Orientadores: Jose Alberto Cuminato, Maria Cristina de Castro Cunha / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-07-23T19:43:09Z (GMT). No. of bitstreams: 1 Boaventura_Maurilio_D.pdf: 2491219 bytes, checksum: 867f05e9f0a13670568238a19f88b98d (MD5) Previous issue date: 1998 / Resumo: Apresentamos, neste trabalho, uma técnica paralela baseada em uma decomposição de domínio para resolver as equações de Navier-Stokes com superfícies livres em coordenadas cartesianas e cilíndricas em duas dimensões. Essa técnica é baseada no código apresentado por Tomé [1993] e Tomé e co-autores [1996], a qual por sua vez é baseada no método SMAC apresentado por Amsden e Harlow [1971], que resolve as equações de Navier-Stokes em três passos: a equação de momento, a equação de Poisson e o movimento das partículas. A primeira equação é discretizada por diferenças finitas explícitas. A paralelização é realizada dividindo-se o domínio original de cálculo em vários subdomínios verticais e atribuindo cada um deles a um processador. Todos os cálculos podem ser realizados usando comunicação somente com o processador vizinho mais próximo. No final, apresentamos testes comparando a performance do código paralelo com o seqüencial e discutimos a questão do balanceamento de carga. / Abstract: A parallel technique "Qased on domain decomposition for solving free surface Navier-Stokes equations in cartesian and cylindrical coordinates in two dimensions is described. It is based on the code by Tomé [1993] and Tomé et.al. [1996], which in turn is based on the SMAC method by Amsden & Harlow [1971], which solves the Navier-Stokes equations in three steps: the momentum equation and Poisson solvers and particle movement. The first equation is discretized by explicit finite differences. The paralIelization is performed by splitting the computation domain into vertical strips and assigning each of these to a processor. All the computation can then be performed using nearest neighbour communication. We present run tests comparing the performance of the parallel with the serial code, and discuss the load balancing question. / Doutorado / Doutor em Matemática Aplicada

Orientador: Milton Mori / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-07-18T18:59:10Z (GMT). No. of bitstreams: 1 Steffani_Evandro_M.pdf: 2084852 bytes, checksum: 83b4e22bb98d52c5e934872728f0ee19 (MD5) Previous issue date: 1993 / Resumo: Este trabalho consiste na elaboração de uma rotina de cálculo para a simulação do escoamento laminar de fluidos em dutos cilíndricos. As equações da continuidade e a componente axial da equação de Navier-Stokes são resolvidas utilizando-se o método de colocação ortogonal em elementos finitos. Como resultado deste trabalho tem-se um programa fácil de se utilizar que calcula os perfis de velocidade, para o escoamento de um fluido newtoniano, no interior de tubos. O programa é testado fazendo-se simulações do escoamento laminar de ar a 25°C a diferentes números de Reynolds, variando-se também o tamanho da malha, ou seja, o número de elementos finitos utilizados nas direções axial e radial. Os resultados obtidos são comparados à solução analítica para perfil desenvolvido / Abstract: This work presents a computer program for the simulation of the laminar flow of fluids in cylindrical ducts. The continuity equation and the axial component of Navier-Stokes equation are solved using the orthogonal collocation on finite elements method. As a result we have a simple program which gives the velocity profiles for the flow of a Newtonian fluid. The program is tested using air at 25°C at different Reynolds numbers and different grid sizes. The results are compared to the analytical solution for fully developed flow / Mestrado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química

Orientador: Jose Luiz Boldrini / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-19T10:58:48Z (GMT). No. of bitstreams: 1 Bonfim_LuciaResendePereira_M.pdf: 1568473 bytes, checksum: 9f17158e81a9dd55608b4071e38102be (MD5) Previous issue date: 1994 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática Aplicada

Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.

No description available.

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated, and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences and a complex-variable approach. Several simplifying approximations to the complete linearization of the residual are also presented. A first-order approximation to the dependent variables is implemented in the adjoint and design equations, and the effect of a "frozen" eddy viscosity and neglecting mesh sensitivity terms is also examined. The resulting derivatives from these approximations are all shown to be inaccurate and often of incorrect sign. However, a partially-converged adjoint solution is shown to be sufficient for computing accurate sensitivity derivatives, yielding a potentially large cost savings in the design process. The convergence rate of the adjoint solver is compared to that of the flow solver. For inviscid adjoint solutions, the cost is roughly one to four times that of a flow solution, whereas for turbulent computations, this ratio can reach as high as ten. Sample optimizations are performed for inviscid and turbulent transonic flows over an ONERA M6 wing, and drag reductions are demonstrated. / Ph. D.

An unsteady Reynolds Averaged Navier-Stokes (URANS) based turbulence model, the Spalart-Allmaras (SA) model, was used to investigate the flow pulsation phenomenon in compound rectangular channels for isothermal flows. The computational fluid dynamics (CFD) commercial package ANSYS CFX-11.0 was used for the simulations. The studied geometry was composed of two rectangular subchannels connected by a gap, on which experiments were conducted by Meyer and Rehme [34] and were used for the validation of the numerical results. Two case studies were selected to study the effect of the advection scheme. The results using the first order upwind advection scheme had clear symmetry and periodicity. The frequency of the flow pulsations was underpredicted by almost a factor of two. Due to the inevitable numerical diffusion of the first order upwind scheme, it was more appropriate to use a second order accurate in space advection scheme for comparison with the experiments. The span-wise velocity contours and the velocity vector plots at planes parallel to the bulk flow, together with the time traces of the velocity components at selected monitor points showed the expected cross-flow mixing between the subchannels through the gap. Although the SA model does not solve directly for the turbulence kinetic energy, a kinetic energy associated with the unsteady solutions of the momentum equations was evaluated and qualitatively compared with the experimental turbulence kinetic energy. The calculated kinetic energy followed the trends of the experimental turbulence kinetic energy at the gap area, predicting two peaks at the edges of the gap. The dynamics of the gap pulsations were quantitatively described through temporal auto-correlation and auto-power spectral density functions and the numerical predictions were in agreement with the experiments. Studies on the effect of the Reynolds number and the computational length of the domain were also carried out. The numerical results reproduced the relationship between the Reynolds number and the frequency of the auto-power spectral density functions. The impact of the channel length was tested by simulating a longer channel. It was found that the channel length did not significantly affect the predictions. Simulations were also performed using the (kappa) -(epsilon) model. While flow pulsations were predicted with this model, the frequency of the pulsation was in poor agreement with the experimentally measured value. / Thesis / Master of Applied Science (MASc)

Accurate finite volume solution algorithms for the two dimensional Navier Stokes equations and the three dimensional Euler equations for both structured and unstructured grid topologies are presented. Results for two dimensional quadrilateral and triangular elements and three dimensional tetrahedral elements will be provided. Fundamental to the solution algorithm is a technique for generating multidimensional polynomials which model the spatial variation of the flow variables. Cell averaged data is used to reconstruct pointwise distributions of the dependent variables. The reconstruction errors are evaluated on triangular meshes. The implementation of the algorithm is unique in that three reconstructions are performed for each cell face in the domain. Two of the reconstructions are used to evaluate the inviscid fluxes and correspond to the right and left interface states needed for the solution of a Riemann problem. The third reconstruction is used to evaluate the viscous fluxes. The gradient terms that appear in the viscous fluxes are formed by simply differentiating the polynomial. By selecting the appropriate cell control volumes, centered, upwind and upwind-biased stencils are possible. Numerical calculations in two dimensions include solutions to elliptic boundary value problems, Ringleb’s flow, an inviscid shock reflection, a flat plate boundary layer, and a shock induced separation over a flat plate. Three dimensional results include the ONERA M6 wing. All of the unstructured grids were generated using an advancing front mesh generation procedure. Modifications to the three dimensional grid generator were necessary to discretize the surface grids for bodies with high curvature. In addition, mesh refinement algorithms were implemented to improve the surface grid integrity. Examples studied include a Glasair fuselage, High Speed Civil Transport, and the ONERA M6 wing. The role of reconstruction as applied to adaptive remeshing is discussed and a new first order error estimator is presented. Numerical examples of the remeshing procedure include both smooth and discontinuous flows. / Ph. D.

Dans cette thèse, nous nous intéressons à la simulation numérique d'écoulements instationnaires de deux fluides visqueux non miscibles, séparés par une interface mobile. Plus particulièrement des écoulements sans choc constitués d'une phase gazeuse et d'une phase liquide sont considérés. Pour modéliser de tels écoulements, une approche dans laquelle le gaz est décrit par les équations de Navier-Stokes compressible et le liquide par les équations de Navier-Stokes incompressible est proposée. C'est le couplage de ces deux modèles qui constitue l'originalité et l'enjeu principal de de cette thèse. Pour traiter cette difficulté majeure, une méthode globale (i.e. la même dans chaque phase) et simple à mettre en oeuvre est élaborée. L'utilisation des équations de Navier-Stokes formulées de façon unifiée pour les inconnues primitives (pression, vitesse et température) constitue le point de départ pour la construction de notre méthode qui repose sur les composants suivants: une méthode d'éléments finis stabilisés pour la discrétisation spatiale des équations de Navier-Stokes; une approche Level Set pour représenter précisément l'interface dont l'équation de transport a été résolue par une méthode de type Galerkin Discontinu; et des grandeurs moyennes pour traiter les discontinuités à l'interface. Le bon comportement de notre approche est illustré sur différents tests mono et bi-dimensionnels. / In this work, we are interested in the numerical simulation of instationnary viscous flows of two immiscible fluids, separated by a mobile interface. In particular, flows without shock composed of a gas phase and a liquid phase are considered. In order to modelize such flows, an approach in which the gaz is described by compressible Navier-Stokes equations and the liquid by incompressible Navier-Stokes équations is proposed. The coupling between these two models is the originality and the stake of this thesis. To treat this important difficulty, a global (i.e. the same for each phase) and simple method is elaborated. In our procedure we propose, using the Navier-Stokes equations formulated in set of primitives unknowns (pressure, velocity and temperature), to elaborate a strategy that relies on the follow components: the stabilized finite element method to discretize spatially the Navier-Stokes equations; the Level Set method for tracking the interface precisely with a discontinuous Galerkin method to solve the associated transport equation; and some averaged quantities to treat the discontinuities at the interface. The good behaviour of this approach is performed on both one and two spatial dimensions.

Dans cette thèse, nous étudions les écoulements de fluides compressibles décrits par les équations de Navier-Stokes-Fourier dans les cas stationnaire et instationnaire et avec des conditions de bord assurant l’isolation thermique et mécanique du fluide. On commence par le cas stationnaire barotrope et des conditions de Navier à la frontière du domaine. La pression est donc de la forme p(%) = % où est appelé coefficient adiabatique et nous arrivons à montrer l’existence de solutions faibles pour > 1.On généralise ensuite ce résultat aux équations de Navier-Stokes-Fourier avec conduction de la chaleur et glissement (partiel ou total) au bord, toujours dans le cas stationnaire. On montre cette fois-ci l’existence de solutions faibles particulières appelées solutions entropiques variationnelles respectant l’inégalité d’entropie pour > 1 et l’existence de solutions faibles respectant le bilan de l’énergie totale au sens faible pour > 5/4. On travaille ensuite sur les écoulements instationnaires décrits par les équations de Navier-Stokes-Fourier sur une large variété de domaines non bornés, tout d’abord pour des conditions de bord d’adhérence puis pour des conditions de Navier à la frontière (ce qui restreintquelque peu la diversité des domaines non bornés admissibles). On arrive à montrer l’existence de solutions faibles particulières respectant l’inégalité d’entropie et une inégalité de dissipation remplaçant l’égalité de conservation d’énergie totale dans le volume qui n’a plus de sens dans les domaines non bornés. Par après, on met en place une inégalité dite d’entropie relative dont on montre qu’elle est respectée par certaines des solutions faibles exhibées auparavant. Ces solutions sont appelées solutions dissipatives. On parvient à prouver que pour chaque donnée initiale, il existe au moins une solution dissipative. Cette inégalité d’entropie relative nous permet de démontrer le principe d’unicité forte-faiblepour nos solutions dissipatives. Précisément, cela signifie qu’une solution dissipative et une solution forte issues des mêmes données initiales coïncident sur le temps maximal d’existence de la solution forte. La propriété d’unicité forte-faible donne un fondement à la notion de solution dissipative pour les domaines non bornés. / In this thesis, we study the Navier-Stokes-Fourier system describing the flow of compressible fluids both in the steady and unsteady case and we suppose that the fluid is thermally and mechanically isolated. We start with the case of a steady barotropic fluid and Navier boundary conditions. In this situation, the pressure law considered is of the form p(%) = %, where is called the adiabatic constant. We show the existence of weak solutions for > 1. We then extend this result to the complete Navier-Stokes-Fourier system with heat conductivity and slip or partially slip boundary conditions, once again in thesteady case. In this setup, we prove the existence of a specific type of weak solutions, called variationnal entropy solutions, which satisfy the entropy inequality for > 1 and the existence of weak solutions satisfying the conservation of total energy in its weak formulation for > 5/4. We then treat the unsteady flows described by the complete Navier-Stokes-Fourier system on a large class of unbouded domains, first with no-slip boundary conditions and then with the Navier boundary conditions which reduce the class of the admissible unbounded domains. We manage to prove the existence of a specific type of weak solutions verifying the entropy inequality and a dissipation inequality instead of the global conservation of total energy which is no more relevant in the unbounded domains. Afterwards, we establish a new inequality called relative entropy inequality and we show that it is satisfied by some of the weak solutions presented previously. These are called dissipative solutions. Next we show that for any given initial data there exists at least one dissipative solution. This observation allows us toperform the proof of the weak-strong uniqueness principle in the class of dissipative solutions. Precisely, it means that a dissipative solution and a classical one emanating from the same initial data coincide as long as the latter exists. The weak-strong uniqueness property justifies the concept of dissipative solutions in the situation of unbounded domains.