This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.

This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.

A metodologia LES (Large Eddy Simulation) é uma alternativa viável para a solução numérica de escoamentos de interesse prático em virtude da limitação computacional imposta pela resolução direta de todas as escalas presentes em escoamentos turbulentos. Entretanto, a compreensão detalhada do fenômeno da turbulência é ainda uma tarefa desafiadora em consequência do seu comportamento não linear e alta sensibilidade às condições iniciais e de contorno. Dessa forma, o sucesso de simulações LES está associado à utilização de um código computacional eficiente, com modelagem submalha que represente corretamente a dinâmica do escoamento, juntamente com a especificação de condições iniciais turbulentas fisicamente consistentes. Nesse contexto, o presente trabalho tem como objetivo o desenvolvimento de um código LES de alta ordem aliado a um método de geração de perturbações para o estudo de escoamentos turbulentos em camada limite sobre superfície plana. Foi adotada a formulação vorticidadevelocidade. A metodologia numérica baseia-se no método de diferenças finitas em malhas colocalizadas, onde as derivadas nas direções longitudinal e normal ao escoamento são aproximadas usando diferenças compactas de alta ordem. Esse estudo assume periodicidade na direção transversal do escoamento e então um método espectral é adotado nessa direção. A integração temporal é feita através do método Runge-Kutta de 4a ordem e a solução da equação de Poisson se dá por meio de um método multigrid. Para a modelagem submalha é adotado o modelo WALE (Wall-Adapting Local Eddy-viscosity). O método RFG (Random Flow Generation) foi responsável pela geração das flutuações de velocidade. Os resultados obtidos mostraram-se em boa concordância com os dados DNS (Direct Numerical Simulation) e LES presentes na literatura. / LES methodology is a viable alternative for the numerical solution of practical interest flows due to the computational limitations imposed by the direct resolution of all scales presented in turbulent flow. However, the detailed understanding of the turbulence phenomenon is still a challenging task as a result of its non-linear behavior and high sensitivity to initial and boundary conditions. Thus, the success of LES simulations is associated with the use of an efficient computational code, wherein the subgrid scale modeling accurately represents the flow dynamics, together with the specification of realistic inicial boundary conditions. In this context, this study aims to develop a high-order LES code combined with a method for generating velocity fluctuations to compute turbulent boundary layer flows over a flat plate. The vorticity-velocity formulation was adopted. The numerical scheme is based on the finite difference method in collocated grid, where the derivatives in the streamwise and wall-normal are approximated using high order compact finite difference schemes. We also assume periodicity in spanwise direction therefore it is adopted a spectral method in this direction. The method chosen for the temporal evolution is the 4th order Runge-Kutta method and the solution of Poisson equation solution is accessed via a multigrid algorithm. For subgrid modelling it is adopted the Wall-Adapting Local Eddy-viscosity (WALE) model. The RFG (Random Flow Generation) method was responsible for the generation of unsteady turbulent velocity signal. The results obtained were in good agreement with DNS (Direct Numerical Simulation) and LES from the literature.

A metodologia LES (Large Eddy Simulation) é uma alternativa viável para a solução numérica de escoamentos de interesse prático em virtude da limitação computacional imposta pela resolução direta de todas as escalas presentes em escoamentos turbulentos. Entretanto, a compreensão detalhada do fenômeno da turbulência é ainda uma tarefa desafiadora em consequência do seu comportamento não linear e alta sensibilidade às condições iniciais e de contorno. Dessa forma, o sucesso de simulações LES está associado à utilização de um código computacional eficiente, com modelagem submalha que represente corretamente a dinâmica do escoamento, juntamente com a especificação de condições iniciais turbulentas fisicamente consistentes. Nesse contexto, o presente trabalho tem como objetivo o desenvolvimento de um código LES de alta ordem aliado a um método de geração de perturbações para o estudo de escoamentos turbulentos em camada limite sobre superfície plana. Foi adotada a formulação vorticidadevelocidade. A metodologia numérica baseia-se no método de diferenças finitas em malhas colocalizadas, onde as derivadas nas direções longitudinal e normal ao escoamento são aproximadas usando diferenças compactas de alta ordem. Esse estudo assume periodicidade na direção transversal do escoamento e então um método espectral é adotado nessa direção. A integração temporal é feita através do método Runge-Kutta de 4a ordem e a solução da equação de Poisson se dá por meio de um método multigrid. Para a modelagem submalha é adotado o modelo WALE (Wall-Adapting Local Eddy-viscosity). O método RFG (Random Flow Generation) foi responsável pela geração das flutuações de velocidade. Os resultados obtidos mostraram-se em boa concordância com os dados DNS (Direct Numerical Simulation) e LES presentes na literatura. / LES methodology is a viable alternative for the numerical solution of practical interest flows due to the computational limitations imposed by the direct resolution of all scales presented in turbulent flow. However, the detailed understanding of the turbulence phenomenon is still a challenging task as a result of its non-linear behavior and high sensitivity to initial and boundary conditions. Thus, the success of LES simulations is associated with the use of an efficient computational code, wherein the subgrid scale modeling accurately represents the flow dynamics, together with the specification of realistic inicial boundary conditions. In this context, this study aims to develop a high-order LES code combined with a method for generating velocity fluctuations to compute turbulent boundary layer flows over a flat plate. The vorticity-velocity formulation was adopted. The numerical scheme is based on the finite difference method in collocated grid, where the derivatives in the streamwise and wall-normal are approximated using high order compact finite difference schemes. We also assume periodicity in spanwise direction therefore it is adopted a spectral method in this direction. The method chosen for the temporal evolution is the 4th order Runge-Kutta method and the solution of Poisson equation solution is accessed via a multigrid algorithm. For subgrid modelling it is adopted the Wall-Adapting Local Eddy-viscosity (WALE) model. The RFG (Random Flow Generation) method was responsible for the generation of unsteady turbulent velocity signal. The results obtained were in good agreement with DNS (Direct Numerical Simulation) and LES from the literature.

Submitted by PPG Engenharia e Tecnologia de Materiais (engenharia.pg.materiais@pucrs.br) on 2018-06-05T13:28:29Z No. of bitstreams: 1 frantz2018simulacoes.pdf: 23131075 bytes, checksum: e748910d1820968a07c86be9461b7489 (MD5) / Approved for entry into archive by Sheila Dias (sheila.dias@pucrs.br) on 2018-06-12T12:40:17Z (GMT) No. of bitstreams: 1 frantz2018simulacoes.pdf: 23131075 bytes, checksum: e748910d1820968a07c86be9461b7489 (MD5) / Made available in DSpace on 2018-06-12T12:49:08Z (GMT). No. of bitstreams: 1 frantz2018simulacoes.pdf: 23131075 bytes, checksum: e748910d1820968a07c86be9461b7489 (MD5) Previous issue date: 2018-03-09 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / This work investigates the method of large-eddy simulation (LES) in the context of gravity currents, which is found necessary since it allows a substantial increase in the order of magnitude of the characteristic Reynolds number used in numerical simulations, approaching them with natural scales, in addition to significantly reducing the computational cost. The implicit large eddy simulation (ILES) methodology, based on the spectral vanishing viscosity model, is unprecedentedly employed in the context of gravity currents, is compared against with explicit methods such as the static and dynamic Smagorisnky. The evaluation of the models is performed based on statistics from a direct numerical simulation (DNS). Results demonstrate that the first model based purely on numerical dissipation, introduced by means of the second order derivative, generates better correlations with the direct simulation. Finally, experimental cases of the literature, in different flow configurations, are reproduced numerically showing good agreement in terms of the front position evolution. / Este trabalho investiga o m?todo de simula??o de grandes escalas (LES) no contexto de correntes gravitacionais. O mesmo se faz necess?rio, visto que possibilita um aumento substancial da ordem de grandeza do n?mero de Reynolds caracter?stico utilizado em simula??es num?ricas, aproximando os mesmos de escalas naturais, al?m de reduzir significativamente o custo computacional dos c?lculos. A avalia??o dos modelos ? realizada utilizando uma base de dados de simula??o num?rica direta (DNS). A metodologia de simula??o de grandes escalas impl?cita (ILES), baseada no modelo de viscosidade turbulenta espectral, ? colocado a prova de maneira in?dita no contexto de correntes de gravidade com m?todos expl?citos dispon?veis na literatura. Resultados demonstram que o mesmo, baseado puramente em dissipa??o num?rica introduzida por meio do comportamento dos esquemas de derivada de segunda ordem, gera melhores correla??es com as estat?sticas baseadas em campos m?dios da simula??o direta. Por fim, casos experimentais da literatura, em diferentes configura??es de escoamento, s?o reproduzidos numericamente.