A numerical method (SIMPLE DIRK Method) for unsteady incompressible viscous flow simulation is presented. The proposed method can be used to achieve arbitrarily high order of accuracy in time-discretization which is otherwise limited to second order in majority of the currently used simulation techniques. A special class of implicit Runge-Kutta methods is used for time discretization in conjunction with finite volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field in a lid-driven square cavity. In the test case calculations, power law scheme was used in spatial discretization and time discretization was performed using a second-order implicit Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was obtained from the proposed method and compared with that obtained from a commercial computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state solution from the present method was compared with the numerical solution of Ghia, Ghia, and Shin and that of Erturk, Corke, and Goökçöl. Good agreement of the solution of the proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke, and Goökçöl establishes the feasibility of the proposed method.

A numerical method (SIMPLE DIRK Method) for unsteady incompressible viscous flow simulation is presented. The proposed method can be used to achieve arbitrarily high order of accuracy in time-discretization which is otherwise limited to second order in majority of the currently used simulation techniques. A special class of implicit Runge-Kutta methods is used for time discretization in conjunction with finite volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field in a lid-driven square cavity. In the test case calculations, power law scheme was used in spatial discretization and time discretization was performed using a second-order implicit Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was obtained from the proposed method and compared with that obtained from a commercial computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state solution from the present method was compared with the numerical solution of Ghia, Ghia, and Shin and that of Erturk, Corke, and Goökçöl. Good agreement of the solution of the proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke, and Goökçöl establishes the feasibility of the proposed method.

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Orientador: João Batista Campos Silva / Banca: Ricardo Alan Verdú Ramos / Banca: Edson Luiz Zaparoli / Resumo: O objetivo principal deste trabalho é a simulação numérica de escoamentos de fluidos incompressíveis pelo método de elementos finitos baseado em volumes de controle (CVFEM) utilizando a metodologia de simulação das grandes escalas. As equações governantes são filtradas para a simulação das variáveis de grandes escalas e as escalas sub-malhas, que aparecem devido ao processo de filtragem, são modeladas por meio do modelo de viscosidade turbulenta de Smagorinsky. O domínio é discretizado em malha não estruturada formada por elementos finitos triangulares de seis nós e as equações são integradas em volumes de controle formados em torno dos nós dos elementos. O presente código numérico foi validado aplicando-o a alguns problemas-testes e os resultados, comparados com os disponíveis na literatura. Os casos testes foram o escoamento em uma cavidade quadrada induzido pelo movimento da parede superior, e escoamento por convecção natural em uma cavidade quadrada. Os resultados obtidos, no presente trabalho, concordaram com os resultados da literatura. / Abstract: The main purpose of this work is the numerical simulation of incompressible fluid flows by a control volume finite element method (CVFEM) using the methodology of large-eddy simulation. The domain is discretized using unstructured mesh of six-noded triangular finite elements and the equations are integrated into control volumes around the nodes of the finite elements. The government equations are filtered for simulation of the large scales variables and the sub-grid scales appearing due to the filtering process are modeled through the eddy viscosity model of Smagorinsky. Two-dimensional benchmark problems are solved to validate the numerical code and the results are presented and compared with available results from the literature. The test cases were the lid-driven cavity flow and natural convection flow inside a square cavity. The obtained results, in the present work, agree with results from the literature. / Mestre

Made available in DSpace on 2014-06-11T19:23:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-12-18Bitstream added on 2014-06-13T18:48:30Z : No. of bitstreams: 1 zachi_jm_me_ilha.pdf: 1606668 bytes, checksum: df36f4d5d30c079b2b8faf62fd202730 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo principal deste trabalho é a simulação numérica de escoamentos de fluidos incompressíveis pelo método de elementos finitos baseado em volumes de controle (CVFEM) utilizando a metodologia de simulação das grandes escalas. As equações governantes são filtradas para a simulação das variáveis de grandes escalas e as escalas sub-malhas, que aparecem devido ao processo de filtragem, são modeladas por meio do modelo de viscosidade turbulenta de Smagorinsky. O domínio é discretizado em malha não estruturada formada por elementos finitos triangulares de seis nós e as equações são integradas em volumes de controle formados em torno dos nós dos elementos. O presente código numérico foi validado aplicando-o a alguns problemas-testes e os resultados, comparados com os disponíveis na literatura. Os casos testes foram o escoamento em uma cavidade quadrada induzido pelo movimento da parede superior, e escoamento por convecção natural em uma cavidade quadrada. Os resultados obtidos, no presente trabalho, concordaram com os resultados da literatura. / The main purpose of this work is the numerical simulation of incompressible fluid flows by a control volume finite element method (CVFEM) using the methodology of large-eddy simulation. The domain is discretized using unstructured mesh of six-noded triangular finite elements and the equations are integrated into control volumes around the nodes of the finite elements. The government equations are filtered for simulation of the large scales variables and the sub-grid scales appearing due to the filtering process are modeled through the eddy viscosity model of Smagorinsky. Two-dimensional benchmark problems are solved to validate the numerical code and the results are presented and compared with available results from the literature. The test cases were the lid-driven cavity flow and natural convection flow inside a square cavity. The obtained results, in the present work, agree with results from the literature.

O objetivo desta dissertação de mestrado é estudar técnicas numéricas para simular escoamentos incompressíveis multifásicos e implementar uma ferramenta computacional utilizando malhas hierárquicas e discretizações por diferenças finitas. São apresentados a formulação matemática e o desenvolvimento do método numérico, levando em consideração o caráter multifásico do escoamento. Foi adotado o modelo de força superficial contínua e a representação da interface foi feita pelo método de acompanhamento de fronteira. São expostos todos os testes realizados durante o desenvolvimento da ferramenta para checar cada etapa do método. Finalmente, testes visando verificar o código foram feitos e os resultados obtidos foram considerados satisfatórios para a verificação da ferramenta aqui desenvolvida. / The objective of this masters degree essay is to study numerical techniques to simulate incompressible multiphase flows and to implement a computational tool using hierachical meshes and discretizations by finite diferences. We introduce the mathematical formulation and the development of the numerical method, for the multiphase flow problem. A continuum surface force model is employed with the interface representation by the front tracking method. We show all tests performed to verify each stage of the methods development. Finally, results obtained in classical benchmark flow tests show good agreement with previous published results, corroborating the validity of this newly developed numerical tool.

Foram feitas simulações de um jato plano livre e incompressível usando o modelo de uma equação Spalart-Allmaras padrão e um modelo Spalart-Allmaras modificado através da alteração da escala de comprimento turbulenta. Sabe-se da literatura que no caso de jatos livres o modelo Spalart-Allmaras não consegue predizer adequadamente os resultados observados experimentalmente. Os resultados das simulações foram comparados com experimentos da literatura através de perfis de velocidade e da taxa de expansão do jato. Como esperado, os resultados obtidos das simulações utilizando o modelo Spalart-Allmaras padrão foram considerados insatisfatórios, porém o modelo Spalart-Allmaras modificado teve uma melhor concordância com os resultados experimentais. Além disso, o modelo Spalart-Allmaras modificado foi usado para simular os casos do escoamento sobre uma placa plana sem gradiente de pressão e o escoamento em um degrau com separação e gradiente adverso de pressão. Quando comparados com resultados experimentais da literatura e com resultados obtidos usando o modelo padrão, os resultados do modelo modificado obtidos para ambos os casos foram muito satisfatórios, concluindo-se que a modificação da escala de comprimento permite obter uma maior generalidade para o modelo Spalart-Allmaras. / Simulations of a plane and incompressible free jet using the standard Spalart-Allmaras model and a Spalart-Allmaras model modified by changing the turbulent length scale were carried out. It is known from literature that, in the case of the free jet, the Spalart-Allmaras model fails to adequately predict the experimentally observed results. The results of our simulations were compared with published experiments using the velocity profiles and the jet spreading rate. As expected, the results of simulations using the standard Spalart-Allmaras model were considered unsatisfactory while the modified Spalart-Allmaras model had a better agreement with the experimental results. Furthermore, the modified Spalart-Allmaras model was used to simulate the cases of flow over a flat plate with no pressure gradient and flow through a backward facing step with separation and adverse pressure gradient. When compared with experimental results from the literature and with results obtained using the standard model, the results of the modified model for both cases were very satisfactory, allowing the conclusion that the change in the length scale provided a greater generality for the Spalart-Allmaras model.

Dans cette thèse, une nouvelle méthode de frontières immergées a été développée pour la simulation d'interaction fluide-structure, appelée la méthode de frontières immergées mobiles (en langage anglo-saxon: MIBM). L'objectif principal de cette nouvelle méthode est de déplacer arbitrairement les solides à géométrie complexe dans un fluide visqueux incompressible, sans remailler le domaine fluide. Cette nouvelle méthode a l'avantage d'imposer la condition de non-glissement à l'interface d'une manière exacte via une force sans introduire des constantes artificielles modélisant la structure rigide. Cet avantage conduit également à la satisfaction de la condition CFL avec un pas de temps plus grand. Pour un calcul précis de la force induite par les frontières mobiles, un système linéaire a été introduit et résolu par la méthode de gradient conjugué. La méthode proposée peut être intégrée facilement dans des solveurs résolvant les équations de Navier-Stokes. Dans ce travail la MIBM a été mise en œuvre en couplage avec un solveur fluide utilisant une méthode de projection adaptée pour obtenir des solutions d'ordre deux en temps et en espace. Le champ de pression a été obtenu par l'équation de Poisson qui a été résolue à l'aide de la méthode du gradient conjugué préconditionné par la méthode multi-grille. La combinaison de ces deux méthodes a permis un gain de temps considérable par rapport aux méthodes classiques de la résolution des systèmes linéaires. De plus le code de calcul développé a été parallélisé sur l'unité graphique GPU équipée de la bibliothèque CUDA pour aboutir à des hautes performances de calcul. Enfin, comme application de nos travaux sur la MIBM, nous avons étudié le couplage "fort" d'interaction fluide-structure (IFS). Pour ce type de couplage, un schéma implicite partitionné a été adopté dans lequel les conditions à l'interface sont satisfaites via un schéma de type "point fixe". Pour réduire le temps de calcul inhérent à cette application, un nouveau schéma de couplage a été proposé pour éviter la résolution de l'équation de Poisson durant les itérations du "point fixe". Cette nouvelle façon de résoudre les problèmes IFS a montré des performances prometteuses pour des systèmes en IFS complexe. / In this thesis a novel non-body conforming mesh formulation is developed, called the moving immersed boundary method (MIBM), for the numerical simulation of fluid-structure interaction (FSI). The primary goal is to enable solids of complex shape to move arbitrarily in an incompressible viscous fluid, without fitting the solid boundary motion with dynamic meshes. This novel method enforces the no-slip boundary condition exactly at the fluid-solid interface with a boundary force, without introducing any artificial constants to the rigid body formulation. As a result, large time step can be used in current method. To determine the boundary force more efficiently in case of moving boundaries, an additional moving force equation is derived and the resulting system is solved by the conjugate gradient method. The proposed method is highly portable and can be integrated into any fluid solver as a plug-in. In the present thesis, the MIBM is implemented in the fluid solver based on the projection method. In order to obtain results of high accuracy, the rotational incremental pressure correction projection method is adopted, which is free of numerical boundary layer and is second order accurate. To accelerate the calculation of the pressure Poisson equation, the multi-grid method is employed as a preconditioner together with the conjugate gradient method as a solver. The code is further parallelized on the graphics processing unit (GPU) with the CUDA library to enjoy high performance computing. At last, the proposed MIBM is applied to the study of two-way FSI problem. For stability and modularity reasons, a partitioned implicit scheme is selected for this strongly coupled problem. The interface matching of fluid and solid variables is realized through a fixed point iteration. To reduce the computational cost, a novel efficient coupling scheme is proposed by removing the time-consuming pressure Poisson equation from this fixed point interaction. The proposed method has shown a promising performance in modeling complex FSI system.

The modern gas turbine engine industry needs a simpler and faster method to facilitate the design of gas turbine combustors due to the enormous costs of experimental test rigging and detailed computational fluid dynamics (CFD) simulations. Therefore, in the initial design phase, a couple of preliminary designs are conducted to establish initial values for combustor performance and geometric characteristics. In these preliminary designs, various one-dimensional models using analytical and empirical formulations may be used. One of the disadvantages of existing models is that they are typically geometric dependant, i.e. they apply only to the geometry they are derived for. Therefore the need for a more versatile design tool exists. In this work, which constitutes the first step in the development of such a versatile design tool, a single equation-set network simulation model to describe both steady state compressible and incompressible isothermal flow is developed. The continuity and momentum equations are solved through a hybrid type network model analogy which makes use of the SIMPLE pressure correction methodology. The code has the capability to efficiently compute flow through elements where the loss factor K is highly flow dependant and accurately describes variable area duct flow in the case of incompressible flow. The latter includes ducts with discontinuously varying flow sectional areas. Proper treatment of flow related non-linearities, such as flow friction, is facilitated in a natural manner in the proposed methodology. The proposed network method is implemented into a Windows based simulation package with a user interface. The ability of the proposed method to accurately model both compressible and incompressible flow is demonstrated through the analyses of a number of benchmark problems. It will be shown that the proposed methodology yields similar or improved results as compared to other’s work. The proposed method is applied to a research combustor to solve for isothermal flows and flow splits. The predicted flows were in relatively close agreement with measured data as well as detailed CFD analysis. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2005. / Mechanical and Aeronautical Engineering / unrestricted

L'Interaction Fluide-Structure (IFS) décrit une classe très générale de problème physique, ce qui explique la nécessité de développer une méthode numérique capable de simuler le problème FSI. Pour cette raison, un solveur IFS est développé qui peut traiter un écoulement de fluide incompressible en interaction avec des structures différente: élastique ou rigide. Dans cet aspect, le solveur peut couvrir une large gamme d'applications.La méthode proposée est développée dans le cadre d'une formulation monolithique dans un contexte Eulérien. Cette méthode consiste à considérer un seul maillage et résoudre un seul système d'équations avec des propriétés matérielles différentes. La fonction distance permet de définir la position et l'interface de tous les objets à l'intérieur du domaine et de fournir les propriétés physiques pour chaque sous-domaine. L'adaptation de maillage anisotrope basé sur la variation de la fonction distance est ensuite appliquée pour assurer une capture précise des discontinuités à l'interface fluide-solide.La formulation monolithique est assurée par l'ajout d'un tenseur supplémentaire dans les équations de Navier-Stokes. Ce tenseur provient de la présence de la structure dans le fluide. Le système est résolu en utilisant une méthode élément fini et stabilisé suivant la formulation variationnelle multiéchelle. Cette formulation consiste à décomposer les champs de vitesse et pression en grande et petite échelles. La particularité de l'approche proposée réside dans l'enrichissement du tenseur de l'extra contraint.La première application est la simulation IFS avec un corps rigide. Le corps rigide est décrit en imposant une valeur nul du tenseur des déformations, et le mouvement est obtenu par la résolution du mouvement de corps rigide. Nous évaluons le comportement et la précision de la formulation proposée dans la simulation des exemples 2D et 3D. Les résultats sont comparés avec la littérature et montrent que la méthode développée est stable et précise.La seconde application est la simulation IFS avec un corps élastique. Dans ce cas, une équation supplémentaire est ajoutée au système précédent qui permet de résoudre le champ de déplacement. Et la contrainte de rigidité est remplacée par la loi de comportement du corps élastique. La déformation et le mouvement du corps élastique sont réalisés en résolvant l'équation de convection de la Level-Set. Nous illustrons la flexibilité de la formulation proposée par des exemples 2D. / Numerical simulations of fluid-structure interaction (FSI) are of first interest in numerous industrial problems: aeronautics, heat treatments, aerodynamic, bioengineering... Because of the high complexity of such problems, analytical study is in general not sufficient to understand and solve them. FSI simulations are then nowadays the focus of numerous investigations, and various approaches are proposed to treat them. We propose in this thesis a novel monolithic approach to deal with the interaction between an incompressible fluid flow and rigid/ elastic material. This method consists in considering a single grid and solving one set of equations with different material properties. A distance function enables to define the position and the interface of any objects with complex shapes inside the volume and to provide heterogeneous physical properties for each subdomain. Different anisotropic mesh adaptation algorithms based on the variations of the distance function or on using error estimators are used to ensure an accurate capture of the discontinuities at the fluid-solid interface. The monolithic formulation is insured by adding an extra-stress tensor in the Navier-Stokes equations coming from the presence of the structure in the fluid. The system is then solved using a finite element Variational MultiScale (VMS) method, which consists of decomposition, for both the velocity and the pressure fields, into coarse/resolved scales and fine/unresolved scales. The distinctive feature of the proposed approach resides in the efficient enrichment of the extra constraint. In the first part of the thesis, we use the proposed approach to assess its accuracy and ability to deal with fluid-rigid interaction. The rigid body is prescribed under the constraint of imposing the nullity of the strain tensor, and its movement is achieved by solving the rigid body motion. Several test case, in 2D and 3D with simple and complex geometries are presented. Results are compared with existing ones in the literature showing good stability and accuracy on unstructured and adapted meshes. In the second, we present different routes and an extension of the approach to deal with elastic body. In this case, an additional equation is added to the previous system to solve the displacement field. And the rigidity constraint is replaced with a corresponding behaviour law of the material. The elastic deformation and motion are captured using a convected level-set method. We present several 2D numerical tests, which is considered as classical benchmarks in the literature, and discuss their results.