CBC e TVD. O desempenho do esquema PEDPUS é investigado na solução das equações de advecção de escalares, Burgers, Euler e MHD. O novo esquema é então aplicado para simular escoamentos incompressíveis envolvendo superfícies livres móveis. Para tanto, o esquema PFDPUS é implementado dentro do software CLAWPACK para problemas compressíveis, e no código Freeflow para poblemas incompressíveis. Os resultados numéricos são comparados com dados experimentais, numéricos e analíticos This work is dedicated to the development, analysis and implementation of a new high-resolution upwind scheme (called PFDPUS) for approximation of convective terms in conservation laws and related fluid mechanics problems. By using the normalized variables of Leonard, the PFDPUS scheme is based on a piecewise polynomical function that satisfies the CBC and TVD stability criteria. The performance of the PFDPUS scheme is assessed by solving advection of scalars, Burgers, Euler and MHD equations. Then the new scheme is applied to simulate incompressible flows involving moving free surfaces. The PFDPUS scheme is implemented into the CLAWPACK software for compressible problems, and in the Freeflow code for incompressible problems. The numerical results are compared with experimental, numerical and analytical data

Neste trabalho apresenta-se um novo esquema prático tipo upwind de alta resolução, denominado EPUS (Eight-degree Polynomial Upwind Scheme), para resolver numericamente equações de conservação TVD e é implementado no contexto do método das diferenças finitas. O desempenho do esquema é investigado na resolução de sistemas hiperbólicos de leis de conservação e escoamentos incompressíveis complexos com superfícies livres. Os resultados numéricos mostraram boa concordãncia com outros resultados numéricos e dados experimentais existentes Is this work a new practical high resolution upwinding scheme, called EPUS (Eight-degree Polynomial Upwind Scheme), for the numerical solution of transient convection-dominated conservation equations is present. The scheme is based on TVD stability criterion and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving hyperbolic systems of conservation laws and complex incompressible flows with free surfaces. The numerical results displayed good agreement with other existing numerical and experimental data

A tomografia por sensoriamento térmico é muito utilizada em diferentes aplicações industriais, tais como a determinação de propriedades térmicas de novos materiais, o controle da produção de calor e a temperatura no processo de manufatura. Entretanto, o emprego de técnicas tomográficas em processos industriais envolvendo transferência de calor ainda carece de métodos robustos e computacionalmente eficientes. Nesse contexto, o principal objetivo deste trabalho é contribuir para o desenvolvimento de uma técnica não intrusiva de medição do coeficiente de convecção a partir de medidas externas de temperatura e fluxo de calor baseada na solução do problema térmico inverso. Para tanto é necessário resolver um problema de condução acoplado a um problema de convecção de calor. Este acoplamento ocorre através do coeficiente de convecção no interior do domínio do problema, cuja determinação pode ser feita através da aplicação de um fluxo de calor e medição das temperaturas resultantes na superfície externa. A tomografia térmica é tratada como um problema de minimização global, cuja função objetivo é um funcional de erro que quantifica a diferença entre as medidas externas não intrusivas (temperatura real) e as medidas calculadas no modelo numérico (temperatura aproximada). A natureza mal condicionada do problema assim formulado se manifesta na superfície de minimização por produzir topologias problemáticas tais como múltiplos mínimos locais, pontos de sela, vales ao redor da solução, platôs, etc. Desse modo, uma técnica bastante sofisticada, capaz de convergir para a solução correta mesmo na presença dessas patologias é necessária para obtenção da solução. Neste trabalho optou-se pelo método de Newton para a minimização deste funcional em que a inversa da matriz Hessiana é substituída por uma pseudo-inversa construída a partir da técnica de Decomposição em Valores Singulares Truncados. Os resultados mostram que a técnica proposta foi capaz de superar os problemas de convergência associados à natureza intrínseca mal condicionada do problema inverso e o coeficiente de convecção foi reconstruído com precisão razoável. Tomography by thermal sensing is widely used in different industrial applications, such as the determination of thermal properties of new materials, the control of heat production and the temperature in manufacturing processes. However, the application of tomographic techniques in industrial processes involving heat transfer still lacks robust and computationally efficient methods. In this context, the main objective of this thesis is to contribute to the development of a non-intrusive technique for measuring of the convection coefficient from external temperature and heat flow measurements based on the solution of the inverse thermal problem. This requires solving a conduction problem coupled with a heat convection problem, which is coupled through an internal convection coefficient, determined by applying a heat flux and measuring the resulting temperatures on the external boundary. The thermal tomography is treated as a global minimization problem in which the fitness function is an error functional that quantifies the difference between non-intrusive external measurements (actual temperature) and measurements calculated in a numerical model (approximate temperature). The ill-conditioned nature of the problem manifests itself in the minimization problem for producing problematic topologies, such as multiple local minima, saddle points, valleys around the solution, plateaus, etc. Thus, a very sophisticated technique that can converge to the correct solution even in the presence of these pathologies is necessary to obtain the solution. In this thesis the Newton\'s method was used for the minimization of this functional in which the inverse Hessian matrix was replaced by a pseudo-inverse built from the truncated singular value decomposition technique. Results show that the proposed technique was capable of overcoming the convergence problems associated with the intrinsic ill-conditioned nature of the inverse problem and the convection coefficient was reconstructed within reasonable precision.

O transporte de fluidos e produtos petroquímicos através de malhas dutoviárias é uma opção extremamente difundida, tanto em aplicações industriais envolvendo longas distâncias quanto em sistemas de distribuição nos quais um determinado fluido deve ser entregue a um grande número de usuários ou processos. Em ambos os casos, para uma operação eficiente e segura da malha, é necessário um sistema de detecção de vazamentos, que detecta e avalia rapidamente a ocorrência de um vazamento, especialmente quando o fluido transportado for tóxico e/ou inflamável. Neste sentido, a análise hidráulica em escoamentos transitórios tem sido particularmente útil aos propósitos de detecção de vazamentos. Sistemas de observação para essa análise podem revelar uma quantidade substancial de informações relativas às propriedades físicas e o nível de integridade do sistema, pois as ondas de pressão resultantes são afetadas pelos diversos dispositivos e fenômenos, incluindo os vazamentos. Este trabalho apresenta a construção e validação de um modelo de simulação numérica adequado para uma nova técnica de detecção de vazamento, baseada na inspeção acústica ativa da tubulação, capaz de detectar vazamentos pré-existentes. Resultados numéricos foram comparados com os obtidos de ensaios experimentais realizados no oleoduto piloto do Laboratório de Escoamentos Multifásicos Industriais da Universidade de São Paulo, no campus de São Carlos - SP e de dados experimentais da literatura. Os resultados confirmam que o modelo numérico capta corretamente a física do fenômeno de propagação. Particularmente, uma boa concordância foi encontrada entre parâmetro de atenuação experimental e numérico, o que valida o modelo como um preditor on-line para ser usado em um sistema de detecção de vazamento. The transportation of petrochemical products through pipelines is the most common option, both in industrial applications involving long distances as well as in distribution networks in which a product must be delivered to a number of processes or customers. Due to safety and environmental reasons, the operation of such pipelines must include an on-line Leak Detection System (LDS) which promptly detects and assesses the occurrence of a leak, particularly if the transported product is toxic or inflammable. Analysis of hydraulic transients has been particularly useful for leak detection purposes. System observation for such analysis can reveal a substantial amount of information concerning physical properties and the integrity of the system, since pressure waves are affected by different features and phenomena, including leaks. This work presents the construction and validation of a numerical model suited to the simulation of a new leak detection technique, based on active acoustic inspection of the pipeline, which is capable of detecting pre-existing leaks. Numerical results were compared to the ones obtained from experimental tests conducted at the pilot pipeline of the Industrial Multiphase Flow Laboratory at University of São Paulo in the campus of São Carlos - SP and experimental data from literature. Results confirm that the numerical model captures the correct physics of the propagation phenomena. Particularly, a good agreement was found between experimental and numerical attenuation parameter, which validates our model as an on-line predictor to be used in a LDS system.

Esta dissertação trata da solução numérica de problemas em dinâmica dos fluidos usando dois novos esquemas upwind de alta resolução, denominados FDPUS-C1 (Five-Degree Polynomial Upwind Scheme of \' C POT. 1\' Class) e SDPUS-C1 (Six-Degree Polynomial Upwind Scheme of \'C POT.1\' Class), para a discretização de termos convectivos lineares e não-lineares. Os esquemas são baseados nos critérios de estabilidade TVD (Total Variation Diminishing) e CBC (Convection Boundedness Criterion) e são implementados, nos contextos das metodologias de diferenças finitas e volumes finitos, no ambiente de simulação Freeflow (an integrated simulation system for Free surface Flow) para escoamentos imcompressíveis 2D, 2D-1/2 e 3D, ou no código bem conhecido CLAWPACK ( Conservation LAW PACKage) para problemaw compressíveis 1D e 2D. Vários testes computacionais são feitos com o objetivo de verificar e validar os métodos numéricos contra esquemas upwind populares. Os novos esqumas são então aplicados na resolução de uma gama ampla de problemas em CFD (Computational Fluids Dynamics), tais como propagação de ondas de choque e escoamentos incompressíveis envolvendo superfícies livres móveis. Em particular, os resultados numéricos para leis de conservação hiperbólicas 2D e equações de Navier-Stokes incompressíveis 2D, 2D-1/2 e 3D demosntram que esses novos esquemas convectivos tipo upwind polinomiais funcionam muito bem This dissertation deals with the numerical solution of fluid dynamics problems using two new high resolution upwind schemes,. namely FDPUS-C1 and SDPUS-C1, for the discretization of the linear and non-linear convection terms. The Schemes are based on TVD and DBC stability criteria and are implemented in the context of the finite difference and finite volume methodologies, either into the Freeflow code for 2D, 2D-1/2 and 3D incompressible flows or in the well-known CLAWPACK code for 1D and 2D compressible flows. Several computational tests are performed to verify and validate the numerical methods against other popularly used upwind schemes. The new schemes are then applied to solve a wide range of problems in CFD, such as shock wave propagation and incompressible fluid flows involving moving free msurfaces. In particular, the numerical results for 2D hyperbolic conservation laws and 2D, 2D-1/2 and 3D incompressible Navier-Stokes eqautions show that new polynomial upwind convection schemes perform very well